# Year 6 - Programme of Study (Level 6)

__Number__

## Number & Place Value

- read, write, order and compare numbers up to 10 000 000 and determine the value of each digit
- 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 all of the above.

## Addition, Subtraction, Multiplication and 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

· identify common factors, common multiples and prime numbers

· use their 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 operations 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 (Including 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 > 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 [for example, 4 1 × 2 1 = 8 1 ]

· divide proper fractions by whole numbers [for example, 3 1 ÷ 2 = 6 1 ]

· associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 8 3 ]

· 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.

__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, 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
- 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 (cm
^{3 }) and cubic metres (m^{3}), and extending to other units [for example, mm^{3}and km^{3}].

__Geometry__

## 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 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 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__

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