# Key learning in Maths

Number - number and place value

• Count forwards or backwards in steps of integers, decimals, powers of 10

• Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

• Identify the value of each digit to three decimal places

• Identify, represent and estimate numbers using the number line

• Order and compare numbers including integers, decimals and negative numbers

• Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more/less than a given number

• Round any whole number to a required degree of accuracy

• Round decimals with three decimal places to the nearest whole number or one or two decimal places

• Multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

• Use negative numbers in context, and calculate intervals across zero

• Describe and extend number sequences including those with multiplication and division steps, inconsistent steps, alternating steps and those where the step size is a decimal

Solve number and practical problems that involve all of the above

Number - fractions, decimals and percentages

• Compare and order fractions, including fractions > 1 (including on a number line)

• Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

• Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375 and )

• 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. x = )

• Divide proper fractions by whole numbers (e.g. ÷ 2 = )

• Find simple percentages of amounts

• Solve problems involving fractions

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

Solve problems involving the calculation of percentages (e.g. of measures and such as 15% of 260) and the use of percentages for comparison

Ratio and proportion

• Solve problems involving the relative sizes of two quantities where missing values can be found using integer multiplication/division facts

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

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

• Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)

• Select a mental strategy appropriate for the numbers in the calculation

• Recall and use addition and subtraction facts for 1 (with decimals to two decimal places)

• Perform mental calculations including with mixed operations and large numbers and decimals

• Add and subtract whole numbers and decimals using formal written methods (columnar addition and subtraction)

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

• Use knowledge of the order of operations to carry out calculations

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

Solve problems involving all four operations, including those with missing numbers

Number - multiplication and division

• Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)

• Identify common factors, common multiples and prime numbers

• Use partitioning to double or halve any number

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

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

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

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

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

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

• Use knowledge of the order of operations to carry out calculations

Solve problems involving all four operations, including those with missing numbers

Geometry - properties of shapes

• Compare/classify geometric shapes based on the properties and sizes

• Draw 2-D shapes using given dimensions and angles

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

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

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

Find unknown angles in any triangles, quadrilaterals, regular polygons

Geometry - position and 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 axes

Statistics

• Continue to complete and interpret information in a variety of sorting diagrams (including sorting properties of numbers and shapes)

• < > and construct pie charts and line graphs and use these to solve problems

Solve comparison, sum and difference problems using information presented in all types of graph

Calculate and interpret the mean as an average

Algebra

• Use simple formulae

• 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

• Use, read and write standard units of length, mass, volume and time using decimal notation to three decimal places

• Convert between standard units of length, mass, volume and time using decimal notation to three decimal places

• Convert between miles and kilometres

• Recognise that shapes with the same areas can have different perimeters and vice versa

• Calculate the area of parallelograms and triangles

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

• 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)

• Calculate differences in temperature, including those that involved a positive and negative temperature

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate