talk about and use the materials and equipment provided to carry out an activity;

Number and Algebra

• use, estimate, add and subtract numbers up to at least 10; for example state if they think a set contains more than 5 or fewer than 5, add and subtract numbers practically e.g. using counters. Technology & Designfor example, discuss the numbers on a clock.
• understand conservation of number; for example pupils explain that when they rearrange objects the number of objects remains the same.
• create and describe repeating patterns using objects, numbers or pictures; for example make a repeated pattern using sets of shapes or beads e.g. red bead, blue bead, yellow bead, red bead, blue bead, …; 1, 2, 3, 1, 2, … and red square, blue triangle, red square …
• recognise and use coins; for example engage in role play, showing recognition of coins and an understanding of the concept of exchanging goods for money. Home Economicsfor example, with help, discuss how you would purchase ingredients for a recipe.

Shape, Space and Measures

• use everyday language associated with length, ‘weight’, capacity and area to describe, compare and order three objects; for example, pupils place plants in order of height from shortest to tallest and use balance scales to find which object is heavier. Home Economicsfor example, use balance scales to determine which food item is heavier/lighter.
• sequence familiar events; for example pupils order picture cards to show the sequence of a familiar activity. e.g. make meal, set table, eat meal, wash up Home Economicsfor example order picture cards to show the sequence of a familiar activity, such as making a cup of teaTechnology & Designfor example, discuss the picture cards for showing the stages in the process of vacuum forming
• know the days of the week and their sequence; for example pupils insert missing cards showing the days of the week, for example, Sunday, Monday, …...., Wednesday, Thursday, ……., Saturday
• recognise ‘special’ times on the clock; for example recognise break time and lunch time on clock picture cards
• sort 2-D and 3-D shapes and make and describe 2-D and 3-D constructions; for example pupils sort real objects for one criterion, for example sort by colour, by shape or by size, talk about the shapes used to make a picture or 3-D construction
• use language and follow instructions, in practical situations, for position and movement; for example pupils follow instructions to place an object under the table, inside the box, outside the room; follow instructions to walk backwards, run forwards and turn through a whole turn.

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example sort a collection of flowers by type and then re-sort by colour, and sort animals with two legs/not two legs and re-sort by can fly/cannot fly; Home Economicsfor example, sort a collection of ingredients into dry or not dry (wet) and re-sort by measured using scales/not scales (jugs)
• collect information and record using real objects or drawings; for example, use a photograph or drawing to self-register, and use cubes to record the number of people with blue/brown eyes.

talk about how to approach an activity;

Number and Algebra

• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example, talk about the coins that could be used to pay for shopping; suggest counting on to give change from 50p or £1 Home Economicsfor example, talk about the coins that could be used to pay for shopping.
  for example, talk about the coins needed to buy ingredients for a practical lesson such as making beans on toast or smoothies.

Shape, Space and Measures

• identify and use non-standard units to measure length, ‘weight’, capacity and area; for example, pupils explain how they will compare two or more objects using pencils for length, cubes for 'weight', cups for capacity; use steps to find the length of the corridor;
• understand the need standard units and know the most commonly used units in length, 'weight', capacity and time; for example, talk about why pupils counting steps to find the length of the corridor have different results and therefore recognise the need for standard units;
• sort 2-D and 3-D shapes, giving reasons for sorting; for example, pupils suggest the criteria used to sort shapes, for example, sort into 2-D and 3-D shapes, shapes with 3 sides/more than 3 sides; Technology & Designfor example, discuss how shapes of signs represent different things, that is circles for orders, triangles for warnings and rectangles for information

Handling Data

• sort and classify objects for two criteria using Venn, Carroll and Tree diagrams; for example pupils suggest the criteria they will use to sort objects, for example, birds with long beaks/not long beaks and webbed feet/not webbed feet, and sort odd numbers/not odd numbers and sort pupils in the class into boys/girls and wearing blazer/not wearing blazer Sciencefor example, discuss criteria which could be used to sort pond life such as shell or no shell, rounded or not rounded bodies.Technology & Designfor example, discuss how tools can be sorted on a Venn diagram to show the tools for wood, for plastic and for both
• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; For example, discuss how to collect and display information, for example, suggest using a simple table to record the number of each type of bird at the bird table and suggest displaying the data on a pictogram. Geographyfor example, suggest using a simple table to record the number of pupils who have visited different holiday destinations and suggest displaying the data on a block graph.Home Economicsfor example, discuss how to collect and display information such as pupils' favourite fruit, choose to record this on a simple table and display the data in a block graphScienceFor example, discuss how to collect and display information , suggest using a simple table to record the number of each mini beast found and displaying the data on a pictogram.

select and use the materials, equipment and mathematics required;

Number and Algebra

• add and subtract within 100; For example, decide to use the 100 square or other apparatus to add or subtract 2 numbers (without bridging the 10) such as add or subtract points scored in a game.
• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example compile a shopping list to keep within a specified budget, they talk about their choices explaining that they will add to find the total cost; suggest adding costs to find ways in which to spend a specific amount of money.

Shape, Space and Measures

• identify and use non-standard units to measure length, 'weight', capacity and area; For example, select balance scales, cubes or marbles for a weighing activity.
• name and order the days of the week, months of the year and seasons; for example, insert missing cards showing the months of the year, for example, January, February, ........, April; mathch the names of the seasons to corresponding pictures
• read simple digital and analogue clock displays; for example, read the time from a clock or watch showing o'clock, half past and a quarter past.
• use language and follow instructions, in practical situations for turning movements; for example, program a robot to turn a half/quarter turns and turn left/right.

Handling Data

• sort and classify objects for two criteria using Venn, Carroll and Tree diagrams; for example, use a Venn diagram to sort children who play football and/or tennis; Sciencefor example,use a Caroll diagram to sort plant life.
• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; for example collect information on a simple table and complete horizontal or vertical block graphs or simple pictograms. Home Economicsfor example, choose to use a block graph to display data for favourite fruitSciencefor example, decide to display data about types of leaves in a block graph or pictogram.Technology & Designfor example, complete a simple table showing materials, an image and their definition

suggest different ways an activity might be approached;

Number and Algebra

• understand, use, add and subtract whole numbers up to at least 1000; for example, suggest different methods for adding for example, adding mentally by partitioning or adjusting or using pencil and paper methods as appropriate.
• use quick recall of number facts up to 20; for example, discuss the use of number facts up to 20 to solve larger number problems e.g. 7 + 8 = 15 so 70 + 80 = 150;
• approximate to the nearest 10 or 100; for example, suggest that 27 + 41 can be estimated by rounding to 30 + 40
• explore and use division in practical situations; for example, suggest methods to demonstrate how to share 26 sweets equally among 5 children and understand that 1 remains.
• use number skills in the context of money up to £10; for example, suggest counting on from the total cost up to £10 to find the change from £10 or suggest adding to find the total cost and subtracting to find the change Home Economicsfor example, suggest adding prices to decide if all the ingredients from a recipe can be purchased from a given budget, less than £10Technology & Designfor example, when calculating the cost of materials for a bird feeder project suggest repeated addition to find the cost of the different quantities of materials and addition to get the total cost

Shape, Space and Measures

• find the area of shapes by counting whole and half squares; for example, when finding the area of a shape suggest counting two half squares as one whole square and add to the number of whole squares. Technology & Designfor example, when finding the area of a 2D design on squared paper suggest counting all the whole squares first then adding on the half squares recognising that two half squares equal one whole square
• recognise one line of symmetry in common 2-D shapes; for example, suggest using a mirror or folding to identify a line of symmetry. Technology & Designfor example, suggest using a ruler or piece of card to help recognise a line of symmetry in a simple design?
• recognise right angles in the environment and understand angle as a measure of turn; for example, suggest a range of items which could be used as a right angle tester and suggest how to use this to identify angles that are bigger than/smaller than a right angle. Technology & Designfor example, suggest using a tri-square to check for right angles

Handling Data

• collect and record relevant data for a given activity; for example, suggest obtaining information from books/internet, through questioning or observation. Geographyfor example, suggest searching the internet to collect data in relation to fair trade/population/weather;Home Economicsfor example, suggest carrying out a survey to find what pupils eat for breakfastSciencefor example, discuss and decide what information to collect about pupil characteristics, such as hair colour, eye colour etc and suggest recording the data on a tally chart;

select and use the appropriate materials, equipment and mathematics required;

Number and Algebra

• understand, use, add and subtract whole numbers up to at least 1000; for example, know to subtract when finding how many beads are left in a box of 100 when 26 have been used; to fin Home Economicsfor example, know to subtract when finding how much flour is left over from 1 kg bag of flour after using 375 g.Technology & Designfor example, to find the size of a resistor up to 1000 ohms, use the colour code and place the numbers in the correct order with the appropriate number of zeros
• add and subtract mentally two 2-digit numbers within 100; for example, without bridging the 10, use partitioning to add mentally two 2 digit numbers such as 66 + 23 = 66 + 20 + 3 = 89 Technology & Designfor example, choose to subtract when calculating the amount of waste material
• know 2, 3, 4, 5 and 10 multiplication facts; Geographyfor example, find the height of a landmark on an OS map by counting contour lines (4m and 10m intervals);
• use number skills in the context of money up to £10; for example, discuss a range of strategies which could include adding and then subtracting when finding change from £10 after buying an item at £1.50 and another at £3.00. Home Economicsfor example, discuss a range of strategies which could include adding and then subtracting when finding the change from £10 after buying the ingredients to bake an apple pieTechnology & Designfor example, use addition when calculating the cost of materials for a bird feeder project

Shape, Space and Measures

• choose and use appropriate standard units to estimate, measure and record length, capacity, volume, ‘weight’, time and temperature; for example, use metres to measure the length of a carpark and millilitres to measure the liquid in a cup etc; Geographyfor example, choose to use °C to record temperature;Home Economicsfor example, use grams to measure the quantities of dry ingredients and millilitres to measure the volume of liquidsSciencefor example, select the appropriate measuring equipment and units, such as a thermometer for temperature in degrees celsius, measuring cylinder for volume of liquid in ml;Technology & Designfor example, choose to measure a length in cm using a ruler or measuring tape
• read simple measuring instruments with an appropriate degree of accuracy; for example, measure the length of a table to the nearest cm and the volume of liquid to the nearest 100ml Geographyfor example, measure temperature to the nearest degree on a analogue thermometer;Home Economicsfor example, reading measuring jugs to the nearest 100 ml and weighing scales to the nearest 500 g.Sciencefor example, read the volume of a liquid in a measuring cylinder at eye level to avoid parallax error; measure liquid to the nearest 100 ml; when investigating friction, use a force meter to measure the force;Technology & Designfor example, read cm on a ruler to measure the length of a material

Handling Data

• collect and record relevant data for a given activity; for example, when measuring choose the most appropriate instrument by understanding its special characteristics, for example, a thermometer to measure room temperature or a stop watch to measure the time taken to run a race. Geographyfor example, record  temperature and rainfall readings  on a simple weather data collection sheet;Home Economicsfor example choose an appropriate data collection sheet such as a tally chart to record choices for breakfastSciencefor example, collect and record data about pupil characteristics given a table with column headings

decide how an activity might be approached and compare their approaches with others;

Number and Algebra

• estimate answers to calculations and approximate by rounding; for example decide to estimate the answer to 21 × 19 using 20 × 20, or 327 + 879 using 300 + 900;
• use the relationship between addition and subtraction to check calculations; for example understand that to find the change from £100 after spending £50 and £30, add £50 to £30 and subtract the answer from £100; check this by adding £50, £30 and the change (£20) to ensure the total equals £100. Sciencefor example, suggest checking the change in mass of magnesium by adding this value to the original mass to ensure it equals the mass after heating,
• understand and use multiples and factors; for example use pairs of factors to work out how many different equal teams can be made from a class of 30 pupils;
• make choices about spending and value for money; for example, when comparing two offers plan to calculate the cost of each and take into consideration all relevant factors. Home Economicsfor example, choosing the appropriate source, e.g. internet, fliers, TV ads etc., to allow a comparison of best price on deals for buying food products.Technology & Designfor example, consider all relevant variables when choosing materials for a manufacturing project to ensure that the cost is kept below £5

Shape, Space and Measures

• estimate and measure length, 'weight'/mass and time and temperature, working to an appropriate degree of accuracy; for example, decide to measure the length of a long jump to the nearest centimetre and the capacity of a bucket to the nearest litre Sciencefor example, predict the order of the masses of 3 different materials then discuss how this can be done more accurately and decide to measure the mass of the objects.Technology & Designfor example, discuss how to mark out woodwork joints template, using a template or ruler.
• add and subtract common measures; for example decide to add to find the perimeter of a room. Home Economicsfor example, decide to add the protein contents of foods eaten to find total protein content in a person's dietSciencefor example, explain how to find the change in mass of the magnesium by finding the difference in mass of crucible + magnesium before and after heating.Technology & Designfor example, in design work decide to find the amount of material wasted by subtracting the area of the design from the amount of material provided
• estimate area and volume of shapes by counting squares/cubes; for example, decide to use a centimetre square overlay to estimate the area of a leaf by counting more than half a square as a whole square.

Handling Data

• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and data bases; for example, decide to record data on a frequency table and display it on a bar chart. Geographyfor example, plan to record information from a traffic survey on a frequency table and to use this to draw a bar chart;Home Economicsfor example, decide to display sugar content of an energy drink on a bar chartSciencefor example, decide to compare solubility of a variety of substances by recording on a table the times taken for them to dissolve and displaying the information on a bar chart;

identify and use appropriately the materials, equipment and mathematics required;

Number and Algebra

• read, write and order whole numbers within 10000 Technology & Designfor example, to find the size of a resistor up to 10000 ohms, use the colour code and place the numbers in the correct order with the appropriate number of zeros
• add and subtract numbers with up to two decimal places; for example, choose to add 4.2 km and 2.68 km together to find the total distance cycled. Geographyfor example, add 4.2 km and 2.68 km together to find total distance travelled;Home Economicsfor example, decide to add the fibre content of a sandwich to find the total fibre.Sciencefor example, decide to subtract to find the change in mass of magnesium before and after heatingTechnology & Designfor example, add 3.2 and 2.8 to find the total resistance in K ohms?
• use the relationship between addition and subtraction to check calculations; for example, decide to check change from £20 by adding the cost to the change to ensure the answer is £20. Home Economicsfor example, decide to check the change from £20 after catering for a party by addingSciencefor example, decide to check the change in mass of magnesium by adding this value to the original mass to ensure it equals the mass after heating
• understand and use multiples and factors; for example, work out how many different equal teams can be made from a class of 30 pupils.
• perform simple calculations involving unitary fractions; for example choose to divide by 5 when calculating one fifth of 20; add 1/3 to 1/3 to find the total fraction of a book that has been read over two days. Technology & Designfor example, measure a length and divide by 2 to mark the mid point
• understand and use simple percentages; for example decide to divide by 4 to find 25% of £80 Home Economicsfor example, compare percentage fat content using traffic light/GDA labelling on food packagesTechnology & Designfor example, know to divide by 10 when finding the 10% tolerance of resistors with a silver band

Shape, Space and Measures

• estimate and measure length, ‘weight’/mass and time and temperature, working to an appropriate degree of accuracy; for example decide to use metres to estimate the width of a room; measure and record the length of an envelope in millimetres; and measure the temperature of water to the nearest degree Celsius; Geographyfor example, estimate the width of a room in metres or the length of a hockey pitch in metres;Home Economicsfor example, choose the appropriate equipment for measuring liquids to the nearest 10 ml and weighing ingredients to the nearest 10 g.Sciencefor example, decide to measure the mass of materials in g or kg using digital scales correct to 2dp;Technology & Designfor example, measure a length and mark the position of a hole to be cut in the material
• understand the relationship between metric units; for example understand that 1 m 25 cm is the same length as 125 cm; Home Economicsfor example, understand that 1 kg 500 g is the same as 1500 g.Technology & Designfor example, understand that all lengths must be in the same units and understand that 8 cm is equal to 80 mm.
• add and subtract common measures; for example, choose to add 4.2 km and 2.68 km together to find the total distance cycled. Geographyfor example, choose to add 4.2 km and 2.68 km together to find total distance travelled;Home Economicsfor example, if I have 1 kg of flour and use 300 g to make scones, choose to subtract 300 from 1000 to find how much flour is left.Sciencefor example, decide to subtract to find the change in mass of magnesium before and after heatingTechnology & Designfor example, know to add together the lengths of the components required to make a desk tidy to see if all components can be cut from the given sheet of wood
• work out perimeters of simple shapes; for example choose the appropriate equipment, method and unit of measurement to measure the perimeter of the playground; add the lengths of the sides of a rectangle or square or triangle to calculate the perimeter;

Handling Data

• collect, group, record and present data with given class intervals; for example use the given class intervals 1 – 5, 6 – 10, 11 – 15, etc, to record ages of patients waiting in A&E; Geographyfor example, use the given class intervals 1 – 5, 6 – 10, 11 – 15, etc, to organize collected information about the width of various stones, rounded to the nearest cm;Sciencefor example, suggest recording information for resting heart rate on a data collection sheet using given class intervals and displaying the data in a frequency diagram.
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, decide to use a frequency diagrams to organise discrete data (grouped or ungrouped), independently draw and label both axes; draw and interpret bar charts with given class intervals; compare frequencies by interpreting a simple pie chart; Geographyfor example, use information from a traffic survey to independently draw a bar chart; interpret a bar chart showing pebble size identifying the group with the largest number of stones;Sciencefor example, decide to present data about pupil characteristics on a frequency table and bar chart

plan and decide how an activity might be approached;

Number and Algebra

• make informed choices about personal budgeting and spending; for example, plan a week of leisure activities for a family of four with a budget of £500. Home Economicsfor example, decide how best to spend monthly wages in relation to a household budgetTechnology & Designfor example, plan purchase of materials for a design task, such as build a bridge by budgeting. Bill of materials in circuit wizard?

