 ### The science that deals with the logic of shape, quantity and arrangementEssential to everyday life, critical to science, technology and engineering, and necessary for many forms of employment ## Key Stage 1

At each Key Stage, your child will learn different maths-related topics when attending school. Here, we provide you with some details of what your child will learn as they progress through their academic years. ### 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
• Understanding analogue and digital clocks
• Telling the time to the quarter hour
• Putting events in the correct order. ## 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)

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)
• 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
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. ## 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
• 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. ## Key Stage 4 Various topics are covered in years 10 and 11.

### Years 10 & 11

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