Number & Place Value

Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit e.g. Find the difference between the largest and smallest whole numbers that can be made of three digits.

Round any whole number to a required degree of accuracy.

Use negative numbers in context and calculate intervals across zero.

Solve number and practical problems that involve ordering and comparing numbers to 10 000 000 rounding to a required degree of accuracy, using negative numbers and calculating intervals across zero

Demonstrate an understanding of place value including decimals e.g. 28.13 = 28 + ? + 0.03 Demonstrate an understanding of place value including decimals e.g. 28.13 = 28 + ? + 0.03

Addition and Subtraction

Perform mental calculations with mixed operations to carry out calculations involving the four operations.

Solve multi-step problems in contexts, deciding which operations and methods to use and why e.g. find the change from £20 for three items that cost £1.24, £7.2 and £2.55; a roll of material is 6m long: how much is left when 5 pieces of 1.15m are cut from the roll?; a bottle of drink is 1.5 litres, how many cups of 1275ml can be filled from the bottle, and how much drink is left?

Solve problems involving addition and subtraction.

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Multiplication & Division

Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.

Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.

Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context.

Perform mental calculations, including with mixed operations and large numbers.

Use formal written methods to solve multi-step problems.

Identify common factors, common multiples and prime numbers.

Use his/her knowledge of the order of operations to carry out calculations involving the four operations

Solve addition and subtraction multi-step problems in contexts, deciding which operation and methods to use and why.

Solve problems involving addition, subtraction, multiplication and division

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Fractions (decimals & percentages)

Use common factors to simplify fractions

use common multiples to express fractions in the same denomination

Read and write decimal numbers as fractions e.g. 0.71 = 71/100 8.09 = 8 and 9/?

Compare and order fractions, including fractions > 1

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Multiply simple pairs of proper fractions, writing the answer in its simplest form e.g. ¼ x ½ = 1/8.

Divide proper fractions by whole numbers e.g. 1/3 ÷ 2 = 1/6

Associate a fraction with division and calculate decimal fraction equivalents e.g. know that 7 divided by 21 is the same as 7/21 and that this is equal to 1/3 and e.g. 0.375 is equivalent to 3/8

Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.

Multiply one-digit numbers with up to two decimal places by whole numbers.

Use written division methods in cases where the answer has up to two decimal places.

Solve problems which require answers to be rounded to specified degrees of accuracy.

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts e.g. one piece of cake that has been cut into 5 equal slices can be expressed as 1/5 or 0.2 or 20% of the whole cake

Recognise the relationship between fractions, decimals and percentages and can express them as equivalent quantities.

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts e.g. find 7/9 of 108

Solve problems involving the calculation of percentages e.g. of measures, and such as 15% of 360 and the use of percentages for comparison

Solve problems involving similar shapes where the scale factor is known or can be found

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Algebra

Use simple formulae e.g. perimeter of a rectangle or area of a triangle

Generate and describe linear number sequences

Express missing number problems algebraically

Find pairs of numbers that satisfy an equation with two unknowns

Enumerate possibilities of combinations of two variables

Measurement

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places.

Convert between miles and kilometres Recognise that shapes with the same areas can have different perimeters and vice versa

Recognise when it is possible to use formulae for area and volume of shapes

Calculate the area of parallelograms and triangles

Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³, and extending to other units e.g. mm³ and km³)

Properties of Shape

Draw 2-D shapes using given dimensions and angles

Recognise, describe and build simple 3-D shapes, including making nets

Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

Recognise angles where they meet at a point, are on a straight line, or are vertically opposite and find missing angles

Position & Direction

Describe positions on the full coordinate grid (all four quadrants)

Draw and translate simple shapes on the coordinate plane, and reflect them in the axis

Statistics

Interpret and construct pie charts and line graphs and use these to solve problems

Calculate and interpret the mean as an average