Shape, Space and Measures

• use the four operations to solve problems related to measures; for example, decide to divide 1000 by 120 to find how many 120 ml glasses can be filled from a one litre bottle. Home Economicsfor example, decide to divide 1000 by 120 to find how many 120 ml glasses can be filled from a one litre bottle.Technology & Designfor example plan to use division and subtraction to accurately mark centre points for drilling or calculate a missing measurement from a working drawing.
• calculate areas of squares, rectangles and right-angled triangles and volumes of cubes and cuboids; for example, identify the steps needed to find the price of painting a rectangular fence given its dimensions and the coverage and cost of one tin of paint; ScienceFor example, draw all the rectangles with an area of 36 cm² to investigate the effect of the shape of a parachute on the time it takes to fallTechnology & Designfor example, decide to calculate areas when using CAD or a bedroom plan.
• calculate perimeters of a range of shapes; for example decide to find missing lengths to enable calulation of the perimeter.
• understand and use scale in the context of simple maps and drawings; for example, plan the steps needed to draw a scale drawing of the playground using a scale such as 1 cm = 5 metres; Geographyfor example, plan the steps needed to draw a scale diagram of the playground;
• draw nets of 3-D shapes; for example use cm squared paper to draw the net of a box when designing a container. Technology & Designfor example produce a cardboard net of a casing design prior to manufacturing

Handling Data

• collect, organise, record and represent data; for example, appreciate when data should be grouped and decide on appropriate discrete class intervals; identify how best to record and represent data e. g. when to draw a line graph or a dual bar chart. Geographyfor example plan how best to record, process and display measurements of the depth of a river at regular intervals along its course;Home Economicsfor example choose to use dual bar chart to compare nutritional content in a variety cerealsSciencefor example, decide to collect information on resting heart rate and realise the need to record the data in groups, choose appropriate discrete class intervals and plan to display on a frequency diagram.Technology & Designfor example, create an online survey such as survey monkey, to find information to influence the design of a product.
• design and use a data collection sheet; for example, decide what information is required and design a suitable data collection sheet. Geographyfor example, decide what information to collect about traffic passing the school gates and design a data collection sheet to collect the information;Home Economicsfor example, design a data collection sheet for a consumer survey deciding what information is relevent such as opening hours, facilities, price, etcSciencefor example, design and use a data collection sheet to collect information on resting heart rate and blood pressure. Choose suitable headings such as Name, Heart Rate, Systolic and Diastolic PressureTechnology & Designfor example, design a data collection sheet to record the results of a bridge strength test.
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example, consider the nature of given or collected data and decide how best to represent it e. g. by drawing a line graph or a dual bar chart; Geographyfor example, decide to draw a dual bar chart to compare the annual monthly temperatures for Belfast and Marbella;Home Economicsfor example choose to construct a dual bar chart to compare the amount of each ingredient in two similar productsSciencefor example, decide to compare nutrient content in food on a dual bar chart.
• understand, calculate and use mean and range; for example, in an experiment calculate the mean of three readings and use the mean as a representive value. Geographyfor example, decide to calculate the mean monthly temperature for the summer months in Belfast by adding the average temperatures for June, July and August and dividing by 3;Sciencefor example, in an experiment calculate the mean of three readings and use the mean as a representive value. for example, given masses of babies born to smokers and non-smokers, choose to calculate the mean and range in order to evaluate the effect of smoking during pregnancy.Technology & Designfor example, decide to find the mean of anthropometric data to design a product

identify and use efficiently the materials, equipment, mathematics and strategies required;

Number and Algebra

• calculate fractions and percentages of quantities including money; for example, use an appropriate method to find 3/4 of £22.88, 30% of 180, 2/3 of 10
• express and use formula in words and/or symbolic form for example, recall and use the formula length x width x height to find the volume of a cuboid Geographyfor example, use the Cailleux roundness chart and the formula
  "(2r × 1000) / a" to calculate the roundness index of pebbles;Sciencefor example, decide to use the formula Moment = Force x Distance to calculate the moment and determine if a see-saw is in equilibrium;

Shape, Space and Measures

• understand and use scale in the context of simple maps and drawings; for example, given a scale of 1 cm = 2 m calculate the actual length of a classroom which measures 4.6 cm on a scale drawing Geographyfor example, use a scale such as 1 cm = 5 km when interpreting a map;Technology & Designfor example using scales 1:2, 1:5 etc. to produce a working drawing of a chosen design using CAD software such as SolidWorks.
• reflect 2-D shapes in a line; for example use squared paper to reflect shapes and check using a mirror; Technology & Designfor example, choose a marking gauge to mark out a symmetrical shape on a piece of wood.
• estimate, measure, draw and label angles up to 360 degrees; for example use a 360° angle measurer to draw or measure angles; Geographyfor example, plan to use a clinometer to find the gradient of a river bank;Sciencefor example, use a protractor to measure the angles of incidence, reflection and refractionTechnology & Designfor example, choose a tri-square to measure a 90° angle or a sliding bevel to measure any angle.

Handling Data

• collect, organise, record and represent data; for example enter additional data appropriately in a spreadsheet or database; Geographyfor example decide to collect and record weekly data from the Stevenson Screen and enter the readings on to a spreadsheet;Sciencefor example, decide to record on a table the results of an experiment to investigate the extension in a spring when different masses are hung from it and plan to draw a line graph of the data for example, decide to group data on heart rates of boys and girls and plan to compare these by drawing and interpreting a dual bar chart
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example choose appropriate graph paper to draw a line graph or dual bar chart, plot data accurately with suitable scales and labels on the axes Geographyfor example, appreciate that readings for depth of a river along its length are best displayed on a line graph and that a dual bar chart would be best to compare methods of transport to a rural school and to a city school;Home Economicsfor example choose appropriate graph paper to draw a dual bar chart to compare nutritional content in a variety cereals choose appropriate scales and labels on the axesSciencefor example, decide to present the results of an experiment investigating Hooke's Law, within the elastic limit, as a straight line graph

plan for an activity by identifying and sequencing component steps;

Number and Algebra

• understand, use and calculate ratio and proportion; for example, given an ingredients list that serves 4, identify the steps needed to calculate the ingredients needed to serve 30 Home Economicsfor example, if the ingredients for a bun recipe are given in the ratio 2:4:6 use this to increase or decrease the recipeSciencefor example, given nutritional information for 100ml of energy drinks plan to calculate the sugar content for standard sizes of bottles such as 250ml, 330ml and 500ml by multiplying appropriately;Technology & Designfor example calculating the gear ratios when working out the speed in the mechanical car project
• use equivalences between fractions, decimals and percentages to solve problems; for example, given that 40% of a cereal bar is carbohydrate, pupils decide to calculate how many degrees would represent carbohydrate on a pie chart by using equivalences Geographyfor example given that 40% of the trade price of a product is for labour, identify the steps needed to calculate how many degrees would represent labour on a pie chart;Home Economicsfor example, ”If 40% of a cereal bar is carbohydrate, decide on the mathematics required to work out how many degrees would represent carbohydrate on a pie chart?” e.g. divide 40 by 100 then multiply by 360
• calculate percentage increase and decrease in relevant contexts; for example, identify the steps needed to calculate the percentage decrease when a bike is reduced from £450 to £300 in a sale.
• use appropriate formulae; for example, when calculating the area of a circle identify the correct formula and use it appropriately ScienceFor example to compare speed of a vehicle on different slopes, measure the time taken to travel a specified distance and calculate the speeds using the formula S=D/T
• use and interpret graphs from real situations; for example, to find the speed for part of a journey shown on a travel graph, indentify the distance and time from the graph and the appropriate calculation to be carried out Sciencefor example, to determine why salt is spread on roads in winter, decide to draw a graph of 'salt added' against 'melting point' to investigate the effect of salt on the melting point of water
• apply mathematical concepts to a range of financial situations; for example, identify the steps taken to decide the best option for buying a car - a deposit and monthly repayments or paying in full by borrowing money at a given simple interest rate Geographyfor example, identify the steps needed to calculate the projected population of a town of 35000 given an estimated % increase of 2.5% over a year;

Shape, Space and Measures

• use, convert and calculate measures involving metric, and where appropriate, imperial units; for example, to find how many laps of a 400 m track should be run to complete a 1 mile race identitfy the correct conversion and calculation Home Economicsfor example, convert from pounds and ounces to kg and g using a tala measure for dry ingredients.Technology & Designfor example working out the diameter of an LED in millimetres when it is given in inches
• calculate perimeters and area of composite shapes involving squares, rectangles and triangles; for example, partition an irregular 2D shape to calculate the perimeter and/or area.
• calculate surface area and composite volumes of cubes and cuboids; for example, to find the surface area of a drinks container decide to draw the net, calculate the area of each 2D shape and add the areas together; to find the volume of a 3D shape suggest partitioning into cuboids, calculating the volume of each and adding the volumes together

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, to analyse times in a 5k park run choose appropriate class intervals, complete a frequency table and draw an approriate frequency diagram
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, choose the appropriate graph and scale for the data, include labels, title Sciencefor example, plan to investigate the relationship between systolic and diastolic blood pressure by drawing a scatter diagram and interpreting the correlation
• work out and use the median and mode; For example, decide to conduct a survey about shoe size and use this to identify the mode.
• work out the mean, median and mode of a frequency distribution; for example, using a frequency table complete the fx column, total the fx values and divide by the total frequency
• use one of the measures of average to compare two sets of data; for example, suggest which class has performed better in a test by calculating and comparing the mean or median test results Sciencefor example, in order to discuss the effect of smoking during pregnancy, decide to calculate the mean weight of babies born to smokers and non-smokers, compare these and draw appropriate conclusions;

consider and identify a range of materials/equipment, mathematical techniques and problem-solving strategies required to meet the purpose of activities;

Number and Algebra

• use conventional notation in algebra; for example, having found a pattern for expanding squares, consider rectangular arrangements, denoting terms to unknown values; find a global formula with two variables expressed in conventional notation

Shape, Space and Measures

• work out dimensions using scale; for example use a ratio scale of 1 : 25 000 to work out the length in km of a lake measuring 5 cm on a map Geographyfor example, identify how to use a ratio scale such as 1 : 25 000 to calculate real life or scaled dimensions;

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, recognise whether or not it is appropriate to group data
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, identify the most appropriate way to represent given data; choose appropriate graph paper for a graph; choose and use a protractor to draw the angles on a pie chart; Home Economicsfor example, pupils choose and use a protractor to draw the angles on their pie chart to represent the nutritional composition of a cereal barSciencefor example, choose to draw a scatter diagram to investigate the relationship between systolic and diastolic pressure, recognising that a positive correlation would suggest that as systolic pressure increases so too does diastolic pressure;
• use one of the measures of average to compare two sets of data; for example, compare test results of two classes by calculating either the mean, mode or median for each class Home Economicsfor example, choose the mean, mode or median to compare sugar content in energy drinks and other soft drinksSciencefor example, to determine the effect of smoking during pregnancy, consider the raw data and decide to calculate the mean/median weight of babies born to smokers and non-smokers, compare these and draw appropriate conclusions;

plan an activity, explaining their reasons for their chosen structure and approach;

Number and Algebra

• calculate the original quantity given the result of a percentage change; for example identify the steps needed to calculate the original price after a % price increase or decrease; Geographyfor example, outline the steps needed to solve a problem such as "The population of a town has decreased by 15% after a natural disaster and is now 45 000. What was population prior to the disaster?"; appreciate that 45,000 represents 85% of the population, use this to work out 1% and hence the original population;Home Economicsfor example, use reverse percentages to calculate the original amount of fat in a chicken and ham pie given that after government legislation the fat content is now 18g after a 15% reductionScienceFor example, given the oxygen pressures of exhaled air in mmHg and the % change in this pressure by breathing, decide to use reverse percentages to calculate the oxygen pressures of inhaled air in mmHg.
• calculate repeated proportional change; pupils plan to use repeated proportional change to calculate compound interest when considering options for borrowing/investing money; Geographyfor example, decide to use repeated percentage change to calculate the projected population of a town given the current popuation and the expected percentage growth rate;Home Economicsfor example, if the retail value of fairtrade coffee in the UK is £49 million and is predicted to increase by 33% each year, decide to calculate its value in 2 years time using repeated proportional change.ScienceFor example, given that the local council intends to increase the amount of recycling by 5% each year for the next few years, decide to use repeated proportional change to estimate the mass of recyclable materials in 3 years" time.
• formulate linear equations; for example identify the steps needed to solve a problem algebraically such as ‘The length of a rectangle is three times its width. Its perimeter is 24 centimetres. Find its area’; ScienceFor example, conduct an experiment to find the relationship between the mass attached to a spring and the extension of the spring. Record, in a table, the results of the experiment and draw a straight line graph. Recognise that they can formulate this linear relationship and deduce F=ke where they can obtain k as the gradient of their graph.
• solve two linear equations simultaneously by a graphical method; for example to find the break even point for a manufacturing process that can be represented by two linear equations in two unknowns, plan to draw two straight lines on a graph and identify the coordinates at which they intersect;
• make informed decisions involving money; for example decide how best to make an informed decision about borrowing or investing money, taking all relevant factors into consideration; Home Economicsfor example, plan to explore options, including compound interest, when making decisions about investing money or buying household goods.

Shape, Space and Measures

• perform length and area calculations on a composite shape including those involving the circle; for example decide to find the area of a composite shape which includes a circle or part of a circle, by partitioning it, finding the area of the component shapes, and combining these to find the area of the composite shape;
• solve complex problems involving perimeter, surface area and volume; for example plan how to use knowledge of 2-D and 3-D shapes, perimeter, area and volume to solve unfamiliar spatial problems requiring complex operations.
• understand and apply Pythagoras’ Theorem; for example choose to use Pythagaras' Theorem to calculate the third side of a right-angled triangle as one step towards solving a complex spatial problem;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example choose a hypothesis such as 'Year 10 pupils spend more time doing homework than Year 13 pupils', plan how to collect the relevant data and how best to process the data in order to compare the results for the two year groups; ScienceFor example, state an hypothesis such as "the extension of a spring increases proportionally as the mass increases". Decide to conduct an experiment to find the relationship between the mass attached to a spring and the extension of the spring, varying the masses attached and measuring the extension. Record the results of the experiment and draw a straight line graph. Use the graph to formulate a linear relationship and deduce F=ke and check this with a mass not already used;
• construct and interpret frequency tables and diagrams for sets of continuous data; for example plan how best to compare two sets of continuous data, choosing to draw cumulative frequency curves and/or box plots as appropriate, depending on the form of the given data; plan to investigate the relationship between two variables by drawing a line of best fit on a scatter diagram and using it to identify intermediate values; Sciencefor example, decide to investigate the relationship between systolic and diastolic blood pressure by drawing a scatter diagram. Plan to comment on the strength of the correlation, draw a line of best fit and use this to predict the diastolic pressure given the systolic.
• estimate the mean of a set of grouped data and identify the limits of the median and modal group; for example decide to calculate an estimate for the mean when the data is presented in a grouped frequency table, using mid-values to represent each class. Sciencefor example, in order to discuss the effect of smoking during pregnancy, where the data is given in a grouped frequency table, decide to estimate the mean weight of babies born to smokers and non-smokers and compare these, drawing appropriate conclusions;
• choose the most appropriate average (mean, median, mode) for a given line of enquiry; for example consider the nature, range and number of anomalies in given data to identify which average is most appropriate to use, explaining the reason for their choice; Sciencefor example, consider data from an investigation on external influences affecting plant growth, identifying any anomalous values before deciding which average would be most appropriate to use for comparing growth;

consider and identify, with some justification, the materials/equipment, mathematical techniques and problem-solving strategies required;

Number and Algebra

• use the advanced functions on a calculator to perform complex calculations; for example use √(12^2 - 7^2 ) to find a short side in aright angled triangle, use 50 000 ×1.04^3 to calculate population of a town after 3 years Geographyfor example, use 50 000 ×(1.04)³ to calculate the population, after 3 years, of a town with 50 000 inhabitants and a projected increase of 3% per annum;ScienceFor example, given that the local council intends to increase the amout of recycling by 5% each year for the next few years, use , current mass of recycling ×〖1.04〗^3 , to estimate the mass of recyclable materials in 3 years time.
• round to an appropriate number of decimal places and significant figures; for example when solving a problem recognise that the given numbers have 2 significant figures and decide to also round the answer to two sf; ScienceFor example, having used repeated percentage change to estimate the recycling target in 3 years time, consider the accuracy of the current mass and round the target to the same or less significant figures.
• calculate the original quantity given the result of a percentage change; for example show clearly how to solve the problem: “A shirt cost £18.70 after a 15% reduction. What was the original price?”, by recognising that £18.70 represents 85% of the original price, calculating 1% and then 100% of the original price.
• calculate repeated proportional change; for example, solve problems such as : ‘Investigate the future population in a town which currently has a population of 50,000 and a projected population growth rate of 4% per annum', by using repeated percentage increase to calculate the population in the town for the next few years, realising that this is just an estimate; Geographyfor example, decide to use repeated percentage change to find the population of a town in 5 years time given the current population and the estimated percentage increase per annum, realising that this is just an estimate;Sciencefor example, given that the local council intends to increase the amout of recycling by 5% each year for the next few years, use current mass of recycling ×〖1.04〗^3 to estimate the mass of recyclable materials in 3 year time explaining that this is the most efficient way of calculating the target as intermediate values are not required.
• formulate linear equations; for example solve a problem such as ‘The length of a rectangle is three times its width. Its perimeter is 24cm. What is its area?’, by drawing a sketch, letting the width be ‘x’, forming and solving an equation in 'x' and therefore finding the area.
• manipulate simple algebraic expressions, equations and formulae; for example pupils rearrange C = 2πr to make r the subject in order to use this as the most efficient way to find the radius/diameter of a circle when given the circumference; Technology & Designfor example, rearrange the formula for ohms law depending on the unknown (voltage V=IxR; current I=V/R; or resistance R=V/I) as the most efficient way to find the unknown
• make informed decisions involving money; for example using the formula for compound interest and considering the monthly payments for each option, solve the problem: 'Peter has taken out a loan for his first car. He borrowed £4,500 from his local credit union. It is offering a borrowing rate of 5% with the option of paying it back over either 3, 4 or 5 years. What would be best time period for him to choose and why?',

Shape, Space and Measures

• perform length and area calculations on a composite shape including those involving the circle; for example find the area/perimeter of a composite shape by partitioning it, deciding on the most efficient way to do this and showing the method clearly;
• solve complex problems involving perimeter, surface area and volume; for example calculate the volume of a composite 3-D shape either by splitting it into 2 or more common 2-D shapes or by finding the area of the constant cross-section and multiplying by the length;
• use three figure bearings to define direction; for example, pupils use a map to find the bearing of one town from another to plan a helicopter round-trip from Ballymena to Antrim, understanding that there is a difference of 180ᵒ between these related bearings; Geographyfor example pupils decide to find and use the bearing of one town from another, to plan a helicopter round-trip from Ballymena to Antrim. They understand that there is a difference of 180ᵒ between these related bearings;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example pupils choose a hypothesis, collect the relevant data considering how much data to collect and the most efficient way to collect it, test the data using the most appropriate methods explaining the reasons for their choice, evaluate results and present work clearly and efficiently, justifying their choice of presentation; ScienceFor example, state an hypothesis such as 'the extention of a spring increases proportionally as the mass increases', decide to conduct an experiment to find the relationship between the mass attached to a spring and the extension of the spring, varying the masses attached and measuring the extension, record the results of the experiment and draw a straight line graph. Use the graph to prove a linear relationship and deduce F=ke and check this with a mass not already used.
• construct and interpret frequency tables and diagrams for sets of continuous data; For example given a box plot for one data set and a grouped frequency table and the highest and lowest data values for a second data set, draw a cumulative frequency table and graph for the second set and therefore construct a box plot so that the two data sets can be directly compared; ScienceFor example, decide to investigate the relationship between systolic and diastolic blood pressure by drawing a scatter diagram. Plan to comment on the strength of the correlation, draw a line of best fit and use this to predict the diastolic pressure given the systolic understanding that the result is only an estimate.
• estimate the mean of a set of grouped data and identify the limits of the median and modal group; for example given a grouped frequency table, calculate an estimate for the mean using mid-values to represent each class, appreciating that these are estimates and should only be calculated if the raw data is unavailable; Sciencefor example, given data, in a grouped frequncy table, on birth weights of babies calculate an estimate for the mean, find the median and modal group and use this information to comment on the effect of smoking during pregnancy,
• choose the most appropriate average (mean, median, mode) for a given line of enquiry; for example, consider the range and any anomalies in a data set to identify the most appropriate average to use, such as choosing the median instead of the mean when there is one extreme value;
• understand and use relative frequency as an estimate of probability and calculate expected frequency; for example understand the need to conduct an experiment to find estimates of the probabilities for outcomes of a biased dice; understand that increasing the number of trials improves the estimate of the probability and choose to repeat the experiment an appropriate number of times; calculate Relative Frequency = number of times an event happens ÷ total number of trials;

use some mathematical notation;

Number and Algebra

• use, estimate, add and subtract numbers up to at least 10; for example, count a number of buttons up to 10 and record the number as a numeral or in words and use 0 to represent the empty set. Technology & Designfor example, recognise the numbers on a clock.
• create and describe repeating patterns using objects, numbers or pictures; for example, complete repeating patterns using numerals i.e. 1, 2, 3, 1, 2, …; 6, 7, 8, 6, 7, … ; 1, 1, 2, 2, 1, …
• recognise and use coins; for example, recognise and match coins to prices to buy items, use coin stamps to make totals i.e. use the 1p coin stamp to make 3p, use the 2p coin stamp to make 8p and use the 5p coin stamp to make 10p.

Shape, Space and Measures

• recognise 'special' times on the clock; for example, recognise that it is break time by the numerals on a clock

Handling Data

• collect information and record using real objects or drawings; for example, pupils collect and record data using written numerals to show how many people with blue / brown eyes.

show some organisation in their practical work;

Number and Algebra

• use, estimate, add and subtract numbers up to at least 10; for example, match objects to find which group has more / fewer. Technology & Designfor example, order the numbers on a clock.
• understand conservation of number; for example,understand that the total number of objects remains the same after rearranging on a Carroll diagram.
• create and describe repeating patterns using objects, numbers or pictures; for example, continue a pattern using object or drawings e.g. red bead, blue bead, yellow bead, red bead, blue bead . . .
• recognise and use coins; for example, engage in shopping role plays matching coins to prices to buy from the supermarket.

Shape, Space and Measures

• use everyday language associated with length, ‘weight’, capacity and area to describe, compare and order three objects; for example, place pencils in order from shortest to longest; place shopping bags in order from lightest to heaviest, and containers in order from empty to full. Home Economicsfor example, use balance scales to place food items in order from lightest to heaviest
• sequence familiar events; for example, place picture cards in order of daily activities e.g. wake up, wash and dress. Home Economicsfor example, place pictures in order to show the sequence for making toastTechnology & Designfor example, place the picture cards in order to show the stages of the vacuum forming process
• know the days of the week and their sequence; for example, pupils order the days of the week starting on any day and pupils complete a sequence given 3 days with one missing, for example, Sunday, ________, Tuesday
• sort 2-D and 3-D shapes and make and describe 2-D and 3-D constructions; for example, sort shapes for one criterion, such as 2-D or 3-D shapes; talk about different 2-D and 3-D constructions for example, select the shapes to be used to create a 3-D construction

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example sort a collection of flowers by type and then re-sort by colour, sort animals with two legs / not two legs and re-sort fly/can not fly. Sciencefor example, use a Carroll diagram to sort living and non living things, re-sort into their ecosystems
• collect information and record using real objects or drawings; for example, self-register using a photograph; use cubes to record the number of people with blue / brown eyes. Geographyfor example, use cubes/pictures to record the number of people travelling to school by car, bus etc.;Sciencefor example, use mapping to match animals to their habitats

use appropriate mathematical notation;

Number and Algebra

• understand that the place of the digit indicates its value; for example, understand that 57 is 5 tens and 7 units and 75 is 7 tens and 5 units;
• use quick recall of number facts up to 10; for example, recognise and use symbols such as +, - and = in calculations as 5 + 2 = 7, 10 - 6 = 4;
• add and subtract within 20 mentally and in written form; for example recognise and use symbols such as +, - and =in calculations for example 10 + 5 + 1, 19 - 7
• add and subtract within 100; for example use a 100 number square or other structured apparatus to carry out calculations such as 47 - 23 = ?, 21 + 35 = ? without bridging the 10;
• understand the use of a symbol to stand for an unknown number; for example 14 = 6 + □ and 2, 4, 6, Δ, 10;

Handling Data

• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; for example, use a mark to record data on a simple table (link to simple table in illustrations) Sciencefor example, when studying animals complete a given table to record how many worms, snails, slugs, woodlouse, millipedes etc are found and illustrate this information by completing a block graph on a template, given axes, labels, categories and vertical scale

organise their practical work and check what they have done;

Number and Algebra

• add and subtract within 100; for example, use the 100 number square or other stuctured apparatus to add or subtract two 2 digit numbers without bridging the 10; when adding 47 and 21, pupils start at 47 on the 100 square and count down 2 and across 1;
• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example, use replica coins to show various ways to make up an amounts of money up to£1, in role play show three different ways to spend 35p choosing from a selection of items; use replica coins to work out the total cost, check by repeating the process.

Shape, Space and Measures

• use language and follow instructions, in practical situations, for turning movements; for example, give instructions such as half turn and quarter turn, and left and right to move a robot; follow instructions for turning half and quarter turns and left and right;

Handling Data

• sort and classify objects for two criteria using Venn, Carroll and Tree diagrams; for example, sort birds with long beaks/not long beaks and webbed feet/not webbed feet on a tree diagram, check that all the birds have been sorted and no bird appears more than once; Sciencefor example, use a Carroll diagram to sort living and non living things into their ecosystems, count the total number on the Carroll diagram and check this is equal to the total number givenTechnology & Designfor example, sort tools onto a Venn diagram showing the materials they can be used on, such as sandpaper on wood, wet and dry paper on plastic and screws on both
• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; for example, use marks to record information on a simple table and given frequencies complete horizontal or vertical block graphs. Geographyfor example, complete a block graph showing the number of pupils travelling to school by different modes of transport and check that the total number of block is the same as the number of pupils;Home Economicsfor example, use marks to record information on a simple table and given totals complete horizontal or vertical block graphs.Sciencefor example, complete a simple table showing inherited/changeable characteristicsTechnology & Designfor example, read and/or complete a simple table showing materials, an image and their definition

use a range of appropriate mathematical notation;

Number and Algebra

• understand and use the concept of place value in whole numbers; for example, use of place value columns when showing that the place of the digit indicates its value, zero is a place holder and the digits on the left are of greatest value; Geographyfor example, order the population of towns from smallest to largest;Technology & Designfor example, use the colour code and place the numbers in the correct order with the appropriate number of zeros to find the size of the resistor up to 1000 ohms
• know 2, 3, 4, 5 and 10 muliplication facts; for example use the 'x' symbol when multiplying; Home Economicsfor example, increasing recipes - using the 'x' symbol when doubling the recipe ingredients
• understand and use simple fractions in context; for example, if a bag of sweets has 3 blue and 1 red, then ¾ are blue and ¼ are red; Geographyfor example, describe the amount of cloud cover as a fraction using a cloud fraction grid;Home Economicsfor example, if a pizza is cut up into 8 equal slices and 3 slices are eaten then 3/8 of the pizza has been eaten and 5/8 remainsSciencefor example, understand that dry air is approximately 1/5 oxygen.
• use number skills in the context of money up to £10; for example, record money using £ or p (Please note that money notation is not the same as decimal notation). Home Economicsfor example, record money using £ or pTechnology & Designfor example, record the total cost of all the components of a bird feeder in £ and p

Shape, Space and Measures

• choose and use appropriate standard units to estimate, measure and record length, capacity, volume, ‘weight’, time and temperature; for example, record lengths using cm or m, ‘weight’ using g and kg etc. GeographyFor example use °C to record temperatureHome Economicsfor example, record weight using 'g' and 'kg', use 'ml' and 'l' when recording liquidsSciencefor example record 'weight' of magnesium in grams,Technology & Designfor example, record the length of a material to the nearest cm
• read simple measuring instruments with an appropriate degree of accuracy; for example, use a ruler to measure a length in cm or mm
• read and interpret a calendar; for example, given a calendar for the month of May identify which day April 30th falls on Sciencefor example, use a calendar tracking the lunar cycle to determine how long it takes the moon to orbit the earth. (reference picture of lunar calendar month)
• read digital and analogue clock displays; for example, read time on the analogue clock in five minute intervals past and to the hour and relate these to am and pm digital displays; Home Economicsfor example, calculate and read the finishing time when cooking pizza in the oven for 15 mins, beginning on the hour, half hour or quarter past the hourTechnology & Designfor example, when designing a clock, read analogue clock times.
• use grid references in practical situations; for example, on a map identify a square using two points of reference, such as, the treasure is in B2. Geographyfor example, identify on a simple map, a square using two points of reference such as 'the school is in B2';

organise their work and know how to check its accuracy;

Number and Algebra

• understand, use, add and subtract whole numbers up to at least 1000; for example, when adding vertically place the numbers in the correct columns and begin with the units and work to the left. Home EconomicsFor example, find combined weight by adding 300 g of flour and 150 g of sugar.
• understand and use the concept of place value in whole numbers; for example, use place value columns to show that the place of the digit indicates its value, zero is a place holder and the digits on the left are of greatest value. Technology & Designfor example, use the colour code and place the numbers in the correct order with the appropriate number of zeros to find the size of the resistor up to 1000 ohms and use a multimetre to check if the answer is accurate
• add and subtract mentally two 2-digit numbers within 100; for example, use partitioning to add mentally two sets of scores to find the total such as 66 + 23 = 66 + 20 + 3 = 89, then subtract 66 from 89 to check it makes 23
• approximate to the nearest 10 or 100; for example, when estimating the answer to the calculation 58 + 203, add 60 and 200 to give an estimate of 260;
• use number skills in the context of money up to £10; for example, when using a pencil and paper method to add sums of money correctly align the pounds and pence (Please note that money notation is not the same as decimal notation). Home Economicsfor example, add prices to decide if all the ingredients from a given recipe can be purchased from a given budget, less than £10

Shape, Space and Measures

• read simple measuring instruments to an appropriate degree of accuracy for example, measure a length in mm and repeat the measurement to ensure accuracy Sciencefor example, read a measuring cylinder, check that the results are reasonable and repeat the reading if required;Technology & Designfor example, measure a length of material to the nearest cm and remeasure to check accuracy, 'measure twice, cut once' and/or peer checking
• find the area of shapes by counting whole and half squares; for example when finding the area of a shape, count two half squares as one whole square and add to the number of whole squares;
• read and interpret a calendar; for example, using a calendar for a single month, find the date and day 5 days from now and count back to check the original starting day;
• recognise one line of symmetry in common 2-D shapes; for example check for a line of symmetry by folding the shape in half; Technology & Designfor example, check a line of symmetry in a simple design by folding

Handling Data

• collect and record relevant data for a given activity; for example, record data on a given observation sheet ensuring all sections have been completed; for a frequency table check that the sum of the tallies is the same as the total frequency Geographyfor example, systematically complete a given observation sheet for a traffic survey, checking that all of the information has been recorded;Home Economicsfor example, carry out a survey to find the different types of fruit liked by the pupils in a class.Sciencefor example, collect data about pupil characteristics eg. hair colour, eye colour etc. Use a given template with column headings provided to record the data and ensure that total frequency equals class size.

use a range of appropriate mathematical techniques and notation;

Number and Algebra

• read, write and order whole numbers within 10000 Technology & Designfor example, use the colour code and place the numbers in the correct order with the appropriate number of zeros to find the size of the resistor up to 10000 ohms
• approximate within 10 000 to the nearest 10, 100 and 1000; for example round 6473 to either 6470, 6500 or 6000 depending on expectations; Geographyfor example, round the population of towns to the nearest 1000;
• understand place value to two decimal places; use knowledge of decimal place value to order numbers such as 0.56, 5.65, 0.65 and 5.06; Sciencefor example, compare the gravitational pull of the planets in the Solar System given to a maximum of 2dp.
• estimate answers to calculations and approximate by rounding; for example estimate the cost of uniforms for 21 members of staff at £19 each using 20 × 20, or estimate the number of pupils in a school with 327 boys and 479 girls using 300 + 500;
• add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; for example add and subtract mentally any two 2-digit numbers within 100 (without any apparatus), show working out for multiplying two whole numbers up to 100 and use a calculator to divide a whole number within 10 000 by another whole number within 10 000; use division to find out the number of buses required for a school trip; Geographyfor example, add the daily rainfall in mm to find the total for a week;Home Economicsfor example, use appropriate operation when adapting quantities from a recipeScienceFor example, work out the cost of electricity given a fixed charge, the cost per unit of electricity (to the nearest pence) and the number of units used.Technology & Designfor example, divide by 2 to find the centre or mid point of pieces of material.
• add and subtract numbers with up to two decimal places; for example add 5.4 m and 1.76 m to find the total length of fencing required; Please note that this does not include adding and subtracting money. ScienceFor example, find the change in mass of the magnesium by subtracting the mass of crucible + magnesium before and after heating.
• know multiplication facts up to 10 × 10 and derive associated division facts; for example understand that as 6 × 7 = 42, then 42 ÷ 7 = 6; use '÷' symbol as appropriate;
• use fractions to describe quantities; for example, describe as container of liquid as 'about one third full' Sciencefor example, when designing a lava lamp with two-thirds vegetable oil and one-third water or making slime with two-thirds corn flour and one third water
• perform simple calculations involving unitary fractions; for example to calculate the discount on a multi pack of crisps costing £3.60 with ⅓ off, divide £3.60 by 3; Geographyfor example, calculate the wages an employee earns in production of a fair trade product using a given unitary fraction such as 1/10;Home Economicsfor example divide £3.60 by 3 to calculate the discount on a multi pack of crisps given that there is ⅓ offTechnology & Designfor example, divide a length by 2 to find the midpoint.
• understand and use simple percentages; for example understand that 25% of a pizza is the same as a quarter; calculate 10%, 20%, 25% and 50% of a quantity using equivalent fractions; use '%' symbol as appropriate; Geographyfor example, calculate the wages that the employee earns in production of a Fair Trade product using a given simple percentage such as 10%;Home Economicsfor example understand that 25% of a pizza is the same as a quarter;Sciencefor example, understand that dry air is approximately 20% oxygen and know that this is the same as a fifth.Technology & Designfor example, calculate 10 % of the resistance to find the tolerance of resistors with a silver band.
• interpret and apply simple rules expressed in words; for example, given the formula Area = length x width calculate the area of a rectanglar room giving answer in m2
• interpret a calculator display when solving money problems; for example understand that 5.4 represents £5.40;

Shape, Space and Measures

• estimate and measure length, ‘weight’/mass and time and temperature, working to an appropriate degree of accuracy; for example estimate the width of a room to the nearest metre; measure and record the length of an envelope in millimetres; and measure the temperature of water to the nearest degree Celsius from an analogue thermometer; Geographyfor example, choose and use a trundle wheel rather than a ruler to measure the length of a hockey pitch;Technology & Designfor example, measure the length of a material to the nearest mm
• understand the relationship between metric units; for example understand that 1 m 25 cm is the same length as 125 cm; Geographyfor example, measure the width of a pebble in cm and mm and express it in mm only;Home Economicsfor example, understand that 1 kg 500 g is the same as 1500 g.Technology & Designfor example, understand that a length of 24 mm is equal to 2 cm 4 mm
• add and subtract common measures; for example subtract 1.76 m from 3.3 m; Home Economicsfor example, subtract 300 from 1000 to work out how much flour is left in a 1 kg bag if 300 g is used?ScienceFor example, find the change in mass of the magnesium by subtracting the mass of crucible + magnesium before and after heating.Technology & Designfor example, subtract lengths when cutting materials
• estimate area and volume of shapes by counting squares/cubes; for example estimate the area of a leaf by counting more than half a square as a whole square; GeographyFor example, subtract 1.76 m from 3.3 m to find the difference in the depth of a river at two points;
  for example,calculate the difference in height between two spot heights on an OS map;Sciencefor example, use a centimetre square overlay to estimate the area of a leaf by counting more than half a square as a whole square.
• understand and use digital and analogue clock displays, using am, pm and 24-hour notation; for example 16:20 is the same as 4:20 pm; add a given time to a time of day and calculate duration between two times; read a simple timetable with one bus/train/event, times bridging the hour; Geographyfor example, use a simple timetable with one bus/train to plan a journey;
• recognise and draw lines of symmetry in a variety of 2-D shapes; for example draw lines of symmetry on squares, rectangles, triangles and hexagons; Sciencefor example recognise the symmetry in nature - butterflies, zebra faces, tigers, flowers, snowflakes etc
• know the eight points of the compass; for example North (N), North East (NE), East (E), South East (SE), South (S), South West (SW), West (W), North West (NW); Geographyfor example, identify the location of a landmark on a map, given that it is due North of point A and due west of point B;Technology & Designfor example, know the compass points when designing a weather vane
• use coordinates in the first quadrant; for example plot and label coordinates such as (3, 4) and (6, 0); Geographyfor example, on a map, give the location of a landmark as a 4 figure grid reference;Technology & Designfor example, understand coordinates to use a CNC machine

Handling Data

• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, use frequency diagrams to organise discrete data (grouped or ungrouped), independently draw and label both axes; draw and interpret bar charts with given class intervals; compare frequencies by interpreting a simple pie chart; Geographyfor example, independently draw a bar chart to show the number of each type of vehicle passing the school over a given period of time;Home Economicsfor example, use the 'Eat Well Guide', pie chart to help plan a balanced mealSciencefor example, display information about solubility of substances on a bar chart, drawing and labelling both axes.

organise their own work and work systematically;

Number and Algebra

• read, write and order whole numbers within 10 000; for example place the populations in order of size, 23456, 12578, 56734, 84520 and 77562; Technology & Designfor example, use the colour code and place the numbers in the correct order with the appropriate number of zeros to find the size of the resistor up to 10000 ohms and use a multimetre to check if the answer is accurate
• use knowledge of place value to multiply and divide whole numbers by 10 and 100; for example 30 x 100; 4200 ÷ 10; Technology & Designfor example, multiply by 10 to convert cm to mm
• understand and use multiples and factors; for example use factors to work out how many different equal teams can be made from a class of 30 pupils;
• interpret and apply simple rules expressed in words; for example use the given formula ‘Area = Length x Width’ to find the area of a rectangle; Sciencefor example use the given formula ‘Area = Length x Width’ to find the area of a rectangle and Pressure = Force/ area to find pressure; (NA(4)o)
• make choices about spending and value for money; for example show clearly how to decide whether it is better value to buy 3 cans of cola or a litre bottle, and consider other variables that need to be taken into consideration when deciding on best value; Home Economicsfor example, decide whether it is better value to buy 3 cans of cola or a litre bottle, and take into account other considerations when deciding on best value.

Shape, Space and Measures

• estimate and measure length, ‘weight’/mass and time and temperature, working to an appropriate degree of accuracy; for example estimate the width of a room to the nearest metre; measure and record the length of an envelope in millimetres; and measure the temperature of water to the nearest degree Celsius; Home Economicsfor example, subtract 300 from 1000 to work out how much flour is left in a 1 kg bag if 300 g is used?Sciencefor example, consider a selection of objects and discuss how to place in order according to mass. Choose to use digital scales and measure the mass of the objects to 2decimal places.Technology & Designfor example, measure a length and mark the position of a hole to be cut in the material
• understand the relationship between metric units; for example understand that for comparison, all measurements must be in the same units a table measuring 1 m 25 cm is the same length as 125 cm; Home Economicsfor example, understand that 1 kg 250 g is the same as 1250 g.Technology & Designfor example, understand that all lengths must be in the same units
• add and subtract common measures; for example subtract 1.76 m from 3.3 m to see how much is left; Home Economicsfor example, subtract 300 from 1000 to calculate how much flour is left in a 1 kg bag.Sciencefor example, find the mass of a crucible of magnesium before and after heating then calculate the change in mass of the magnesium by subtracting these values.Technology & Designfor example, add together the lengths of the components required to make a desk tidy to see if all components can be cut from the given sheet of wood
• work out perimeters of simple shapes; for example add the given lengths to find the perimeter of a rectangular garden;
• understand and use digital and analogue clock displays, using am, pm and 24-hour notation; for example, find when to take a turkey out of the oven if it needs to cook for 3 hours 20 minutes; read a simple timetable to find the length of a bus journey which starts at 11:40 am and arrives at its destination at 1:15 pm; Home Economicsfor example, form time plans when cooking
• use coordinates in the first quadrant; for example plot and label coordinates such as (3, 4) and (6, 0);

Handling Data

• collect, group, record and present data with given class intervals; for example use the class intervals 1 – 5, 6 – 10, 11 – 15, etc, to record ages of patients waiting in A&E; Home Economicsfor example, use the given class intervals 0-9, 10-19, 20-29, 30-39, 40-49 etc to record the time spent on various activities for 1 week (e.g. walking, running, cycling etc)Sciencefor example, collect information on resting heart rate using a heart rate monitor or App, record the class data on a frequency table with class intervals given and display appropriately. Use the information to identify the most common group.
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, use frequency diagrams to organise discrete data (grouped or ungrouped), independently draw and label both axes; draw and interpret bar charts with given class intervals; compare frequencies by interpreting a simple pie chart; Geographyfor example, systematically collate information from an observation sheet on holiday destinations and record onto a frequency table;Home Economicsfor example, use a bar chart to compare the iron content in different foods.

review their work and check for accuracy;

Number and Algebra

• estimate answers to calculations and approximate by rounding; for example estimate to check if the answer to a calculation is reasonable
• use the relationship between addition and subtraction to check calculations; for example understand that to find how much money is left from £100 after spending £50 and then £30, it can be worked out by subtracting £50 from £100 and then subtracting a further £30 and checking this by adding £50 and £30 and subtracting the total from £100; Sciencefor example, suggest checking the change in mass of magnesium by adding this value to the original mass to ensure it equals the mass after heating

Shape, Space and Measures

• estimate and measure length, 'weight'/mass and time and temperature, working to an appropriate degree of accuracy; for example, measure the length of the sides of a shape in mm and repeat ensure accuracy Technology & Designfor example, evaluate a project by creating a video resource, evaluate against the specification such as my product should weigh 25 g does it?

