### Mathematics

### The science that deals with the logic of shape, quantity and arrangement

Essential to everyday life, critical to science, technology and engineering, and necessary for many forms of employment

## Mathematics

## Key Stage 1

### Year 1

**Counting**

- Counting up to 20 objects and beyond
- Counting forwards and backwards from 0 to 20, and then beyond
- Reading and writing numbers from 0 to 20, and beyond
- Counting on and back in twos, fives and tens
- Using a number line to put numbers in the correct order
- Recognising patterns in numbers
- Recognising odd and even numbers
- Estimating amounts of objects and then counting to check.

**Calculating**

- Learning simple addition and subtraction
- Recognising mathematical words and symbols
- Using money – paying and giving change
- Learning which pairs of numbers add up to 10 (number bonds)
- Doubling and halving
- Sharing objects out into groups.

**Time**

- Telling the time to the hour and half hour
- Putting the days of the week and months of the year in order.

**Shapes**

- Recognising, naming and describing common 2D and 3D shapes
- Using shapes to make patterns, models and pictures
- Using ICT to record and change shapes.

**Handling data**

- Using a diagram to sort objects into groups
- Collecting information and recording it using tables or pictures.

**Measuring**

- Measuring, weighing and comparing different objects
- Using different instruments for measuring, such as scales, jugs or metre sticks
- Recording their results using pictures and numbers.

### Year 2

**Counting and calculating**

- Counting up to 100
- Putting the numbers one to 100 in the correct order
- Recognising sequences and patterns
- Adding and subtracting one- and two-digit numbers
- Doing simple mental maths
- Learning doubles and halves of numbers to ten
- Starting to use simple division and multiplication
- Adding and subtracting using money.

**Number facts**

- Reading and writing two- and three-digit numbers
- Partitioning numbers into tens and ones
- Recognising the symbols < and >
- Identifying odd and even numbers
- Finding pairs of numbers that add up to ten and then 20 (number bonds)
- Learning the two, five and ten times tables.

**Shape**

- Sorting and making shapes
- Describing shapes
- Finding lines of symmetry
- Identifying edges, faces and vertices
- Finding half, quarter and three quarters
- Beginning to understand angles
- Describing position and movement using mathematical language.

**Handling data and measuring**

- Sorting information on a diagram
- Drawing block graphs and pictograms
- Measuring and weighing objects
- Reading and understanding scales
- Understanding analogue and digital clocks
- Telling the time to the quarter hour
- Putting events in the correct order.

## Mathematics

## Key Stage 2

### Year 3

**Counting, partitioning and calculating**

- Mentally adding one- and two-digit numbers
- Adding two- and three-digit numbers on paper
- Reading, writing, ordering and partitioning two- and three-digit numbers
- Rounding two- and three-digit numbers to the nearest 10 or 100
- Solving one- or two-step problems dealing with numbers, money or measuring
- Multiplying by 10 and 100
- Checking calculations by doing the opposite sum (for example, subtracting to check an addition)
- Reading and writing fractions.

**Understanding shape**

- Recognising, using and drawing right angles
- Comparing and drawing angles
- Using symmetry to draw and complete shapes
- Understanding direction, using the four points of the compass.

**Number facts**

- Memorising number pairs that total 100
- Learning times tables: two, three, four, five, six and 10
- Recognising multiples of two, five and 10 up to 1000.

**Measuring**

- Understanding the relationship between units of measurement (for example, centimetres to metres)
- Reading scales accurately
- Telling the time on a 12-hour digital clock, and to the nearest five minutes on an analogue clock
- Calculating time intervals.

**Data handling**

- Sorting information using diagrams, lists and tables
- Presenting results using tables and charts
- Using ICT to produce a simple bar chart
- Sorting objects using a Venn diagram.

### Year 4

**Counting, partitioning and calculating**

- Mentally adding and subtracting one- and two-digit numbers
- Adding and subtracting two- and three-digit numbers using the written method
- Working through one- or two-step problems using money, time or measures
- Ordering, partitioning and rounding four-digit numbers
- Revising times tables up to ten
- Calculating doubles and halves
- Working with positive and negative numbers
- Using decimals to represent tenths and hundredths
- Learning about fractions and mixed numbers
- Working with remainders
- Using a calculator.

**Shape**

- Learning about patterns and properties of shapes
- Understanding line symmetry
- Finding fractions of shapes
- Visualising 2D and 3D shapes
- Making solid shapes
- Understanding that angles are measured in degrees
- Calculating the area and perimeter of rectangles
- Plotting horizontal and vertical positions on a grid
- Learning about compass points.

