# Maths Year 6

### By the end of Year 6 most children should be able to:

**Number and Place Value**

- read, write, order numbers up to 10 000 000 and know the value of each digit
- round any whole number
- use negative numbers in context
- solve number and practical problems that involve all of the above.

**Addition, Subtraction, Multiplication and Division**

- multiply multi-digit numbers up to 4 digits by a two-digit whole number
- divide numbers up to 4 digits by a two-digit whole number and interpret remainders as whole number remainders or fractions
- perform mental calculations
- identify common factors, common multiples and prime numbers
- solve addition and subtraction multi-step problems in contexts
- solve problems involving addition, subtraction, multiplication and division
- use estimation to check answers to calculations

**Ratio and Proportion**

- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages [for example 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.

**Fractions, Decimals and Percentages**

- use common factors to simplify fractions
- use common multiples to express fractions in the same denomination
- compare and order fractions, including fractions greater than 1
- add and subtract fractions with different denominators and mixed numbers
- multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1⁄4 × 1⁄2 = 1/8]
- divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
- associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 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

**Ratio and Proportion**

- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages [for example 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
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of numbers that satisfy an equation with two unknowns

**Measurement**

- solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places
- 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 [for example, mm3 and km3].

**Properties of Shapes**

- 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
- 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 and Direction**

- describe positions on the full coordinate grid (all four quadrants)
- draw and translate simple shapes and reflect them in the axes.

**Statistics**

- interpret and construct pie charts and line graphs and use these to solve problems
- calculate and interpret the mean as an average.