Handling Data

• collect, group, record and present data with given class intervals; for example when grouping data in given class intervals check all the data has been included;
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, check that the height of each bar in a bar chart matches the frequency on the table Geographyfor example, when completing a frequency table from an observation sheet on holiday destinations, check that the total frequency is the same as the number of people surveyed;

use a range of appropriate mathematical techniques and notation;

Number and Algebra

• read write and order numbers of any size; ScienceFor example, place the planets in the Solar System in order of diameter (given as whole numbers of km)
• understand place value to three decimal places; for example, understand that for 0.562, ‘2’ represents two thousandths; ScienceFor example, compare the gravitational pull of the planets in the Solar System given to a maximum of 3dp.Technology & Designfor example, understand that 2200 ohms can also be writen as 2.2 K ohms and 3300000 ohms can also be writen as 3.3 M ohms
• round decimals to the nearest whole number; for example, round a calculator answer to the nearest whole number when calculating mean heights; Geographyfor example, when calculating the mean monthly temperature round the answer to the nearest °C;Home Economicsfor example, round a calculator answer to the nearest whole number when calculating mean heightsScienceFor example, calculate the cost of electricity given a fixed charge, the cost per unit of electricity to 2dp and the number of units used, rounding the answer to the nearest penny.
• multiply and divide numbers with up to two decimal places by a whole number; for example, work out 16.75 x 14 when finding the area of a rectangular playground; 1.65 m ÷ 5 when dividing a piece of wood into 5 equal pieces; ScienceFor example calculate the cost of the electricity given a fixed charge, the cost per unit of electricity to 2dp and the number of units used.
• understand and use negative numbers in practical contexts; for example, know that when the temperature rises from -6° C to -1° C, it has risen by 5° and understand that height above sea level can be expressed as a positive number and below sea level as a negative number; Home Economicsfor example, know that when the temperature of a freezer rises from -18° C to -12° C, it has risen by 6° C and understand that the food in the freezer might start to thaw;ScienceFor example, given a table of melting points/boiling points of a variety of substances, identify those that are solids/liquids/gases at room temperature; compare the mean temperature of the planets in the Solar System.Technology & Designfor example, using the digital read out on a milling machine.
• calculate fractions and percentages of quantities, including money; for example, find ¾ of £22.88, 30% of 180; find the cost of an item if the price is increased/decreased by a fraction/percentage, express 40 cm as a fraction of 180 cm; Home Economicsfor example, find the new price of a chicken when decreased by 70% after 6 pm if originally priced at £6.00.ScienceFor example calculate the percentage of pure salt obtained from a sample of rock saltTechnology & Designfor example, calculate the tolerence range of any resistor
• devise and use rules for generating sequences in words and/or symbolic form; for example, identify the position to term rule e.g. “4 × n - 1” when investigating a number pattern;
• express and use formulae in words and/or symbolic form; for example, find the volume of a cuboid using the formula V = l × b × h; Geographyfor example, calculate the discharge of the river using the formula: Discharge of the river = Cross sectional area x Velocity;Home Economicsfor example, use a formula '25 minutes per kg plus half an hour' to work out the total cooking time for a chickenScienceFor example use V=IR to calculate the voltage given current and resistance; use the formula percentage oxygen absorbed = (difference between oxygen in inhaled air and exhaled air )/(amount of oxygen in inhaled air) × 100. Technology & Designfor example, calculate the speed ratio using the formula, speed ratio = circumference of driven pulley/ circumference of driver pulley

Shape, Space and Measures

• convert from one metric unit to another; for example, convert between whole number and decimal quantities, such as, 1245 ml to 1.245 l, 14 mm to 1.4 cm, 1.26 kg to 1260 g, 2.7m to 2m 70 cm Geographyfor example, when measuring the width of pebbles, convert 3.8 cm to 38mm;Home Economicsfor example, convert to and from decimal quantities, 1250 ml to 1.25 l; 1250 g to 1.25 kg;ScienceFor example, convert the length in cm into metres when calculating a moment in NmTechnology & Designfor example, convert 5.6 cm to 56 mm when drawing a design
• use the four operations to solve problems related to measures; for example, calculate how many shelves 45 cm long can be cut from a 2 metre plank of wood by dividing 200 by 45; Home Economicsfor example, calculate how many scones can be made from a 1 kg bag of flour if a recipe for 12 scones uses 350 g of flour.ScienceFor example, use the formula weight = mg to calculate weight in Newtons for a spaceman on different planetsTechnology & Designfor example, calculate a missing measurement from a working drawing.
• calculate areas of squares, rectangles and right-angled triangles and volumes of cubes and cuboids; for example, calculate the area of a rectangular fence to find how much paint is required; ScienceFor example, use a sheet of kitchen towel and fold in pleats, calculate the base area and the area of the kitchen towel and compare to show how the area of absorption can be so much greater than the final base area or when investigating density calculate the volume of a cuboid of a substanceTechnology & Designfor example, calculate areas when using CAD or in a bedroom plan.
• calculate perimeters of a range of shapes; for example, calculate perimeters of regular and irregular shapes with some missing, but attainable measurements;
• understand and use scale in the context of simple maps and drawings; for example, use a simple scale, such as 1 cm = 2 m, to draw and/or interpret a scale diagram; Geographyfor example, use a simple scale, such as 1 cm = 2 m to draw and/or interpret a scale diagram or map;Sciencefor example, use a scale of 1m = 500 million km to construct a scale model of the solar system - considering only the distance of each planet from the sun.Technology & Designfor example, when drawing a design use a simple scale
• read and interpret timetables; for example, plan a journey using a timetable with at least two buses/trains/planes with times bridging the hour;
• reflect 2-D shapes in a line; for example, use squared paper to reflect shapes ScienceFor example, investigate and describe the image formed by a shape/object in a plane mirrorTechnology & Designfor example, use reflection to manufacture a template to ensure left and right handed fit.
• draw nets of 3-D shapes; for example, use cm squared paper to draw how a 3-D shape when opened out flat; Technology & Designfor example, use a net when making a card model
• estimate, measure, draw and label angles up to 360 degrees; for example use a 360° angle measurer to compare angles, and estimate the size of an angle as between 90° and 135°. ScienceFor example, draw and measure angles of incidence and angles of reflection of a ray of light reflected off a plane mirror

Handling Data

• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example, understand when it is appropriate to use a line graph and understand that intermediate values will have a meaning; plot points for experimental data; draw and interpret a dual bar chart; complete and interpret given pie charts with divisions marked; Geographyfor example, plot a line graph showing the depth of a river at regular intervals along its course; draw a dual bar chart to show the monthly rainfall for two countries for the period of a year;Home Economicsfor example, construct a dual bar chart to compare the nutritional content in two cerealsScienceFor example, collect and tabulate the relevant information in an experiment to see how the height of a slope affects the speed of an object rolling down it; draw a line graph and consider the relationship between height and speed
• understand, calculate and use mean and range; for example, find the mean and range of the heights of 20 girls; Home Economicsfor example, compare mean and range of pocket moneyScienceFor example, when conducting and experiment involving measurement, repeat the measurement 3 times and calculate the mean value of the 3 measurementsTechnology & Designfor example, use the mean of anthropometric data to design a product
• place events in order of likelihood; for example, order everyday events using language such as impossible, unlikely, even chance, likely and certain; given a partially finished sample space diagram, complete it to show all the outcomes of rolling two dice; ScienceFor example, complete a punnet square for Blue/Brown eyes, having discussed dominance of genes and use simple probability language to descibe the likelihood of eye colours

plan and work systematically and efficiently;

Number and Algebra

• devise and use rules for generating sequences in words and/or symbolic form; for example, systematically investigate a number pattern by drawing diagrams, constructing a table and identifying the position to term rule e.g. “4 × n - 1”;
• express and use formulae in words and/or symbolic form; for example, find the volume of a cuboid with dimensions 1.2m x 50 cm x 40 cm by first converting units and then applying the appropriate formula; Sciencefor example, to determine whether a see-saw will balance,use given masses to calculate weight(N) and then use the formula Moment = F x d to calculate clockwise and anti-clockwise moments;
• make informed choices about personal budgeting and spending; for example plan a week of leisure activities for a family of four with a budget of £500, taking into consideration their collective and varied interests and requirements; Home Economicsfor example, plan how best to spend monthly wages in relation to needs and wantsTechnology & Designfor example, model batch production to produce a product more efficiently and economically.

Shape, Space and Measures

• convert from one metric unit to another; for example, change units before calculating the area of a rectangle 2 m by 80 cm and give the answer in either cm² or m²; Home Economicsfor example, change 1.5 kg to 1500 g before subtracting 175 gScienceFor example, measure lengths of a wires in cm, convert to m before using this to establish a connection between length and resistance;Technology & Designfor example, calculate how many key rings 5 cm long and 4 cm wide can be cut from a 1 metre square sheet of acrylic by converting 1 metre to 100 cm and then dividing 100 by 5 and dividing 100 by 4;
• calculate perimeters of a range of shapes; for example determine missing measurements before calculating perimeters of regular or irregular shapes;
• understand and use scale in the context of simple maps and drawings; for example, identify and carry out the steps needed to draw a plan of a classroom using a simple scale such as 1 cm = 2 m Geographyfor example, identify the steps needed to draw a plan of a classroom using a simple scale such as 1 cm = 2 mSciencefor example, research the diameter of each of the planets in the solar system and using a scale of 1cm = 2000 km construct a scale drawing of each planet
• read and interpret timetables; for example, plan a journey using a timetable with at least two buses/trains/planes with times bridging the hour; Technology & Designfor example, produce and use a plan of manufacture such as a gannt chart for a project.

Handling Data

• collect, organise, record and represent data; for example, decide on appropriate class intervals (e.g. 1-5, 6-10 etc.) to organise discrete data and represent the data graphically; Sciencefor example, collect information on resting heart rate, choose appropriate class intervals to record the data on a grouped frequency table and independently draw a bar chart to display the information.
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example, design a data collection sheet to collect information on number of books carried by year 8 pupils and Year 13 pupils, collect and collate the relevant data and draw a dual bar chart to show the findings;

review their work, considering if their findings are reasonable and making changes where appropriate;

Number and Algebra

• read, write and order whole numbers of any size; for example check answers to calculations by taking account of the range in which the answer should lie. ScienceFor example, place the planets in the Solar System in order of distance from the sun (given as millions of km) and check the order against the Mnemonic - My Very Excellent Mother Just Served Us NachosTechnology & Designfor example, use the colour code to find the size of a resistor greater than 10000 ohms and use a multimetre to check if the answer is accurate
• check calculations by applying inverse operations; for example calculate the total cost of dinners for four weeks and check by dividing the answer by 4; Home Economicsfor example calculate the total cost of dinners for four weeks and check by dividing the answer by 4;
• devise and use rules for generating sequences in words and/or symbolic form; for example,appreciate when enough information has been generated to devise a position to term rule for a sequence; test a position to term rule such as “4 × n - 1” by predicting the next number and confirming using the term to term pattern or by drawing a diagram;
• make informed choices about personal budgeting and spending; for example when planing a week of leisure activities change as necessary to remain within a given budget

Shape, Space and Measures

• reflect 2-D shapes in a line; for example, check the reflection of a shape using a mirror
• estimate, measure, draw and label angles up to 360 degrees; for example, use a protractor to measure an angle and check the outcome against their estimation Sciencefor example, having drawn and measured angles of incidence and angles of reflection check that the values are appropriate to the angle type (acute/obtuse).

Handling Data

• collect, organise, record and represent data; for example, appreciate when the information collected is appropriate and sufficient for the purpose; when deciding on class intervals for discrete data ensure there is an appropriate number of groups by changing the intervals if there are too few or too many Sciencefor example, consider the collected heart rates, looking for unrealistic values, and repeat the measurement if required and check that their total frequency equals the class size
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example, when drawing a line graph check that all the points have been plotted and that each point has been plotted accurately; Geographyfor example, when drawing a line graph to show depth of river along its length, check that all the points have been plotted and that each point has been plotted accurately;

use a range of appropriate mathematical techniques and notation;

Number and Algebra

• carry out calculations with numbers of any size; for example, calulate the temperature rise from -8°C to 3°C Sciencefor example, given a table of melting points/boiling points of a variety of substances, calculate the difference between the melting and boiling points of the substances.
• add, subtract, multiply and divide decimals; for example, calulate 7.34 + 2.9; 12.6 - 5.81; 1.8x2.35; 23.2÷0.32 Sciencefor example,calculate the speed of the object over a specified distance when time has been measured to 2 decimal places
• round to a given number of decimal places; for example, round answers such as 821.643 to two decimal places or 0.07093 to three decimal places Sciencefor example, when calculating pressure, divide force by area and round answer to 2 decimal places.
• understand and use order of precedence in numerical calculations, including the use of brackets; for example, use order of precedence (BIDMAS) when calculating the area of a trapezium using the formula A= 1/2 (a+b)h;
• understand and calculate square roots; for example, find the length of the side of a square which has an area of 32 cm2 by calculating the √32
• understand, use and calculate ratio and proportion; for example, solve the problem, "Red and yellow paint are mixed in the ratio 2:5 to produce orange paint. How much red and yellow paint is needed to make 1.4 litres of orange paint?"
• add and subtract fractions, including mixed numbers; for example, solve problems such as, "Ruth needs 2 3/4 yards of fabric for a sewing project. She already has 5/8 of a yard. How much more does she need tp buy?"
• use equivalences between fractions, decimals and percentages to solve problems; for example, given that 40% of a cereal bar is carbohydrate, pupils use equivalence to calculate how many degrees would represent carbohydrate on a pie chart Home Economicsfor example, ”If 40% of a cereal bar is carbohydrate, calculate how many degrees would represent carbohydrate on a pie chart?” e.g. divide 40 by 100 then multiply by 360Sciencefor example, given that 40% of a cereal bar is carbohydrate, pupils use equivalence to calculate how many degrees would represent carbohydrate on a pie chart
• calculate percentage increase and decrease in relevant contexts; for example, find the percentage increase in the value of an antique by finding the actual increase and expressing this as a percentage of the original value Sciencefor example, given the composition of inhaled and exhaled air, calculate the percentage of oxygen absorbed
• use appropriate formulae; for example, substitute values into the formula C= 5/9 (F-32) to convert between celsius and fahrenheit Home Economicsfor example, calculate Body Mass Index using BMI = (mass/height^2) where mass is in kg and height is in metres and answer is rounded to a given number of decimal placesScienceFor example, use p = F/A to calculate pressureTechnology & Designfor example, use Ohm's law to calculate voltage, current or resistance of a simple battery and bulb circuit
• use conventional notation in algebra; for example, summarise a number sequence in algebraic form such as 2L+2W+4 or (n-2)2 Sciencefor example, know that if they are using the formula V=IR they know to multiply current by resistanceTechnology & Designfor example, use the formula for ohms law depending on the unknown (voltage, current or resistance). V=IxR; R=V/I; I=V/R
• use and interpret graphs from real situations; for example, use a conversion graph to find the price, in £s, of a camera costing 350 Euro;
• apply mathematical concepts to a range of financial situations; for example, find how much money will be in a savings account after 3 years if £2500 is invested at 2.4% APR (Simple Interest); Home Economicsfor example, calculate the cost of a 1 year loan of £2500 with an APR of 12.4 %.

Shape, Space and Measures

• use, convert and calculate measures involving metric, and where appropriate, imperial units; for example, use the conversion 1 mile = 1.6 km when finding how many laps of a 400 m track should be run to complete a 1 mile race; Home Economicsfor example, convert from pounds and ounces to kg and g using tala measure for dry ingredients
• calculate perimeters and area of composite shapes involving squares, rectangles and triangles; for example, partition an irregular 2D shape to calculate the perimeter and/or area.
• calculate surface area and composite volumes of cubes and cuboids; for example, to find the surface area of a drinks container draw the net, calculate the area of each 2D shape and add the areas together; to find the volume of a 3D shape partition into cuboids, calculate the volume of each and add the volumes together
• calculate the circumference and area of circles; for example, calculate the perimeter and surface area of a flowerbed using the appropriate formula Sciencefor example when investigating the effect of the area of a parachute on the time it takes to fall, pupils calculate the area of a circular parachute.
• work out dimensions using scale; for example, use the scale ratio 1:25000 to work out the length in km of a lake measuring 5 cm on a map Geographyfor example, on a map with a scale of 1:50 000, work out the distance between two landmarks;
  for example, on a map with a scale of 1:50 000, locate a point which is 5 km west of a given point;
• understand and use compound measures; for example, use Speed = Distance ÷ Time and Density = Mass ÷ Volume Sciencefor example Pressure = Force ÷ area;
• use coordinates in all four quadrants; for example plot the points (-6,4), (-6,-4), (4, -4), (4,4) to construct a square and identify the points where the diagonals meet as (-1,-1); Geographyfor example, use a 6 figure grid reference to locate the position of a landmark on an OS Map;

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, choose appropriate class intervals to analyse continuous data such as 1 ≤ n < 5, 5 ≤ n < 10, 10 ≤ n < 15, ...
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, construct and interpret pie charts, sem and leaf diagrams, scatter diagram, frequency diagram for continuous data Geographyfor example, draw/interpret a climate graph;
  for example, draw a scatter graph to investigate the relationship between depth of a river and distance from its source and comment on the correlation between these variables;Home Economicsfor example, produce a pie chart to show the composition of a cereal barSciencefor example, independently draw a scatter diagram to investigate the relationship between systolic and diastolic blood pressure and recognise that there is a positive correlation - as systolic increases so too does diastolic.
• work out and use the median and mode; for example find the median length of babies born in maternity ward; given data from a survey, identify the modal shoe size.
• work out the mean, median and mode of a frequency distribution; for example, calculate the mean, median and/or modal number of goals scored by a football team over 38 matches from a frequency table
• use one of the measures of average to compare two sets of data; for example, work out one of the mean, mode or median test results for two classes and state which class has done better on average . Sciencefor example, investigate the effect of heat on new plant growth by calculating and comparing the mean growth of plants kept at different temperatures
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; for example, express the probability of getting a tail when a coin is tossed; independently draw and use a sample space diagram to show all the outcomes of rolling two dice and use this to find the probabilty of scoring a total of 10"

work systematically and efficiently to a given degree of accuracy;

Number and Algebra

• round to a given number of decimal places; for example round 821.643 to 2 decimal places and round 0.07093 to 3 decimal places Geographyfor example, when prompted, round Human Development Indices to one decimal place;Sciencefor example, pupils round calculated speeds to 2dp
• understand and use order of precedence in numerical calculations, including the use of brackets; for example, use order of precedence (BIDMAS) when calculating the area of a trapezium using the formula A= 1/2 (a+b)h;
• understand, use and calculate ratio and proportion; for example, show clearly how to calculate the amount of red and yellow paint needed to make orange paint, if they are mixed in the ratio 2:5; Sciencefor example, given nutritional information for 100ml of energy drinks, calculate the sugar for standard sizes of bottles eg 250ml 330ml 380ml by multiplying appropriately and give answers to 1 d.p.

