# Maths

## Year Three

## Number

**Number and Place Value:**

- Read, write and use numbers up to 1000 in numerals and words;
- Count in multiples of 4, 8, 50 and 100;
- Understand the place value of each digit in a three-digit number and find 10 or 100 more/less than a number.

**Addition and Subtraction**

- Add and subtract numbers mentally; including 3-digits;
- Add and subtract numbers up to 3-digits using formal written methods;
- Begin to estimate and check answers to calculations using a range of strategies;
- Solve addition/subtraction problems; including the use of number facts.

**Multiplication and Division**

- Use mental recall of multiplication/division facts for 3, 4, 8;
- Begin to use formal written methods to calculate larger multiplications;
- Solve multiplication/division problems; including simple scaling and correspondence problems.

**Fractions (including decimals and percentages)**

- Understand and use unit and non-unit fractions of objects and numbers; including tenths;
- Recognise equivalent fractions with small denominators;
- Begin to compare and order fractions;
- Begin to calculate simple addition and subtraction of fractions; within one whole.

## Measurement, Geometry, and Statistics

**Measurement**

- Use the appropriate units of length (m/cm/mm), mass (kg/g) and volume/capacity (l/ml) to measure, compare, add and subtract;
- Understand how to measure the perimeter of simple 2-D shapes;
- Solve practical problems for adding and subtracting amounts of money, using both £ and p to give change;
- Understand how to tell and record the time; including for analogue, 12-hour, 24-hour and clocks with Roman numerals;
- Use the terms o’clock, a.m./p.m., morning, afternoon, noon and midnight;
- Know a range of equivalent units of time;
- Use known facts to compare the duration of events.

**Geometry - properties of ****shape**

- Accurately draw 2-D shapes;
- Recognise 3-D shapes in different orientations;
- Know that angles are a property of shapes and can be used to describe turns;
- Accurately recognise right angles including a complete turn;
- Begin to identify whether angles are greater or less than a right angle;
- Begin to use the terms horizontal and vertical lines & perpendicular and parallel to describe pairs of lines.

**Statistics**

- Use bar charts, pictograms and tables to present and interpret data;
- Use information in scaled bar charts, pictograms and tables to solve one-step and two-step questions.

## Year Four

## Number

**Number and Place Value**

- Read Roman numerals to 100 Count in multiples of 6, 7, 9, 25 and 1000;
- Understand the place value of each digit in a four-digit number and find 1000 more/less than a given number;
- Round numbers to nearest 10, 100 or 1000;
- Begin to recognise negative numbers.

**Addition and Subtraction**

- Add and subtract numbers mentally using known facts;
- Add and subtract numbers up to 4-digits using formal written methods;
- Routinely estimate and check answers to calculations using a range of strategies;
- Solve two-step addition/ subtraction problems; choosing appropriate operations.

**Multiplication and Division**

- Know and use mental recall of multiplication/ division facts up to 12x12 to derive facts;
- Use factor pairs to support mental calculations;
- Use formal written method to multiply;
- Solve multiplication/addition problems, including applying the rules of arithmetic and two-step problems.

**Fractions (including decimals and percentages)**

- Understand and use hundredths;
- Begin to recognise decimal and fraction equivalents;
- Calculate simple addition and subtraction of fractions beyond one whole;
- Divide by 10/100 and understand the value of the resulting decimal numbers;
- Solve fraction and decimal problems in context, including rounding and comparing up to two decimal places.

## Measurement, Geometry, and Statistics

**Measurement**

- Know how to convert units of measure (e.g. km to m, hour to minutes);
- Know how to measure and calculate the perimeter of rectilinear figures (cm/m);
- Use counting to find the area of rectilinear shapes;
- Solve problems using a different range of measures, including money;
- Use the units of time to convert between analogue and digital clocks;
- Solve problems using conversion between units of time.

**Geometry - properties of shape**

- Use the properties of shape to compare and classify geometric shapes;
- Understand and use the terms acute and obtuse to identify angles;
- Make observations to order angles up to two right angles by size;
- Recognise lines of symmetry in 2-D shapes presented in different orientations.

**Geometry - position and direction**

- Know how to use coordinates to describe position in the first quadrant and plot specified points;
- Use knowledge of coordinates and shape to complete a given polygon;
- Use translation horizontally and vertically to describe movement.

**Statistics**

- Use bar charts and time graphs to present discrete/continuous data;
- Use bar charts, pictograms, tables and other graphs to solve comparison, sum and difference problems.

## Year Five

## Number

**Number and Place Value**

- Read Roman numerals to 1000;
- Read, write and use numbers to at least 1,000,000;
- Count forwards/ backwards and round in powers of 10;
- Begin to interpret negative numbers in context.