**Measuring**

- Estimating, measuring and recording measurements using decimals
- Reading and recording results using partially numbered scales
- Telling the time to the nearest minute
- Measuring time intervals using a clock or timetable
- Understanding am and pm and the 12-hour clock.

**Data handling**

- Collecting and interpreting information
- Constructing and using tally charts, bar charts, pictograms and tables
- Using diagrams and graphs to show results
- Using ICT to present information and results.

### Year 5

**Counting, partitioning and calculating**

- Solving one- and two-step word problems using time, measure or money
- Using a calculator correctly
- Ordering and partitioning whole numbers and decimals
- Finding halves and doubles of decimals
- Practising addition and subtraction of decimals and fractions
- Multiplying and dividing in their heads and using different written techniques
- Calculating factors and common multiples
- Working with percentages
- Counting backwards beyond zero (negative numbers).

**Shape**

- Working out patterns, properties and relationships of shapes
- Visualising 3D and 2D shapes
- Describing properties of 3D and 2D shapes
- Creating models of shapes
- Finding two lines of symmetry
- Drawing positions of shapes after reflection or translation
- Drawing shapes with parallel and perpendicular lines
- Finding the area and perimeter of polygons
- Estimating, measuring and drawing acute and obtuse angles
- Using a set square and protractor.

**Measuring**

- Estimating and measuring weight, length and capacity
- Converting kilograms to grams, and metres to centimetres
- Drawing and measuring lines to the nearest millimetre
- Telling the time using an analogue clock and a digital 24-hour clock
- Using a calendar or timetable to calculate time intervals.

**Date handling**

- Drawing tables and pictograms to show results
- Describing probability
- Finding the mode (average) of a series of events
- Using ICT to present their results.

### Year 6

**Counting, partitioning and calculating**

- Ordering, partitioning and rounding numbers to three decimal places
- Looking at positive and negative integers
- Solving problems involving time, money or measures
- Explaining their methods, reasoning and results
- Multiplying decimal numbers
- Working with fractions and percentages
- Simplifying and ordering fractions
- Calculating square numbers
- Using the correct mathematical symbols
- Using a calculator correctly
- Working with prime numbers smaller than 100.

**Shape**

- Classifying 2D shapes and 3D solids
- Making and drawing shapes accurately
- Identifying and describing parallel and perpendicular faces and edges
- Using a protractor to measure and draw angles
- Calculating the sum of angles in a triangle
- Learning about the rotation, translation and reflection of shapes
- Calculating perimeter and area
- Using co-ordinates to draw shapes
- Understanding that 360 degrees is a complete turn.

**Measuring**

- Estimating and weighing or measuring accurately
- Converting units of measurement, e.g. metres to centimetres
- Interpreting measurements on a range of instruments
- Comparing readings on different instruments.

**Data handling**

- Drawing and interpreting tables, bar charts and line graphs
- Using ICT to present results
- Interpreting pie charts
- Understanding probability
- Calculating the mean, median and mode averages.

## Mathematics

## Key Stage 3

### Years 7–9

**Numbers**

- Decimal notation and place order
- Comparing decimals
- Rounding whole numbers and decimals
- Positioning negative numbers on a number line
- Understanding integers
- Highest common factors
- Lowest common multiples
- The squares of numbers up to 12×12 and their roots
- Simplifying fractions
- Adding and subtracting fractions
- Calculating percentages
- Ratio and proportion
- Calculations with brackets
- Solving problems using mental maths and calculators.

**Algebra**

- Using letters to represent numbers
- Simplifying equations
- Solving simple equations
- Number sequences
- Input, output and mapping diagrams
- Plotting graphs using co-ordinates.

**Geometry and measures**

- Recognising parallel and perpendicular lines
- Calculating the sum of angles on a point, triangle and straight line
- Using the correct geometrical terms
- Geometrical problems using triangles and quadrilaterals
- Reflections, rotations and translations of 2D shapes
- Symmetry of a 2D shape
- Finding co-ordinates of points
- Using a ruler and protractor to draw accurate lines, angles and triangles, and construct 3D shapes
- Estimating and calculating problems involving measuring
- Converting metric units
- Estimating the size of acute, obtuse and reflex angles
- Learning the formula for calculating the area of a rectangle
- Surface area of cubes and cuboids.

**Statistics**

- Collecting data from surveys and experiments
- Designing questionnaires to collect data
- Creating frequency tables
- Calculating statistics
- Finding the mode, median and mean
- Creating and interpreting graphs, pie charts and diagrams showing data, on paper and using ICT
- Writing a statistical report
- Understanding probability terms such as likely, unlikely, impossible, probably
- Estimating probability from a simple experiment
- Comparing probabilities.

## Mathematics

## Key Stage 4

Various topics are covered in years 10 and 11.