Shape, Space and Measures

• calculate perimeters and area of composite shapes involving squares, rectangles and triangles; for example, before calculating the perimeter or area of composite shapes partition the shape and calculate any missing dimensions ensuring that all lengths are expressed in the same units Home Economicsfor example, if the retail value of fairtrade coffee in the UK is £49 million and is predicted to increase by 33% each year, calculate its value in 2 years time using repeated proportional change.
• calculate surface area and composite volumes of cubes and cuboids; for example, when calculating the surface area of a cuboid, work efficiently recognising that opposite faces have the same area
• calculate the circumference and area of circles; for example, give answers to a specified number of decimal places when calculating the circumference or area of a circle
• work out dimensions using scale; for example, show clearly how to use a ratio scale of 1 : 25 000 to work out the length in km of a lake measuring 5 cm on a map

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, group continuous data ensuring there are an appropriate number of class intervals
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, choose an appropriate scale, measure angles for pie charts and plot points accurately for scatter diagrams
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; for example, draw a sample space diagram to show all the possible outcomes of rolling a dice and four-sided spinner and use it to calculate the probabilty of the combined events

review their work, using appropriate checking procedures and evaluating their effectiveness at each stage;

Number and Algebra

• understand, use and calculate ratio and proportion; for example, having divided a quantity in a given ratio, check that the two values add up to the total

Handling Data

• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, evaluate the choice of presentation of data
• work out the mean, median and mode of a frequency distribution; for example, having calculated the mean from a frequency table, check that the answer lies within the range of the data

use a range of appropriate mathematical techniques and notation;

Number and Algebra

• calculate the original quantity given the result of a percentage change; for example, find the original price of a shirt which costs £18.70 after a 15% reduction; Sciencefor example, given the oxygen pressure of exhaled air and the % change in this pressure by breathing, calculate the oxygen pressure of inhaled air
• calculate repeated proportional change; for example, calculate compound interest as one step towards solving a complex financial problem; Geographyfor example, estimate the projected population of a town after 3 years given an initial population of 50 000 and expected 4% increase per year by calculating 50 000 ×(1.04)³;Home Economicsfor example, if the retail value of fairtrade coffee iin the UK is £49 million and is predicted to increase by 33% each year, calculate its value in 2 years time using repeated proportional changeSciencefor example, use the fact that the local council intends to increase the amout of recycling by 5% each year for the next few years to estimate the mass of recyclable materials in 3 year time.
• formulate linear equations; for example, use patterns and relationships found through an investigation to write a linear equation to represent a relationship; Sciencefor example, formulate the relationship F=ke from the straight line graph produced from the results of an experiment, obtaining k as the gradient of their graph.
• manipulate simple algebraic expressions, equations and formulae; for example, rearrange y = mx +c to make x the subject or C = 2πr to make r the subject; multiply out brackets such as (n+1)(n - 10); Sciencefor example, rearrange Ohm's Law, V = IR to make the resistance the subject of the formula, R = V/I.Technology & Designfor example, rearrange the formula for ohms law depending on the unknown (voltage, current or resistance). V=IxR; R=V/I; I=V/R
• solve two linear equations simultaneously by a graphical method; for example, to find the break even point for a manufacturing process that can be represented by two linear equations in two unknowns, draw two straight lines on a graph and identify the coordinates at which they intersect;
• make informed decisions involving money; for example use compound interest when making decisions about investing money or buying household goods. Home Economicsfor example use compound interest when making decisions about investing money or buying household goods.

Shape, Space and Measures

• perform length and area calculations on a composite shape including those involving the circle; for example, find the area of a composite shape by partitioning it efficiently, choose and use correct formulae for each part and accurately combine these to find the total area of the composite shape; Sciencefor example, calculate the area of a parachute made from composite shapes such as a rectangle and two semi-circles.
• solve complex problems involving perimeter, surface area and volume; for example calculate the surface area of a composite 3-D shape by partioning it efficiently, choose and use correct formulae for each part and accurately combine these to find the total surface area of the composite shape; Sciencefor example, investigate the hypothesis "a substance with greater the surface area to volume ratio dissolves more quickly"
• understand that measurements have an error margin of half the given unit; for example understand that a measurement of 12 cm could be as little as 11.5 cm or as much as 12.5 cm; find the maximum area of a table top, measuring 40cm by 110 cm to the nearest cm;
• enlarge a 2 - D shape by a given scale factor; for example, enlarge a 2 - D shape by a given scale factor, given the centre of enlargement;
• use three figure bearings to define direction; for example, using a map, find in degrees the three figure bearing of one town from another and plot the position of a third town given the bearing and distance from one of the towns; Geographyfor example, use three figure bearings to describe the direction of one landmark from another on a map;
• understand and apply Pythagoras’ Theorem; for example, apply the formula a2 + b2 = c2 to find the third side of a right-angled triangle when given two sides;

Handling Data

• construct and interpret frequency tables and diagrams for sets of continuous data; for example, draw a cumulative frequency graph to show the lengths of throws in a javelin competition and use this to estimate the median and interquartile values; analyse two sets of data by comparing strengths of correlation in two scatter graphs; Geographyfor example, draw a line of best fit on a scatter graph showing depth of a river against distance from source and comment on the strength of the correlation between these variables; use the line of best fit to estimate an unknown value;Sciencefor example, having collected information on blood pressure, independently draw a scatter diagram with 'Line of Best Fit' to investigate the relationship between systolic and diastolic blood pressure, deciding on axis scales and labels. Use this to predict one of the variables for a given value of the other.
• estimate the mean of a set of grouped data and identify the limits of the median and modal group; for example, calculate an estimate for the mean weight of school bags when the data is presented in a grouped frequency table, using mid-values to represent each class Sciencefor example, calculate the mean birth weight for babies born to smokers or non smokers, where the data is given in a frequency table.
• choose the most appropriate average (mean, median, mode) for a given line of enquiry; for example, choose to calculate and use the median value rather than the mean when a data set has one extreme value. Sciencefor example, when investigating the effect of compost on new plant growth consider the raw data and whether there are any outliers before choosing to calculate the mean or median growth of plants to compare growth with and without compost

critically review to what extent they succeeded in carrying out activities, checking if the level of accuracy and their findings are appropriate and making an assessment of any limitations;

Number and Algebra

• round to an appropriate number of decimal places and significant figures; for example, recognise that as the numbers given in a data set have 2sf, the answer to any calculations should also be given to 2s.f.;

Shape, Space and Measures

• understand that measurements have an error margin of half the given unit; for example understand that a measurement of 12 cm could be as little as 11.5 cm or as much as 12.5 cm; find the maximum area of a table top, measuring 40cm by 110 cm to the nearest cm and describe how this might affect the number of decorative tiles measuring 5 cm by 5 cm needed to cover it;

Handling Data

• construct and interpret frequency tables and diagrams for sets of continuous data; interpret a scattergraph taking into consideration the strength of any correlation, the number of outliers and the limitations of using a line of best fit to estimate unknown values; Sciencefor example, having drawn a scatter diagram with 'Line of Best Fit' to investigate the relationship between systolic and diastolic blood pressure, discuss the reliability of using the line of best fit as an estimate given the strength of the correlation between the two variables and comment on the impact of any outliers on this.
• estimate the mean of a set of grouped data and identify the limits of the median and modal group; for example, when data is presented in a grouped frequency table calculate and use an estimate for the mean, explaining why this is not as accurate as the mean calculated from raw data; Sciencefor example, given a frequency table showing the birth weight of babies born to smokers and non-smokers,explain that the calculated mean is an estimate, so limiting the accuracy of their findings; also consider the effect of sample size and outliers in their evaluation. they discuss the effectiveness of using the median and modal group as their average and compare their results to that of the mean;
• understand and use relative frequency as an estimate of probability and calculate expected frequency; for example understand that if a dice is biased, probabilities of the outcomes can be estimated by experiment and use 'relative frequency = number of times the event happens ÷ total number of trials' to determine these estimates; comment on the relative frequency estimate of probability, explaining that increasing the number of trials improves the the reliability of estimate.
• apply their knowledge of the rules of probability to calculate an outcome or combination of outcomes; for example, multiply the appropriate fractions to find the probability of a bus being late on two consecutive days given that the probability of the bus being late on any day is 0.3

talk about ways to solve simple everyday problems;

Number and Algebra

• use, estimate, add and subtract numbers up to at least 10; for example, pupil suggests adding the number of apples to the number of pears to find how many pieces of fruit are in the bowl, they suggest counting backwards to find how many will be left after some have been eaten.
• create and describe repeating patterns using objects, numbers or pictures; for example describe how to continue patterns such as red bead, blue bead, yellow bead, red bead, blue bead, …; 1, 2, 3, 1, 2, … and red square, blue triangle, red square, …;
• recognise and use coins; for example, suggest the coins to be used when buying items up to 10p.

Shape, Space and Measures

• use everyday language associated with length, ‘weight’, capacity and area to describe, compare and order three objects; for example, suggest using a balance scale to find which object is heavier;suggest how to order the heights of three pupils Home Economicsfor example, suggest using a balance scale to compare the weights of two objects;
• sort 2-D and 3-D shapes and make and describe 2-D and 3-D constructions; for example, talk about which shapes to select to create a model building or a 2-D picture

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example talk about ways to sort a group of objects e. g. by colour, size or texture
• collect information and record using real objects or drawings; for example, suggest placing spoons beside pictures to record menu choices for a party.

use counting strategies when carrying out activities;

Number and Algebra

• use, estimate, add and subtract numbers up to at least 10; for example, count on from 5 when adding 5 and 4; count back from 8 when subtracting 3 from 8 using prompts such as a number line if required.
• understand conservation of number; for example know that a set of objects contains the same number without having to recount, when they have been re-sorted or rearranged;

use mental strategies to carry out calculations when solving problems/carrying out activities;

Number and Algebra

• read, write and order whole numbers up to at least 100; for example count in 10s to find the missing numbers in the sequence 17 27 __ 47 __ 67 .......;
• understand that the place of the digit indicates its value; for example when adding 43 and 12, add 40 and 10 and then 2 and 3 to get the answer of 55.
• use quick recall of number facts up to 10; for example when adding two or more 2 digit numbers add the units and then add the tens.
• add and subtract within 20 mentally and in written form; for example add 5, 1, and 10 mentally by rearranging the numbers; work out the difference between two numbers by adding on to the smaller one; doubling and adjusting to calculate e.g. 6 + 7 = 6 + 6 + 1=13; Sciencefor example, calculate the differences between two temperatures by adding on
• add and subtract within 100; for example counting on in tens and then units when adding two 2-digit numbers (without bridging the 10);
• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example during role play and working within £1, pupils find the correct coins to pay for items; count on to give change;

use mathematics to solve simple two-stage problems;

Number and Algebra

• understand, use, add and subtract whole numbers up to at least 1000; for example, add together the score for 3 darts and subtract the total from 500 to find how many more points are required; Geographyfor example, use information from a table given to find the difference in length of fetch between two beaches;Sciencefor example, given that an average person produces 726kg of waste annually, 125kg of which is paper and 83kg of which is aluminium cans, add 125 and 83 and then subtract the total from 726 to calculate how much waste is 'other materials'.Technology & Designfor example, read the number from the colour code and place the numbers in the correct order with the appropriate number of zeros to find the size of the resistor up to 1000 ohms
• add and subtract mentally two 2-digit numbers within 100; for example,given that in a group of 50 children, 15 like football, 24 like tennis and the rest like swimming, calculate how many like swimming; Sciencefor example, given that the ingredients of an average 'Quarter Pounder' is 76% Beef and 10% Onion, add these together and subtract from 100% to find the percentage of 'other' ingredients.
• know 2, 3, 4, 5 and 10 multiplication facts; for example, calculate how many pencils there are altogether in 3 packs of 5 and 4 packs of 10;
• explore and use division in practical situations; for example find how many sweets are left over when 26 sweets are shared equally among 5 people; Home Economicsfor example, when decorating buns find how many sweets are left over from a bag of 17 when shared equally among 5 buns
• use number skills in the context of money up to £10; for example, calculate change from £10 after buying an item at £1.50 and another at £3.00; Home Economicsfor example, calculate change from £10 after buying an item at £1.50 and another at £3.00.Technology & Designfor example, calculate the cost of materials for the bird feeder project

Shape, Space and Measures

• read and interpret a calendar; for example, use a calendar to select possible dates for a class outing given that the bus is unavailable on Tuesdsays and Thursdays and there are two other school events already on the calendar;
• read digital and analogue clock displays; for example, use a simple bus timetable to find how long a journey will take between two bus stops; Home Economicsfor example, calculate the finishing time when cooking pizza in the oven for 15 mins, beginning on the hour, half hour or quarter past the hour

Handling Data

• read and interpret information from tables, pictograms, diagrams, lists, bar charts, simple pie charts and databases; for example, given a bar chart showing how pupils travel to school, find how many pupils use public transport by reading the heights of the relevant bars and adding them together; Geographyfor example, from a bar chart, find the number of pupils travelling to school by bus and the number travelling by car and subtract to find the difference;Sciencefor example, given a pie chart showing the composition of air, with 78% nitrogen and 1%'other', calcluate the percentage of air that is oxygen by adding these and subtracting from 100%

use a range of mental calculation strategies;

Number and Algebra

• use quick recall of number facts up to 20; for example, group numbers together when adding - 14 + 9 + 6 can be seen as 14 + 6 + 9, which is 20 + 9, which is 29
• add and subtract mentally two 2-digit numbers within 100; for example, using partitioning and without bridging the 10 calculate 66 + 23 using 60 + 20 + 6 + 3 = 89; round and adjust to make a calculation easier, for example when adding 19 + 7, work out 20 + 7, then adjust by taking away 1; Geographyfor example, from a bar chart showing the number of hours of sunshine for a week, use a mental strategy to calculate the difference for two different days;Sciencefor example add together the 22% of household waste that is paper to the 17% that is card by 22 + 17 = 20 + 10 + 2 + 7 = 30 + 9 = 39%Technology & Designfor example, add together lengths to mark out using running dimensions
• approximate to the nearest 10 or 100; for example, when estimating the answer to the calculation 58 + 203, add 60 and 200 to give an estimate of 260;
• know 2, 3, 4, 5 and 10 multiplication facts; for example,find how many pencils there are in 3 packs of 5;
• explore and use division in practical situations; use the 4 times tables facts to work out how many taxis are required for 18 people if each taxi can take 4 people.
• use number skills in the context of money up to £10; for example calculate change from £10 after buying an item at £6.40 by counting onin pence and then pounds; Home Economicsfor example calculate change from £10 after buying an item at £6.40 by counting on pence and then pounds.

use a range of problem-solving strategies;

Number and Algebra

• use knowledge of place value to multiply and divide whole numbers by 10 and 100; for example divide by 10 to find the discount when an item has been reduced by 10% Technology & Designfor example, find the 10% tolerance of a resistor by dividing the resistance by 10
• add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; for example use addition and division to find how many 2x3 egg boxes are needed when Amy and Tom have collected 246 and 372 eggs Technology & Designfor example, divide a length by 2 to find the midpoint
• understand and use multiples and factors; for example, use the factors of 30 to work out how many different equal teams can be made from a class of 30 pupils.
• understand and use simple percentages; for example knowing that 25% = 1/4, find 25% of £80 by dividing by 4. Technology & Designfor example, find the 10% tolerance of a resistor by dividing the resistance by 10
• make choices about spending and value for money; for example if 5 pencils are needed decide if it is better value to buy a packet of 6 at £1.20 or 5 single pencils at 23 p each by multiplying 23 by 5 and given a reason for the decision Home EconomicsFor example, calculate the total cost of pizza ingredients to investigate whether is it cheaper to make a pizza or buy a pre-made oneTechnology & Designfor example, consider all relevant factors when choosing materials for the bird feeder project to ensure that the cost is kept below £5

Shape, Space and Measures

• estimate area and volume of shapes by counting squares/cubes; for example estimate area by counting more than half a square as a whole square and count rows and columns of cubes that fill/almost fill a container to estimate its volume; Sciencefor example, use a centimetre square overlay to estimate the area of a leaf either by counting more than half a square as a whole square
• work out perimeters of simple shapes; for example find the length of wood required to surround a raised flowerbed by adding the lengths of the sides Geographyfor example, use a trundle wheel to find the perimeter of the assembly hall;
• explore the properties of common 2-D and 3-D shapes; for example identify equal angles and sides in shapes by folding or using tracing paper
• explore the relationship between 2-D and 3-D shapes; for example open 3-D shapes to find which 2-D shapes they consist of. Technology & Designfor example, decide what 2D shapes are used when designing a 3D model/net
• recognise and draw lines of symmetry in a variety of 2-D shapes; for example fold a shape or use a mirror to identify lines of symmetry. Sciencefor example, use a mirror to identify lines of symmetry in flowers

Handling Data

• collect, group, record and present data with given class intervals; for example discuss how to collect and present the information on the ages of patients waiting in A&E given suitable discrete class intervals
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example discuss and decide how best to present information Geographyfor example, when investigating tourism in Northern Ireland, start by making a list of attractions;Home Economicsfor example, decide on the best method of presentation for the sugar content in energy drinks;

use a range of efficient mental calculation strategies;

Number and Algebra

• use knowledge of place value to multiply and divide whole numbers by 10 and 100; for example, divide by 10 when finding 10% of £190
• approximate within 10 000 to the nearest 10, 100 and 1000; for example estimate the total number of fans at a hockey match with 428 from one school and 291 from the other school by rounding to the nearest 100 and then adding 400 and 300
• estimate answers to calculations and approximate by rounding; for example estimate the cost of 28 shirts at £10.75 each using 30 x £10 and checking the answer is sensible;
• add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; for example when adding 36 and 45 mentally add 35 to 45 and then add another 1; to divide 156 by 12, divide 156 by 3 and then divide by 4 Sciencefor example , add together the 28% of household waste that is paper to the 17% that is card by 28 + 17 = 20 + 10 + 8 + 7 = 30 + 15 = 45%
• understand and use multiples and factors; for example to multiply 32 by 20, use the factors of 20, (2x10) and multiply 32 by 2 and then multiply by 10;
• understand and use simple percentages; for example find 5% of a quantity by finding 10% and dividing by 2; Technology & Designfor example, find the 10% tolerance of a resistor by mentally dividing the resistance by 10

Shape, Space and Measures

• understand and use digital and analogue clock displays, using am and pm and 24 hour notation; for example, count on from the start time in hours and then in minutes the time a movie will finish Geographyfor example, from a simple timetable, count on, first in hours and then in minutes, to find the time taken for a journey between two places;Home Economicsfor example, count on from the start time in hours and then in minutes to find the finishing time for a meal in the oven

use a range of problem-solving strategies, suggesting and trying out different approaches when difficulties arise;

Number and Algebra

• use knowledge of place value to multiply and divide whole numbers by 10, 100 and 1000; for example, mentally calculate 435 ÷100 to change cm to m before calculating an area.
• understand and use negative numbers in practical contexts; for example, draw and use a number line to determine how much the temperature has risen from -6° C to 5° C. Geographyfor example, draw and use a number line to help calculate how much the temperature has increased from -2°C to 8°CTechnology & Designfor example, use negative numbers on a milling machine to position holes to be drilled, use negative numbers in CAD for removal of material from an extrusion.
• understand the relationship between common fractions, decimals and percentages; for example, find 40% of a quantity by multiplying by 2/5 or 0.4;
• calculate fractions and percentages of quantities, including money; for example, a coat costs £87 and is reduced by 40% in a sale, how much is saved? Knowing that 40% = 2/5, divide 85 by 5 and multiply by 2. Technology & Designfor example, calculate 5% of the resistance when tolerance band is gold
• use understanding of equivalence to add and subtract fractions; for example use knowledge of equivalent fractions to add ¼ + 3/8 i.e. 2/8 + 3/8 = 5/8. Technology & Designfor example, add gear ratios for compound gear train
• make informed choices about personal budgeting and spending; for example, plan furnishing a bedroom within a given budget, choosing and calculating for different options if over or under spent; Home Economicsfor example, look at income and expenditure for a household and consider ways to reduce expenditure by prioritising and considering needs and wants;Technology & Designfor example, evaluate the budget and make changes to improve manufacturing, balancing cost and performance