**Addition and Subtraction**

- Accurately add and subtract mentally, and using formal written methods;
- Routinely check answers to calculations, including by rounding;
- Solve multi-step addition/subtraction problems; choosing appropriate operations.

**Multiplication and Division**

- Use known facts to mentally multiply and divide;
- Use formal long and short written methods for multiplication and division, including decimal numbers and interpret remainders;
- Recognise and use prime numbers and prime factors;
- Solve multiplication/division problems, including recognition and application of factors, multiples, squares, cubes.

**Fractions (including decimals and percentages)**

- Recognise, compare and order fractions, including mixed numbers and improper fractions;
- Calculate addition and subtraction of fractions, including different denominators;
- Begin to multiply fractions;
- Recognise, compare and round decimals up to 3 decimal places;
- Begin to understand decimal numbers as fractions;
- Solve problems involving simple percentage and decimal equivalents.

## Measurement, Geometry, and Statistics

**Measurement**

- Know how to convert units of metric measure (e.g. km to m, kg to g, l to ml);
- Recognise approximate equivalences between metric units and common imperial units (e.g. inches, pints, pounds);
- Know how to measure and calculate the perimeter of composite rectilinear shapes (cm/m);
- Use estimating, calculating and comparing to find the area of rectangles (including squares) and estimate to find the area of irregular shapes;
- Use practical resources to estimate volume and capacity;
- When solving problems, convert between units of time;
- When solving problems use all four operations to solve problems involving measures using decimal notation and scaling.

**Geometry - properties of shape**

- Use the terms acute, obtuse, and reflex to estimate and compare angles;
- Know how to identify 3-D shapes from 2-D representations;
- Accurately draw and measure angles in degrees (°);
- Know how to use the properties of rectangles to find missing lengths and angles;
- Use knowledge of sides and angles to distinguish between regular and irregular polygons.

**Geometry - position and direction**

- Know how to successfully reflect and translate shapes.

**Statistics**

- Use line graphs to solve comparison, sum and difference problems;
- Identify the necessary information in tables (including timetables) and be able to complete them.

## Year Six

## Number

**Number and Place Value**

- Read, write and use numbers up to 10,000,000;
- Round any whole number to differing degrees of accuracy;
- Calculate intervals across zero when problem solving;
- Use negative numbers in context and problem solving.

**Addition and Subtraction/Multiplication and Division**

- Mentally calculate mixed operations;
- Solve multi-step problems involving addition/subtraction;
- Use efficient formal written methods for multiplication and division, and interpret remainders;
- Solve problems involving all four operations and estimate to check answers;
- Identify and use common factors and multiples;
- Identify prime numbers.

**Fractions (including decimals and percentages)**

- Simplify, compare and order a range of fractions;
- Use equivalence to add and subtract fractions;
- Multiply and divide proper fractions;
- Understand the relationship of division and fractions;
- Recognise and calculate numbers with three decimal places;
- Use equivalences between simple fractions, decimals and percentages.

**Ration and Proportion**

When solving problems:

- Apply multiplication and division facts to calculate proportionality in a range of contexts;
- Accurately calculate and use percentages;
- Understand scale factor.

**Algebra**

- Use and generate simple formulae using symbols and letters;
- Generate linear number sequences;
- Find different possibilities for the variables within equations.

## Measurement, Geometry, and Statistics

**Measurement**

- When solving problems that require the calculation and conversion of units of measures, use decimal notation up to three decimal places;
- Know how to convert between miles and km;
- Investigate the relationship between area and perimeter, identifying examples where the same area can have the same perimeter and vice versa;
- Use the formulae for area and volume of shapes;
- Know how to calculate the area of parallelograms and triangles;
- Be able to calculate, estimate and compare the volume of cubes and cuboids using standard units (cm³, m³).

**Geometry - properties of shape**

- Use given dimensions and angles to draw 2-D shapes;
- Construct 3-D shapes including making nets;
- Know how to find unknown angles in triangles, quadrilaterals, and regular polygons;
- Solve missing angle problems on straight lines;
- Use the knowledge of shape properties to classify geometric shapes;
- Know and use the parts of circles (radius, diameter and circumference).

**Geometry - position and direction**

- Know how to use coordinates to describe position in all four quadrants and plot specified points;
- Know how to draw and translate shapes on the coordinate plane;
- Know how to reflect simple shapes in the axes of a coordinate plane.

**Statistics**

- Know how to construct a pie chart and line graph;
- Use pie charts and line graphs to solve problems;
- Understand the term mean as an average and be able to calculate it.