Shape, Space and Measures

• use the four operations to solve problems related to measure; for example, to find how many 2 litre bottles of water are required to serve 14 people if each person drinks 220 ml, calculate the total volume of water required and divide this by 2 L and round the answer up to the next whole number of bottles. Home Economicsfor example, to find how many 2 litre bottles of water are required to serve 14 people if each person drinks 220 ml, calculate the total volume of water required and divide this by 2 l and round the answer up to the next whole number of bottles;ScienceFor example, try to make a see-saw balance by calculating force x distance and varying the mass and/or the distance from pivot to balance the see-saw.Technology & Designfor example, calculate how many key rings 5 cm long and 4 cm wide can be cut from a 1 metre square sheet of acrylic by how many can fit into the length and how many fit into the width by converting 1 metre to 100 cm and then dividing 100 by 5 and dividing 100 by 4;
• read and interpret timetables; for example, when planning a day out, choose options for transport within time constraints and review if necessary. Geographyfor example, when planning a day out, use a timetable to choose options for transport within time constraints; review and change options if necessary;

Handling Data

• collect, organise, record and represent data; for example recognise when raw discrete data should be grouped and determine appropriate class intervals to organise it; refine the number of classes if there are too many or too few groups
• design and use a data collection sheet; for example, ask appropriate questions to obtain and record information, review if more information is required and add more options if responses are not as expected. Geographyfor example, design and use a data collection sheet to record the width of pebbles at different points along a river bed;Home Economicsfor example, design a data collection sheet for a consumer survey deciding what information is relevent such as opening hours, facilities, price, etc

adapt their approach as needed;

Number and Algebra

• calculate percentage increase and decrease in relevant contexts; for example, having calculated the reduction of two items, recognise that percentage decrease should be used for comparison;

Shape, Space and Measures

• calculate perimeters and area of composite shapes involving squares, rectangles and triangles; for example, realise that the perimeter of an L-shape is the same as that of a rectangle or that when finding the area it can be split in more than one wa;.
• calculate surface area and composite volumes of cubes and cuboids; for example, when finding the volume of an L-shaped prism realise that it can be split in more than one way;
• work out dimensions using scale; for example, recognise that a scale of 1:25000 is the same as 1 cm = 2.5 km and multiply map lengths by 2.5 to find the actual distances in km;

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, having grouped continuous data review the number of class intervals and change class widths if there are too few or too many groups; Geographyfor example, understand that to find the most popular tourist attraction in Northern Ireland, a survey of one age group would not be representative and that data should be collected from people of all ages;

consider alternative approaches and adapt them as required;

Number and Algebra

• calculate repeated proportional change; for example, when solving a financial problem involving compound interest, consider whether it is necessary to calculate 'year on year' values or whether it would be appropriate to use the formula
• solve two linear equations simultaneously by a graphical method; for example, to find the break even point for a manufacturing process that can be represented by two linear equations in two unknowns, draw two straight lines on a graph and identify the coordinates at which they intersect instead of using trial and improvement;

Shape, Space and Measures

• perform length and area calculations on a composite shape including those involving the circle; for example, consider more efficient ways to calculate the area of a composite shapes such as combining two semi-circles to give a full circle;
• solve complex problems involving perimeter, surface area and volume; for example, consider how to calculate the volume of a composite 3-D shape either by splitting it into two or more common 3-D shapes or by finding the constant cross-sectional area and multiplying this by the length;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example, having investigated an hypothesis, evaluate the results and suggest if additional data could be collected to further the investigation; Sciencefor example use the handling data cycle to investigate the impact of smoking on unborn babies - state an hypothesis, collect the relevant data, calculate the mean weight of babies born to smokers and non-smokers, commenting on the median and modal group; draw appropriate conclusions and comment on any limitatons;

look for and talk about patterns;

Number and Algebra

• create and describe repeating patterns using objects, numbers or pictures; for example, pupils look for and talk about patterns in the environment i.e. bricks, floor tiles, fabrics. They talk about how to continue patterns using beads, cubes etc. Technology & Designfor example, discuss the pattern of numbers on a clock when some are replaced by dashes.

Shape, Space and Measures

• sequence familiar events; for example, discuss their daily routines and how to sequence the activities within them Home Economicsfor example, discuss the order of the steps needed to wash clothes.
• know the days of the week and their sequence; for example, pupils discuss which day of the week is 'the day after tomorrow' or 'three day's time' etc

recognise patterns and relationships and make predictions;

Number and Algebra

• read, write and order whole numbers up to at least 100; explore number sequences, including odd/even and identify missing numbers in a sequence such as 8, 18, __, 38, 48 .....; colour all the numbers ending in 7 on a hundred number square;
• understand that the place of the digit indicates its value; for example recognise the patterns when all the numbers with 3 units or 8 tens have been coloured on the 100 square;
• use addition and subtraction patterns within 20 to explore the relationship between addition and subtraction; for example understand that since 6 + 5 = 11, then 5 + 6 = 11 and 11 – 6 = 5;
• add and subtract within 100; make predictions, such as 10 more than 27, and check using the 100 square. Identify and explore patterns in the 100 square, for example knowingthat 3 + 5 = 8 and 13 + 5 = 18, predict that 23 + 5 = 28 and 33 + 5 = 38 etc. and recogise this pattern 100 number square;
• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example, show the different coins that can be used to make 63 p, e.g. 20 p + 20 p + 20 p + 2 p + 1 p , 50 p + 10 p + 1 p + 1 p + 1 p, etc.

Shape, Space and Measures

• understand the need for standard units and know the most commonly used units in length, ‘weight’, capacity and time; carry out measuring activities using non-standard units e.g. pencils for length, cubes, marbles for weight, cups for capacity etc.; predict if it will take the same number of two different length pencils to measure the length of a line and therefore realise the need for a standard unit of measurement.
• name and order days of the week, months of the year and seasons; for example know the month that comes after March and the day of the week between Tuesday and Thursday; Geographyfor example, know the months and weather conditions associated with each of the four seasons;
• use language and follow instructions, in practical situations, for turning movements; for example, half turn and quarter turn, and left and right to predict and test which set of instructions are needed to make Roamer move through a maze.

identify and explain patterns and relationships and make predictions;

Number and Algebra

• understand and use the concept of place value in whole numbers; for example calculate 160 + 170 by using pencil and paper methods using the understanding of 16 + 17 = 33 so 160 + 170 = 330;
• use quick recall of number facts up to 20; for example, recall the pairs of numbers that add to 18;
• identify and describe simple number patterns within the 100 square; for example, identify the pattern made by the answers to the 2,3,4,5 and 10 times tables;
• know 2, 3, 4, 5 and 10 multiplication facts; for example, recognise the relationship between repeated addition and multiplication such as 3 x 4 is the same as 4 + 4 + 4
• understand that multiplication is commutative; for example, understand that 3 rows of 4 items and 4 rows of 3 items both give 12 items;
• explore and use division in practical situations; for example, show all the rectangular arrangements for 24 counters; understand that if taxis are needed for 9 people and each taxi can take up to 4 people then 3 taxis would be required
• use number skills in the context of money up to £10; for example, show the notes and coins that can be used to pay for an item costing £8.59,

Shape, Space and Measures

• read and interpret a calendar; for example, identify all the Thursdays in January to find the dates for a cookery class
• read digital and analogue clock displays; for example, count in 5s to tell the time on an analogue clock
• recognise one line of symmetry in common 2-D shapes; for example experiment by folding paper 2D shapes to identify which have a line of symmetry and which do not;
• recognise tessellations through practical activities; for example, arrange isosceles triangles in a tessellating pattern;

Handling Data

• read and interpret information from tables, pictograms, diagrams, lists, bar charts, simple pie charts and databases; for example predict that most cars passing the school will be silver because most parents’ cars are silver and test this prediction by carrying out a survey;

investigate patterns and relationships, using their findings to make predictions;

Number and Algebra

• know multiplication facts up to 10 × 10 and derive associated division facts; for example derive the relevent division fact from the 6 times tables to find how many teams of 6 can be made from 42 people
• understand and use multiples and factors; for example, use pairs of factors to work out how many different equal teams can be made from a class of 30 pupils;
• understand equivalence of fractions; for example demonstrate understanding of equivalent fractions by drawing pictures/diagrams to show that ⅓ = 2/6 = 4/12
• interpret and apply simple rules expressed in words; for example extend a pattern by drawing diagrams and completing a table then recognise the term to term rule, use this to predict the next number in the pattern and confirm by drawing the appropriate diagram; ScienceFor example, make a see-saw balance using 100g and 200g masses; given the formula Moment = Force x distance , use this to predict where to place the masses.

Shape, Space and Measures

• explore the properties of common 2-D and 3-D shapes; for example pupils practically investigate the angles in triangles and discover that the three angles in any triangle add up to 180 i.e they fit on a straight line;
• explore the relationship between 2-D and 3-D shapes; for example open 3-D shapes to find which 2-D shapes they consist of, and recognise nets of common 3-D shapes;
• recognise and draw lines of symmetry in a variety of 2-D shapes; for example investigate the relationship between the number of lines of symmetry and the number of sides in regular shapes

investigate general statements to see if they are true;

Number and Algebra

• add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; for example investigate whether any even number can be written as the sum of two odd numbers;
• understand and use multiples and factors; for example investigate the statement that every number has at least two factors;
• understand equivalence of fractions; for example, by drawing diagrams investigate what fractions are equivalent to 1/3
• interpret and apply simple rules expressed in words; for example investigate the statement 'Area of a rectangle = length times width' by drawing rectangles on cm squared paper

Shape, Space and Measures

• explore the properties of common 2-D and 3-D shapes; for example investigate whether the sum of the angles in a quadrilateral is always 360°, investigate if a square is a rectangle and if a cube is a cuboid;
• explore the relationship between 2-D and 3-D shapes; for example, investigate if every cuboid has 2 square faces;
• recognise and draw lines of symmetry in a variety of 2-D shapes; for example, investigate if all sports logos have lines of symmetry;

Handling Data

• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, investigate if strawberry ice cream is the most popular flavour
• understand and use the language of probability; for example, investigate to see if it is more likely to rain in May or Sept

make and test predictions;

Number and Algebra

• devise and use rules for generating sequences in words and/or symbolic form; for example, having generated a formula for a sequence, predict the next term and check by drawing a diagram or other method.

Shape, Space and Measures

• describe the properties of regular and irregular 2D shapes in terms of sides, angles, symmetry and tessellations; for example, predict and test if the diagonals of quadrilaterals always intersect at right angles; predict and test if all triangles tessellate

Handling Data

• collect, organise record and represent data; for example, predict whether it is cheaper to holiday at in the north coast of Ireland or in Spain and test by collecting relevent data Sciencefor example, record the masses and equivalant stretch of a spring when investigating Hooke's Law. Predict that the bigger the mass the greater the extension and confirm by recording more results.

make general statements based on findings and test using new examples;

Number and Algebra

• understand and use square, cube and prime numbers; for example, investigate how many factors each number from 1 to 25 has and make a statement such as ‘Square numbers always have an odd number of factors’ then test other square numbers over 25
• devise and use rules for generating sequences in words and/or symbolic form; for example, generate a formula for a number pattern in words or symbolic form and test using a further example

Shape, Space and Measures

• use the four operations to solve problems related to measures: For example, given a fixed perimeter for a rectangle, vary the lengths of sides and determine that a square gives the maximum area confirming by further trials ScienceFor example, determine whether a see-saw will balance by varying the distance of the mass from the pivot and use the results to state that mass x distance on both sides is equal; they confirm by further trials
• describe the properties of regular and irregular 2D shapes in terms of sides, angles, symmetry and tessellations; for example, investigate the relationship between the radius and circumference of a circle and make a general statement such as 'the circumference is about 3 times the radius'

summarise their findings;

Number and Algebra

• devise and use rules for generating sequences in words and/or symbolic form; for example, generate a formula in words or symbolic form to summarise a number sequence.

Shape, Space and Measures

• describe the properties of regular and irregular 2D shapes in terms of sides, angles, symmetry and tessellations; for example, having investigated the tessellating properties of triangles summarise the findings in relation to angle properties

Handling Data

• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example, construct a table to summarise data from a questionnaire or to record findings form a number pattern investigation. GeographyFor example construct a table to summarise data from a questionnaire on holiday destinations.Home Economicsfor example, construct a table to summarise information from a consumer surveySciencefor example, use a table of results from a Hooke's Law experiment to state that the bigger the force, the longer the extension.

make and test predictions, make general statements and draw conclusions;

Number and Algebra

• understand and calculate square roots; for example, use trial and improvement to find the length of the side of a square which has an area of 32 cm2, then check their answer using a calculator
• use conventional notation in algebra; for example, derive an algebraic expression from a pattern and then test the expression using known values; having found the position to term formula for expanding squares, derive and test the formula for rectangular arrangements

Handling Data

• work out and use the median and mode; for example, test a hypothesis such as "more than half of year 10 pupils carry a schoolbag weighing more than 7 kg"
• use one of the measures of average to compare two sets of data; for example, work out one of the mean, mode or median test results for two classes and make a general statement on which class has done better on average Sciencefor example, conduct an experiment to investigate the effect of heat on new plant growth, then calculate the mean growth of plants at room temperature and with extra heat; compare the means and draw relevant conclusions;
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; for example, predict the most common score when two dice are rolled, test the prediction by carrying out an experiment and make a general statement based on the findings

make and test predictions and justify their generalisations;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example, form an hypothesis and test its validity by collecting, processing and interpreting relevant data;
• understand and use relative frequency as an estimate of probability and calculate expected frequency; for example, given that the relative frequency of getting a head on a coin is 0.7 after 50 trials, suggest that the coin may be biased and test this prediction by tossing the coin 100 more times;

talk about and collect information required;

Handling Data

• collect information and record using real objects or drawings; for example, talk about how to collect information about the class e.g. favourite food; suggest using coloured blocks or pictures to represent frequencies; and use cubes to record the number of people with blue / brown eyes;

represent their work using pictures and objects;

Shape, Space and Measures

• sequence familiar events; for example place pictures or drawings in the correct order to show the steps needed to make a cup of tea; Home Economicsfor example, draw pictures to show the steps needed to make breakfastTechnology & Designfor example, place the picture cards in order to show the stages of the vacuum forming process

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example pupils place pictures of classmates on a Venn diagram to show which sports they like; Geographyfor example, sort pictures of different environments (deserts, grasslands etc) into their ecosystems; for example, complete visual representation of food chains by inserting the correct pictures;Home Economicsfor example, sort a collection of ingredients into dry or not dry (wet) and re-sort by measured using scales/not scales (jugs)

discuss the information required and how it can be collected;

Handling Data

• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; for example suggest using a simple table to record the number of pupils preferring different activities; Geographyfor example, suggest using a simple table to record the number of pupils travelling to school by bus, car, taxi and on foot; for example, suggest using a block graph to show the number of pupils travelling to school by bus, car, taxi and on foot;Sciencefor example, talk about how to collate the number of each species in a pond sample and how to record the data on a given template.Technology & Designfor example, read and complete a simple table showing materials, an image and their definition

present the information appropriately and talk about their findings;

Number and Algebra

• understand halves and quarters; for example use a diagram to represent half or quarter of a pizza;

Shape, Space and Measures

• sort 2D and 3D shapes, giving reasons for sorting; for example sort 2-D and 3-D shapes using a tree diagram; Technology & Designfor example, sort signs according to shape and discuss how shapes of signs represent different things, that is circles for orders, triangles for warnings and rectangles for information

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example sort pictures of birds with long beaks/not long beaks and webbed feet/not webbed feet; sort numbers into odd/not odd and greater than 10/not greater than 10; Sciencefor example, use a tree diagram to sort pond animals according to whether they have a shell or no shell and have rounded or not rounded bodies.Technology & Designfor example, sort tools onto a Venn diagram showing the materials they can be used on, such as sandpaper on wood, wet and dry paper on plastic and screws on both
• collect information and record results using simple tables, block graphs, simple pictograms and diagrams; for example, complete horizontal or vertical block graphs, and use Venn, Carroll and Tree diagrams; Geographyfor example, use a Carroll diagram to classify colour and smoothness of pebbles;
  for example, record, on a tally chart, the number of pupils travelling to school by bus, car, taxi and on foot;Home Economicsfor example, collect and display information such as pupils' favourite fruit, record on a given simple table and display the data in a block graphSciencefor example, complete a block graph showing the number of each minibeast found in the school grounds.Technology & Designfor example, complete a simple table showing materials, an image and their definition
• discuss and interpret information; for example discuss information from a simple table, block graph, pictogram or database and answer simple questions about the data. Geographyfor example, identify, from a block graph, the most common method of travel to school ;Sciencefor example, comment on the most/least common eye colour on a block graph showing eye colous of pupils.Technology & Designfor example, read and discuss information from a simple table showing materials, an image and their definition

identify, collect and record the information required;

Handling Data

• collect and record relevant data for a given activity; for example, complete a given data collection sheet, tally chart or frequency table; find information from lists, simple tables and databases; Geographyfor example, use a given observation sheet to record the number of different types of vehicles that pass the school gates during a given period of time;Home Economicsfor example, use a given data collection sheet such as a tally chart or frequency table to collect data on types of breakfast.Sciencefor example, record on a table with given headings, the rise in temperature of the water in a boiling flask when different foods are burnt;

present their findings clearly using a range of appropriate mathematical formats;

Number and Algebra

• identify and describe simple number patterns within the 100 square; for example, shade all the multiples of 4, using the pattern generated to go beyond 4 x 12;
• use number skills in the context of money up to £10; for example record shopping bills in pounds and pence using a £ sign or with a 'p' if under £1; Home Economicsfor example record shopping bills in pounds and pence using a £ sign or with a 'p' if under £1;

Shape, Space and Measures

• choose and use appropriate standard units to estimate, measure and record length, capacity, volume, 'weight', time and temperature; for example use 'mm' to record the length of a piece of wood, 'ml' for the amount of liquid in a jug and 'g' for the 'weight' of a cooking ingredient; Sciencefor example, record information about temperature rise in °C when conducting an experiment to see how much energy is contained in samples of food;

Handling Data

• draw and label pictograms and bar charts; for example, complete and label pictograms where the symbol represents more than one object and complete bar charts (with axes and categories given); Geographyfor example, complete a bar chart showing the number of different types of vehicles passing the school gates, by scaling the vertical axis and drawing the bars to the correct heights;Home Economicsfor example, complete a bar chart (with axes and categories given) for favourite fruits of class members or complete a pictogram to illustrate the types of breakfast eatenSciencefor example, complete a bar chart to show temperature rise when different foods are burnt;

explain their findings;

Handling Data

• read and interpret information from tables, pictograms, diagrams, lists, bar charts, simple pie charts and databases; for example, answer questions such as 'What is the most/least popular food?' from a simple pie chart or interpret a pictogram/bar chart or pie chart by completing a writing frame; Geographyfor example, explain how to identify the month with the highest average temperature from a bar chart;
  for example, explain how to identify he most frequent method travelling to school from a pie chart;Home Economicsfor example, identify the cereal with the least sugar from a pie chartSciencefor example, use a database about pondlife to answer simple questions about the types and main characteristics of the animals found

find, organise and interpret relevant information;

Handling Data

• collect, group, record and present data with given class intervals; for example, record discrete data on a given collection sheet, record data on a grouped frequency table, given appropriate class intervals; present this information on a grouped bar chart Geographyfor example, using a given data collection sheet, record temperature, rainfall, wind speed and wind direction over a given period;Sciencefor example, collect information on resting heart rate for a number of pupils and record the data on a data collection sheet with class intervals given.
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example draw independently frequency diagrams for discrete data, drawing and labeling both axes; draw and interpret bar charts with given class intervals; Geographyfor example, identify the countries with the highest and lowest GDP from a table showing development indicators for different countries; for example, use a wind rose diagram to record wind direction frequency; use a completed wind rose diagram to discuss wind direction frequency for a particular location;Home Economicsfor example, collect information on pocket money and organise on a grouped frequency table with given class intervalsSciencefor example, from a grouped frequency table showing resting heart rates, construct a grouped bar chart and identify the most common heart rate group; use a decision tree diagram to classify living things into categories such as 'mammals', 'birds,' 'reptiles' etc.
• understand and use the language of probability; for example, given data on weather at a particular location, use language such as 'might', 'likely', 'could happen',' impossible', 'unlikely' etc to describe the chance of rain on a particular date; Sciencefor example, interpret data on pondlife in June and in October, making conclusions such as "you might see (a particular organism) in October but you are more likely to see it in June";

present information clearly;

Handling Data

• collect, group, record and present data with given class intervals; for example use the given class intervals 1 – 5, 6 – 10, 11 – 15, etc, to record ages of patients waiting in A&E; Geographyfor example, use the given class intervals 1 – 5, 6 – 10, 11 – 15, etc, to organize collected information about the width of various stones, rounded to the nearest cm;Sciencefor example, organise data on resting heart rates on a grouped frquency table, given discrete class intervals and use a grouped frequency diagram to present the information.
• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example draw independently frequency diagrams for discrete data (grouped or ungrouped), drawing and labelling both axes; draw and interpret bar charts with given class intervals; Geographyfor example, draw a bar chart to show the population to the nearest million of various countries;Home Economicsfor example, given a grouped frequency table on pocket money display the information on a bar chartSciencefor example, given a grouped frequency table, independently draw and label a grouped bar chart to show data on heart rates.
• understand and use the language of probability; for example use language such as impossible, unlikely, even chance ,likely and certain to describe events and fair and unfair to describe games of chance. (HD(4)c Geographyfor example, by observing current weather conditions, discuss how likely it is to rain in the next hour, using the language of probability;

compare methods of presentation;

Handling Data

• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example discuss which presentation shows information more clearly, a table or a bar chart/ a pie chart or a bar chart; Geographyfor example, discuss whether a table or a bar chart is better to display information about the number of rainy days each month;Home Economicsfor example, discuss whether a table, a bar chart or a pie chart shows information about nutritional content of a cereal bar most clearly

identify, obtain, process and interpret information appropriate and sufficient for the activity;

Handling Data

• collect, organise, record and represent data; for example, decide on appropriate class intervals (e.g. 1-5, 6-10 etc.) to organise discrete data ensuring there is an appropriate number of groups; represent the data graphically; construct a grouped frequency table and frequency diagram for continuous data where class intervals (e.g. 0 Geographyfor example, record population densities in class intervals; interpret a choropleth map showing population densities; literacy rates, energy use and income;
  for example, when investigating river depth at different points, consider the river width at each point when deciding how many depth readings to take;ScienceFor example, interpret information about the rate of decay of leaves buried in two different types of bags (small and large mesh) in different months of the year, draw a dual bar chart deciding on their own axes labels and scales. Use it to compare and comment on the rate of decay of the leaves in the two diffrerent types of bag.Technology & Designfor example, create an online survey such as survey monkey, to find information to influence the design of a product.
• design and use a data collection sheet; for example design a data collection sheet suitable for collecting weather information Geographyfor example, design a data collection sheet suitable for carrying out an environmental quality survey;Home Economicsfor example, design a data collection sheet for a consumer survey deciding what information is relevent such as opening hours, facilities, price, etcSciencefor example, design a simple data collection sheet to record information on resting heart rate of boys and girls;Technology & Designfor example, use microsoft forms or survey monkey or fronter to design a database to record the results of a survey
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example understand when it is appropriate to use a line graph and understand that intermediate values may or may not have a meaning; plot points for experimental data; draw and interpret a dual bar chart; complete and interpret pie charts with divisions marked; Geographyfor example, draw/interpret a half population pyramid to show the ages of the inhabitants of a town; for example draw a line graph to show the monthly average temperature in Ireland; for example identify countries with high/medium/low development from a dispersion graph showing Human Index Development Indices for a number of countries;Home Economicsfor example, construct a dual bar chart to compare the nutritional contents in two similar productsSciencefor example, know that a line graphis the most appropriate way to show how water temperature changes with time; know that intermediate values on this graph have a meaning and use the graph to determine intermediate points not plotted.
• understand, calculate and use mean and range; for example find the mean and range of the heights of 20 girls and make a simple statement about the results; Geographyfor example, calculate the mean and the range of the temperature for a given month;Sciencefor example find the mean and range of resting heart rates for a group of pupils and make a simple statement about the results;Technology & Designfor example, calculate the mean of anthropometric data to assist the design of a product

present information accurately and appropriately including the use of mathematical language, symbols and diagrams;

Handling Data

• collect, organise, record and represent data; for example decide on appropriate class intervals (e.g. 1-10, 11-20 etc.) to organise discrete data on a grouped frequency table and represent the data graphically; Geographyfor example, decide on appropriate class intervals to group literacy rates in a large number of countries;Sciencefor example, organise data for resting heart rates on a grouped frquency table, independently selecting discrete class intervals; use this to draw a grouped frequency diagram, scaling and labelling axes correctly.
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example understand when it is appropriate to use a line graph, choose and use appropriate scales, labels and titles when representing data; plot points for experimental data; draw and interpret a dual bar chart; complete and interpret pie charts with divisions marked; Geographyfor example, choose and use an appropriate scale when drawing a line graph showing the depth of the river at regular intervals along its course;
  for example, draw a dual bar chart to compare the average monthly temperature of Belfast and Marbella, selecting an appropriate scale, labelling the axes and including a key;Home Economicsfor example, draw a dual bar chart to compare nutritional content in two similar products, choose appropriate scales on the axes, plot data accurately and label axes appropriatelySciencefor example, use data on pondlife in June and in October to draw a labelled dual bar chart and comment appropriately on the different species of pondlife to be found at these two times of the year;

obtain, process and interpret information from a range of sources;

Number and Algebra

• use and interpret graphs from real situations; for example, interpret a distance-time graph describing different stages of the journey including any stoppages; Sciencefor example, interpret a graph displaying temperature of ice/water, identify melting and boiling points recognising that the temperature remains constant at these points

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, choose and use class intervals to record continuous grouped data on a frequency table; combine information from a variety of sources such as internet, travel brouchers or questionnaires when booking a holiday;
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, construct/interpret a scatter graph showing ice-cream sales and temperature, identify correlation as ‘positive’, ‘negative’ or ‘no correlation” and then explain the relationship between the two variables; construct a frequency diagram to show waiting times for patients, deciding on, and using continuous class intervals; identify the modal class from a grouped frequency table; construct and interpret a line graph for real life situations such as find the average speed of a car from a distance/time graph; construct a pie chart to illustrate ages of people by working out the size of the angle for each sector; draw a stem and leaf diagram to record greenhouse temperatures over 2 weeks and comment on the shape of the distribution; draw a line of best fit on a graph of experimental data for extension and load on a spring, use it to predict the extension for a load that has not been recorded. Geographyfor example, independently draw a pie chart to show the percentage of people engaged in different employment sectors; for example, interpret a population pyramid to show the age of males and females in a town; for example, interpret a climate graph for a given location;Sciencefor example, using a graph of experimental data for extension and load on an elastic band, draw a ‘line of best fit’ and use it to predict the extension for a load that has not been recorded; or independently draw a scatter diagram of systolic blood pressure against diastolic blood pressure, deciding on appropriate axis scales and labels; interpret results recognising that there is positive correlation - as systolic increases so too does diastolic.
• work out and use the median and mode; for example, conduct a survey about shoe size and use this to identify the modal size. Geographyfor example, identify the modal form of transport from given data;
• work out the mean, median and mode of a frequency distribution; for example, from a frequency table showing number of goals scored by a football team in a season, calculate the mean, median and/or modal number of goals scored
• use one of the measures of average to compare two sets of data; for example, work out one of the mean, mode or median test results for two classes and state which class has done better on average . Geographyfor example, calculate the mean or median rainfall for two countries and comment on the results;Sciencefor example, compare the mean weights of babies born to smokers and non-smokers to comment on the effect of smoking during pregnancy.
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; for example, express the probability in fractions, decimals or percentages of a girl being picked to captain a quiz team from 3 boys and 2 girls; draw and use a sample space diagram to show find the probabilty of scoring more than 8 when rolling two dice

use a range of suitable ways to present findings, following accepted conventions;

Number and Algebra

• use conventional notation in algebra; for example, express a number pattern in algebraic form

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, present continuous data in a grouped frequency table where appropriate Home Economicsfor example, collect data about their height and weight and then record it in a grouped frequency table, deciding on their own continuous class intervals
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, when presenting data graphically choose suitable graph paper and scales, include labels/title/keys where appropriate Geographyfor example draw and label a pie chart illustrating the results of a survey on holiday destinations or employment structure; for example, draw and label a climate graph for a given location; for example, draw and label a scatter graph showing roundness of pebbles against distance along the river bed or of GDP against literacy or other development indicatorHome Economicsfor example, draw a pie chart of nutritional content of cereal using the information on the packetSciencefor example, use experimental data for the temperature of ice melting/ water heating to draw a graph, choosing appropriate scales on both axes. for example, use data on blood pressure to independently draw a scatter diagram to investigate the relationship between systolic and diastolic pressure, choosing appropriate scales on both axes.
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; For example, construct a sample space diagram to show all the outcomes of rolling two dice; express probabilites as fractions, decimals or percentages

consider, identify, obtain and analyse data/information from more than one source;

Number and Algebra

• make informed decisions involving money; for example, obtain all the relevant information to make an informed decision about borrowing or investing money, taking all factors such as interest rate, length of loan and affordability of repayments into consideration; Home Economicsfor example, investigate the options of financing a TV, including types of loans, interest rate, compound interest, repayments and the term of the loan linking these together to make an informed decision

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example, form an hypothesis and investigate the relationship between two variables by drawing and analysing a scatter graph, investigate the reliability of your findings by comparing with a second set of data; Sciencefor example, form and investigate an hypothesis about the relationship between age and blood pressure, deciding on how to collect, process and interpret the relevant data; they obtain data from young and from older people, draw box plots or cumulative frequency curves (or interpret ready drawn graphs) and use these to compare the two data sets
• construct and interpret frequency tables and diagrams for sets of continuous data; for example, identify the medians and interquartile ranges from two box plots and use this information to compare the data effectively; Sciencefor example, investigate the heights of boys and girls at the beginning and at the end of year 10 using ready drawn box plots/ cumulative frequency curves or by collecting relevant data and drawing the graphs; they use data from the graphs to compare growth of boys and girls over the time period;

select and use the most appropriate methods to present findings, following accepted conventions;

Number and Algebra

• formulate linear equations; for example, use given information to form a linear equation to represent a relationship, following algebraic conventions,

Shape, Space and Measures

• use three figure bearings to define direction; for example, from a map, describe the bearing of one town from another using conventional notation i.e. a three figure bearing;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example, to investigate an hypothesis relating blood pressure and resting heart rate for males and females, decide to draw scatter graphs, one for females and one for males, to determine any correlation; appreciate that drawing a line of best fit and analysing anomolies on each scattergraph will help with comparison of the data sets.
• construct and interpret frequency tables and diagrams for sets of continuous data; for example, to investigate the relationship between two variables draw a scatter graph then draw a line of best fit, taking into account outliers and use the line to find missing values; Geographyfor example, use a line of best fit on a scatter graph to estimate the GDP per capita of a country, given the adult literacy rate.ScienceFor example, to investigate whether boys or girls grow more in Year 10, analyse data for heights at the beginning and at the end of the year, recognise that drawing box plots or cumulative frequency graphs will best allow comparison of the data sets.
• choose the most appropriate average (mean, median, mode) for a given line of enquiry; for example, given a box plot where the data is distinctly skewed, choose to use the mean rather than the median as a measure of central tendancy;

use appropriate mathematical language to respond to questions about their work;

Number and Algebra

• understand conservation of number; for example, having counted objects explain that when they are arranged differently there is no need to count them again as there will be the same number.
• create and describe repeating patterns using objects, numbers or pictures; for example, describe a number pattern such as 2,2,3,4,2,2,3,4,2 .... talk about which tile comes next in a pattern such as triangle, triangle, square, triangle, triangle, square, . . . .

Shape, Space and Measures

• use everyday language associated with length, ‘weight’, capacity and area to describe, compare and order three objects; for example,compare two objects using language such as: 'this pencil is longer', 'the blocks weigh the same', 'this cup holds less than the other one'; Home Economicsfor example, use statements such as "the potato is heavier than the egg", "the cup holds less than the mug".
• sequence familiar events; for example, use language such as 'first', 'then','after', 'before', 'next' and 'last' to describe daily routines Home Economicsfor example, talk about the order of the steps needed to make a fruit smoothie
• know the days of the week and their sequence; for example, state that today is Tuesday so tomorrow will be Wednesday and yesterday was Monday etc
• recognise ‘special’ times on the clock; for example, from the clock I can see it is breaktime break time/lunch time;
• sort 2-D and 3-D shapes and make and describe 2-D and 3-D constructions; for example: explain how they sorted shapes such as “I put this shape here because it looks the same as the others but it is bigger.”; and talk about the shapes they could use to design a robot;
• use language and follow instructions, in practical situations, for position and movement; for example, describe the positions of objects using language such as under, over, inside, outside, beside, and move using simple directions such as backwards, forwards,up, down and whole turn .

Handling Data

• sort and classify real objects for one criterion and re-sort for a different criterion, using Venn, Carroll and Tree diagrams; for example discuss how they sorted a collection of animals by type e.g.pet/wild and then re-sort by 2 legs/four legs;
• collect information and record using real objects or drawings; for example describe how they used cubes to record the number of people with blue/brown eyes.

use appropriate mathematical language to talk about their work and respond to questions;

Number and Algebra

• understand that the place of the digit indicates its value; for example, decribe 25 as 2 tens and 5 units Sciencefor example, when recording the number of pupils with different coloured eyes, explain how many tens and how many units are in the frequencies.
• understand relationships between all coins up to £1 and use this knowledge to carry out shopping activities; for example, discuss choices when selecting items from a tuck shop list to keep within a budget of £1

Shape, Space and Measures

• understand the need for standard units and know the most commonly used units in length, weight, capacity and area; For example explain that since all pencils are not the same length they cannot be used to measure the length of an object accurately, use mathematical language to describe measures e.g metres, centimetres, litres and milliletres, kilograms and grams and hours and minutes. Sciencefor example, recognise 'millilitres' as a liquid measurement when adding oil and water to make a lava lamp.
• name and order the days of the week, months of the year and seasons; for example, explain that this month is March so next month will be April; identify seasons in pictures giving reasons, 'this is a winter picture because it is snowing' Sciencefor example, when studying seasonal change, discuss the order of the months and which belong to which season.
• recognise and name 2-D and 3-D shapes; for example, name the 2-D shapes in a picture, name the 3-D shapes used for packaging Technology & Designfor example, recognise shapes of signs, that is circles, triangles and rectangles;
• sort 2-D and 3-D shapes, giving reasons for sorting; For example, expain their work e.g.'I put the shapes with 3 sides here and the shapes with more than 3 sides here', 'the 2-D shapes are here and the 3-D shapes are here'; Technology & Designfor example, discuss how shapes of signs represent different things, that is circles for orders, triangles for warnings and rectangles for information
• use language and follow instructions, in practical situations, for turning movements; for example use directional language such as half turn and quarter turn, and left and right to describe a set of instructions to move a robot;

Handling Data

• sort and classify objects for two criteria using Venn, Carroll and Tree diagrams; for example, explain how numbers are sorted into odd/not odd and greater than 10/not greater than 10, e.g. 15 is odd and greater than 10 Sciencefor example, when using a tree diagram to sort pond animals discuss how animals are sorted by having a shell or not and by having a body that is rounded or not rounded.Technology & Designfor example, explain why tools have been sorted on a Venn diagram showing the tools for wood, for plastic and for both
• discuss and interpret information; for examplein answer to simple questions, extract information from a simple table, block graph, pictogram or database; Geographyfor example answer questions such as, "Which place was the coldest?", from a simple table of temperatures;
  for example, answer questions from a simple table, showing facilities in some towns in Co. Down;
  for example, discuss how to match potential residents to different types of houses;Sciencefor example, talk about a block graph showing numbers of different minibeasts, using language such as 'most', 'least', 'more than' and' less than'.

use appropriate mathematical language to discuss and describe their way of working and respond to questions;

Number and Algebra

• understand and use the concept of place value in whole numbers; for example, describe 407 as 4 hundreds, no tens and 7 units Sciencefor example, explain how to read a measuring cylinder scale graduated in tens and hundredsTechnology & Designfor example, describe how resistance is found by using the colour code
• identify and describe simple number patterns within the 100 square; for example, describe number patterns linked with multiplication facts, every third number for 3 times tables, odd and even numbers.
• understand that multiplication is commutative; for example, explain how 3 rows of 4 items and 4 rows of 3 items both give 12 items;
• explore and use division in practical situations; for example, describe all the rectangular arrangements for 24 counters; explain how when sharing 26 sweets equally among 5 people each person would get 5 sweets and 1 sweet would remain
• use number skills in the context of money up to £10; for example, explain the steps and strategies used to calculate change from £10 after buying an item at £1.50 and another at £3.00 Home Economicsfor example, given a budget of up to £10, explain whether you can/cannot afford the ingredients required for a recipe.

Shape, Space and Measures

• choose and use appropriate standard units to estimate, measure and record length, capacity, volume, ’weight’, time and temperature; for example, using the appropriate units of measurement, estimate in metres, using benchmarks such as the height of the door as 2 metres, estimate ‘weight’ in kilograms and estimate the duration of practical activities (1 min, 2 mins, etc.) explaining their estimation in relation to their benchmarks; Sciencefor example, select and name appropriate measuring equipment such as thermometer for temperature,and measuring cylinder for volume of liquid; express the readings using the correct units, explaining the reason for their choices.Technology & Designfor example, explain that they will choose to measure a length of wood in mm
• read and interpret a calendar; for example, using a calendar for June explain that if 30th June is a Tuesday then the 1st July will be a Wednesday because it is the day after;
• recognise, name and describe common 2-D and 3-D shapes; for example, name shapes including hexagon, pentagon, semi-circle, cone, pyramid and prism; describe 2-D shapes such as 'a square has four sides the same length and four right angles'; describe simple properties of 3-D shapes such as a cylinder will roll
• recognise one line of symmetry in common 2-D shapes; for example, explain that if the shape has symmetry then it can be folded and both halves match exactly; Sciencefor example, discuss symmetry in nature where there is one line of symmetry only - eg butterflies, zebra faces, tigers, flowers etc.Technology & Designfor example, explain that a line of symmetry in a simple design divides the shape in half
• recognise tessellations through practical activities; for example, through practical activities using shapes such as squares, triangles, circles or parallelograms identify shapes which do or do not tessellate explaining why they do/do not tessellate;
• recognise right angles in the environment and understand angle as a measure of turn; for example, talk about angles that are bigger than/smaller than a right angle, and describe movements using language such as left/right and clockwise/anti-clockwise to describe turns;
• use grid references in practical situations; for example, describe the position of treasure on a map using two points of reference, the treasure is at B2 Geographyfor example, given its latitude and longitude, identify a country on a map;

Handling Data

• read and interpret information from tables, pictograms, diagrams, lists, bar charts, simple pie charts and databases; for example, explain how to identify the most/least popular food from a simple pie chart and answer simple questions about frequencies from a bar chart. Geographyfor example, identify, from a bar chart, the month with the highest/lowest rainfall;Home Economicsfor example, explain how to identify the most/least popular food from a simple pie chart and answer questions about frequencies from a bar chart such as 'How many chose strawberries?'Sciencefor example, use a bar chart about pupil characteristics such as eye colour to answer questions about the sample group.

use appropriate mathematical language to discuss their work and explain their thinking;

Number and Algebra

• understand place value to two decimal places; for example describe 0.56 as five tenths and six hundredths; Sciencefor example, given masses of a number of objects weighed to 2 d.p., discuss how to place these in 'weight' order using language such as 'unit' and 'decimal point.
• approximate within 10 000 to the nearest 10, 100 and 1000; for example round 6473 to either 6470, 6500 or 6000 depending on expectations explaining their reasons; ScienceFor example approximate the distance of the planets from the sun (given in whole numbers of million km) to the nearest 10 million km explaining when and how to round up.
• estimate answers to calculations and approximate by rounding; for example, explain how estimating was used to check the answer to 21 × 19 using 20 × 20, or 3 games costing £29.99 using 3 x £30 = £90;
• use the relationship between addition and subtraction to check calculations; for example explain how to find the change from £100 after spending £50 and £30 Sciencefor example, when prompted, explain how to use reverse operations to check the change in mass of magnesium before and after heating.
• understand and use multiples and factors; for example, explain that 24 eggs can be packed into 4 boxes with 6 eggs or 3 boxes with 8 eggs
• use fractions to describe quantities; for example, describe the proportion of boys and girls in a class as' 3/8 are boys and 5/8 are girls'; Sciencefor example, discuss how to use fractions to measure the proportion of the sky covered in cloud.
• understand equivalence of fractions; for example explain using pictures/diagrams that ⅓ = 2/6 = 4/12
• understand and use simple percentages; for example explain that to find 25% of a 600 metres, 600 can be divided by 4 because 25% is the same as a quarter; Sciencefor example, explain that to work out 20% for the VAT on an electricity bill, use 20% = 1/5 so the amount can be divided by 5 to find the VAT.Technology & Designfor example, explain that the 10% tolerance of a resistor can be found by dividing the resistance by 10
• make choices about spending and value for money; for example if 5 pencils are needed explain why you may choose to buy a packet of 6 at £1.20 rather than 5 single pencils at 23 p each, Home Economicsfor example, compare costs for the same products, but different brands, from different shopsTechnology & Designfor example, discuss all relevant variables involved when choosing materials for the bird feeder project to ensure that the cost is kept below £5.
• know different ways in which payments for goods can be made; for example, explain that goods and services can be paid for with cash, cheques, store cards, credit and debit cards and that payments for goods and services can be made electronically, such as, through the internet and by setting up a direct debit or standing order with banks or building societies. Home Economicsfor example, explain that food/goods can be purchased with cash, credit/debit cards

Shape, Space and Measures

• estimate and measure length, ‘weight’/mass and time and temperature, working to an appropriate degree of accuracy; for example explain why they have chosen to measure the width of a room in metres and centimetres and why they have chosen to measure to the nearest centimetre; Sciencefor example, discuss how to measure the time taken to disolve a sample of salt in water and whether to express it in minutes and seconds or in seconds only, justifying their choice.Technology & Designfor example, explain why they have chosen to measure a piece of metal in mm
• add and subtract common measures; for example, show clearly how to find how much paint is left in 2 litre container after 300 ml has been used, i.e. 2000 ml - 300 ml = 1700 ml; Home Economicsfor example, explain how to find how much flour is left in a 500 g bag after 75 g has been removed i.e. 500 - 75 = 425.Sciencefor example, describe and show how to calculate the increase in mass of magnesium after burning by subtracting the mass before burning from the mass after burning
• work out perimeters of simple shapes; for example, show how the perimeter of a simple shape is calculated by adding together the lengths of all the sides;
• explore the properties of common 2-D and 3-D shapes; for example use language such as ' line symmetry', 'equal angles', 'equal sides' and 'regular and irregular shapes' to describe the properties of shapes;
• explore the relationship between 2-D and 3-D shapes; for example, describe the 2-D shapes which can be used as a net to make a 3-D shapes;
• recognise and draw lines of symmetry in a variety of 2-D shapes; for example, discuss symmetry in nature where there is more than one line of symmetry e.g. flowers, snowflakes etc.
• know the eight points of the compass; for example, describe a location as 'north east of the school'; Geographyfor example, describe the location of a landmark as 'south west of the light house';
• understand and use the language of line, angle and location; for example, describe a location as 'south west of the light house'; explain that a parallelogram has 2 acute angles and 2 obtuse angles; ScienceFor example draw and compare angles of incidence and angles of reflection of a ray of light reflected off a plane mirror using language such as 'angle', 'acute', 'normal', 'perpendicular', 'equal' etc
• use coordinates in the first quadrant; for example, describe the position of the the lighthouse as (4, 1)

Handling Data

• present and interpret data using a range of graphs, tables, diagrams, spreadsheets and databases; for example, answer questions such as 'How many more pupils travelled by car than by bus?' from a bar chart; interrogate a database to answer questions involving two requirements Geographyfor example, interpret a bar chart showing the results of a traffic survey, commenting on the relative heights of the bars representing the different modes of transport;Home Economicsfor example, answer questions such as 'How many more people chose strawberries than grapes?' when interpreting a bar chart on favourite fruitsSciencefor example, interpret data about pupil characteristics from a frequency table and bar charts For example, discuss how to collect, tabulate and graph information about solubility of substances.
• understand and use the language of probability; for example describe the likelihood of an event as certain, likely, unlikely, could happen, impossible, definitely, definitely not, and fair; suggest an event which is certain, likely, etc. Sciencefor example, Having investigated pupil characteristics such as eye colour, use language of probability eg. likely, unlikely etc

use appropriate mathematical language to express and communicate ideas accurately;

Number and Algebra

• understand place value to three decimal places; for example describe 0.506 as five tenths and six thousandths; ScienceFor example, calculate the mass of air in a balloon to 3 decimal places;Technology & Designfor example, express 2200 ohms as 2.2 K ohms and 3300000 ohms as 3.3 M ohms, measure to 3 decimal places to make a push fit part using a laser cutter.
• check calculations by applying inverse calculations; for example, calculate the cost of dinners for four weeks and describe how to check the calculation by dividing the total cost by 4. Technology & Designfor example, produce a cutting list to calulate how many parts can be cut from a sheet and multiply to check.
• understand and use negative numbers in practical contexts; for example, explain that a negative balance in the bank means the account is overdrawn; a negative height is below sea level; Geographyfor example, explain that -250m means 250m below sea levelScienceFor example, interpret a table showing melting points/boiling points of a variety of substances placing the substances in order of their melting points and indicating clearly those that are solids, liquids or gases at room temperature; they use language such as 'positive', 'negative','greater/less than zero';Technology & Designfor example, setting the depth on a vertical drill
• devise and use rules for generating sequences in words and/or symbolic form; for example, describe a pattern of chairs around a rectangular table as 2 times the number of tables plus 2;
• express and use formulae in words or symbolic form; for example, express the volume of a cuboid as length x breadth x height and show the how to calculate the volume by substituting dimensions; Geographyfor example, express a river"s discharge as "discharge = cross sectional area x velocity";
  for example, express a dependency ratio as "number of youth dependents + number of elderly dependents divided by number of economically active x 100";Sciencefor example, use the formula: % oxygen absorbed = (difference between oxygen in inhaled air and exhaled air )/(amount of oxygen in inhaled air) × 100Technology & Designfor example, calculate pressure for pneumatics using pressure = force/area
• make informed choices about personal budgeting and spending; for example, plan a trip for a family of four with a budget of £100 explaining how consideration of their collective and varied interests and requirements have been taken into account; Home Economicsfor example, plan a meal for a family of 5 within a given budget, taking into consideration different tastes and dietry requirements

Shape, Space and Measures

• use the four operations to solve problems related to measures; for example, when asked to calculate how many 120 ml glasses can be filled from a 1 litre bottle explain that 1 L = 1000 ml and divide 1000 by 120 to give 8.3333 therefore 8 glasses can be filled; Home Economicsfor example, when making a meal calculate the total quantity of flour required and then explore the options for obtaining this amount taking into account the size of packets available and their costScienceFor example, show how to use the formula weight = m x g to calculate weight in Newtons for a 65kg person on different planets , where g is a decimal to either 1 or 2dpTechnology & Designfor example, explain how to find the number of key rings 5 cm long and 4 cm wide that can be cut from a 1 metre square sheet of acrylic. Calculate how much desk space is allocated per pupil based on anthroprometric data.
• calculate areas of squares, rectangles and right-angled triangles and volumes of cubes and cuboids; for example, deduce that the area of a right-angled triangle is half the area of a rectangle and express this as ‘multiply the base by the height, then divide by two’ or using algebra ‘A = ½ x b x h’. ScienceFor example To calculate the density of a 5kg cube of an substance, the volume, explaining orally or in written form. They then use the given formula Density = mass / volume; For example Pupils use a sheet of kitchen towel and fold in pleats to show how the area of absorption can be so much greater than the final base area. They calculate the base area and the area of the kitchen towel and compare. They use this to explain how villi and microvilli are a useful feature aiding absorption in lungs/intestines.
• calculate perimeters of a range of shapes; for example, show how to find the length of missing sides in an L shaped garden and then calculate the perimeter. Technology & Designfor example, calculate the length of tape required to go around a parcel
• understand and use scale in the context of simple maps and drawings; for example, show how to use a simple scale such as 1cm = 5km to find the actual distancein km between two towns by measuring the distance on the map and multiplying that length by 5; Geographyfor example, explain how to find the actual distance between two towns using a map with a scale such as 1cm= 10km;Sciencepupils discuss how to use a scale of 1m = 500 million km to construct a scale model of the solar system - considering only the distance of each planet from the sun. pupils use a scale of 1cm = 2000 km to calculate the dimensions of a scale drawing of each planet in the solar system - considering only the diameter of each planet.Technology & Designfor example, explain the use of a simple scale when drawing a design
• describe the properties of regular and irregular 2-D shapes in terms of sides, angles, symmetry and tessellations; for example, use properties to classify triangles and quadrilaterals and explain the basis for this classification using the language of shape; make statements such as ‘The angles of any triangle add up to 180'; 'all the angles in an equilateral triangle are 60°'; 'this is an equilateral triangle because all the sides and angles are equal and it has three lines of symmetry'.
• describe the properties of 3-D shapes in terms of faces, edges and vertices; for example, pg60 pg61 Technology & Designfor example, designing in CAD

Handling Data

• design and use a data collection sheet; for example, ask appropriate questions in order to obtain information on how employees travelled into work or how children travelled to school and record the findings on a tally chart, or create a data collection sheet to record data from a weather box or class survey Geographyfor example ask appropriate questions to obtain information about holiday destinationsHome Economicsfor example, discuss the layout of a data collection sheet for a consumer survey deciding what information is relevent such as opening hours, facilities, price, etcSciencefor example, design and use a data collection sheet for Heart Rate and blood pressure. Discuss the headings to be used eg. Name, Age, Gender,Heart Rate, Systolic and Diastolic Pressure.Technology & Designfor example, use microsoft forms or survey monkey or fronter to design a database to record the results of a survey
• construct, label and interpret a range of graphs, tables, diagrams, spreadsheets and databases; for example,answer questions by interpreting data from a piechart (divisions marked) or a dual barchart; interrogate a large database to answer a quesion based on a number of requirements Home Economicsfor example,interpret a dual bar chart to compare the amount of each ingredient in two similar productsScienceFor example discuss how to conduct an experiment to see how the height of a slope affects the speed of an object rolling down it. Collect the relevant information and use it to draw a graph to consider the relationship between height and speed. Draw appropriate conclusions.
• understand, calculate and use mean and range; for example, explain how to use the range to choose the most consistent team player; explain that an experiment should be repeated and a mean calculated to get more representative data; Geographyfor example pupils can explain that if the range of temperature is small then the temperatures are consistent.ScienceFor example find the mean resting heart rate of the class and the range and make a simple statement about the results;Technology & Designfor example, calculate the mean of anthropometric data to assist the design of a product
• place events in order of likelihood; for example, use language such as impossible, unlikely, even chance, likely and certain to order everyday events in terms of liklihood; complete a partially finished sample space diagram to show all the outcomes of rolling two dice and use a sample space diagram to place events in order of likelihood. (Need a space diagram in glossary- one included under ‘extra’) ScienceFor example, in basic genetics, consider eye colour, complete a sample space diagram/punnet square for Blue/Brown eyes having discussed dominance of genes explaining the relevance of their finished diagram using simple probability language; discuss the likelihood of a muliple birth

use appropriate mathematical language/notation to communicate and explain their work for a wider audience;

Number and Algebra

• understand and calculate square roots; for example, show each step of a trial and improvement method to find the length of the side of a square which has an area of 32 cm2
• understand, use and calculate ratio and proportion; for example, use 3 : 2 to describe the number of boys to girls in a class of 15 boys and 10 girls
• use appropriate formulae; for example, use A = πr2 to find the area of a circle and ½ (a+b)h to find the area of a trapezium Technology & Designfor example, use Ohm's law to calculate voltage, current or resistance of a simple battery and bulb circuit
• use conventional notation in algebra; for example, write a number sequence as an algebraic expression Technology & Designfor example, use the formula for ohms law depending on the unknown (voltage, current or resistance). V=IxR; R=V/I; I=V/R
• use and interpret graphs from real situations; for example, interpret a distance-time graph, describing different stages of the journey including any stoppages; Geographyfor example, interpret a population pyramid explaining how the population varies according to age; for example pupils interpret information from a climate graph;Sciencefor example, explain how to use the neutralisation curve to determine the point of neutralisation between an acid and alkali;
• apply mathematical concepts to a range of financial situations; for example, given options of investing £250 at 4.3% simple interest for 5 years or £250 at 5.8% simple interest for 3 years communicate clearly which is the better option and why

Shape, Space and Measures

• use, convert and calculate measures involving metric, and where appropriate, imperial units; for example, show the calculation for converting 70 mph into km/h;
• calculate perimeters and area of composite shapes involving squares, rectangles and triangles; for example, show on a diagram how to partition a 2D shape to calculate the perimeter and/or area.
• calculate surface area and composite volumes of cubes and cuboids; for example, draw the net and show the calculation to find the surface area of a drinks container , show on a diagram how to partition a 3D shape to find the volume
• calculate the circumference and area of circles; for example, show clearly how to calculate the perimeter and surface area of a flowerbed using the formula A = πr2
• work out dimensions using scale; for example, show how to use the scale ratio 1:25000 to work out the length in km of a lake measuring 5 cm on a map Geographyfor example, explain how to find the actual distance between two towns shown on a map with a scale such as 1: 50 000;
• understand and use compound measures; for example, show how to substitute values into the formula Density = Mass ÷ Volume to calculate the density of a substance Sciencefor example, explain how to calculate the speed of an an object at the bottom of a slope when planning an experiment to investigate how the height of a slope affects speed;

Handling Data

• collect and record discrete and continuous data using a variety of methods; for example, choose appropriate class intervals to analyse continuous data such as 1 ≤ n < 5, 5 ≤ n < 10, 10 ≤ n < 15, ...
• construct and interpret a variety of diagrams and graphs for discrete and continuous data; for example, construct and interpret pie charts, sem and leaf diagrams, scatter diagram, frequency diagram for continuous data use the mean to draw inferences about the data for example find the median length of babies born in maternity ward; given data from a survey, identify the modal shoe size. Sciencefor example, interpret a scatter diagram of diastolic against systolic blood pressure relating the findings to an hypothesis such as, ' In a blood pressure measurement, as systolic pressure rises so does the diastolic pressure'; they explain that there is a positive correlation, confirming the hypothesis.
• work out the mean, median and mode of a frequency distribution; for example, calculate the mean, median and/or modal number of goals scored by a football team over 38 matches from a frequency table
• use one of the measures of average to compare two sets of data; for example, work out one of the mean, mode or median test results for two classes and state which class has done better on average .
• understand and use the probability scale from 0 to 1 to express likelihood or comparability; for example, express the probability of getting a tail when a coin is tossed; independently draw and use a sample space diagram to show all the outcomes of rolling two dice and use this to find the probabilty of scoring a total of 10

use appropriate mathematical language/notation to explain and justify their findings or solutions;

Number and Algebra

• calculate repeated proportional change; for example calculate compound interest, making reference to the amount (principal), the term and the interest rate; Home Economicsfor example, if the retail value of fairtrade coffee in the UK is £49 million and is predicted to increase by 33% each year, clearly show, using repeated proportional change, how to calculate the expected value in 2 years time
• formulate linear equations; for example, write a linear equation to represent a relationship and use the equation to calculate other unknown values;
• manipulate simple algebraic expressions, equations and formulae; for example rearrange y = mx +c to make x the subject or C = 2πr to make x the subject; multiply out brackets such as (n+1)(n + 10); Sciencefor example, make R the subject of the formula -for Ohm's Law and then calculate the Resistance in Ohms for a given voltage and current;Technology & Designfor example, rearrange the formula for ohms law depending on the unknown (voltage, current or resistance). V=IxR; R=V/I; I=V/R
• solve two linear equations simultaneously by a graphical method; for example, to find the break even point for a manufacturing process that can be represented by two linear equations in two unknowns, draw two straight lines on a graph and identify the coordinates at which they intersect and explain what this means in the context of the question;
• make informed decisions involving money; for example, decide on a solution to the problem, "Peter has taken out a loan for his first car. He borrowed £4,500 from his local credit union. It is offering a borrowing rate of 5% with the option of paying it back over either 3, 4 or 5 years. What would be best time period for him to choose and why?", showing all calculations clearly and justifying the final decision while taking all relevant circumstances such as savings or monthly repayments into consideration; Home Economicsfor example discuss the circumstances to be considered when borrowing money: including types of loans, interest rate, compound interest, repayments and the term of the loan linking these together to make an informed decision.

Shape, Space and Measures

• perform length and area calculations on a composite shape including those involving the circle; for example, show on a diagram how to partition a composite 2 - D shape to find its area and then communicate clearly the steps taken to calculate the area;
• solve complex problems involving perimeter, surface area and volume; for example, show on a diagram how to partition a composite 3 - D shape to find its volume and then communicate clearly the steps taken to calculate the volume;
• understand that measurements have an error margin of half the given unit; for example, find the number of decorative tiles measuring 5 cm by 5 cm needed to cover a table top measuring 40 cm by 110 cm (all measured to the nearest cm), explaining how this number is dependent on the margin of error
• use three figure bearings to define direction; for example, from a map, describe the bearing of one town from another and give the answer as a three figure bearing, using conventional notation;

Handling Data

• pursue their own lines of enquiry, using appropriate methods of data collection, and interpret and present their findings; for example, choose a hypothesis, collect the relevant data, test this data using appropriate methods, present work clearly and evaluate results; relate their findings to the original hypothesis, explaining whether it is supported or not and suggesting if more data is required to further investigate;
• construct and interpret frequency tables and diagrams for sets of continuous data; for example, given two sets of data to compare, draw cumulative frequency tables and hence cumulative graphs; use these to estimate the medians and quartiles and to draw box plots; compare two data sets by considering box plots; Sciencefor example, Interpret cumulative frequency curves or box plots showing heights for girls and boys in Year 10 and compare these with similar plots for a younger/ older age group;
• estimate the mean of a set of grouped data and identify the limits of the median and modal group; for example, from a grouped frequency table, calculate an estimate for the mean by using the mid-values to represent each class, use this value to make inferences about the data but also explaining their limitations, given that the mean has been estimated; Sciencefor example, compare grouped frequency tables of babies’ birth weights for smokers and non smokers by calculating the mean for each and drawing relevant conclusions;
• choose the most appropriate average (mean, median, mode) for a given line of enquiry; for example, pupils explain that the presence of an anomaly means that the median is a more reliable average than the mean, as the mean would be skewed by the anomaly;
• understand and use relative frequency as an estimate of probability and calculate expected frequency; for example, having carried out an experiment to find relative frequency of an event, justify the number of trials and explain that as the number of trials increases so does the reliability of the estimated probablitiy;