How to learn Key stage 1: Mathematics

The national curriculum in England: Key stages 1 and 2 framework document, Key stage 1

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1. Number - addition and subtraction

Addition as combining or putting together two: Understand addition as combining or putting together two groups to find the total
Subtraction as taking away or separating: Understand subtraction as taking away or separating from a group to find how many remain
Reading +, −, and = symbols: Read, write, and interpret the symbols +, −, and = in number sentences
Numbers up to 10 into pairs: Decompose numbers up to 10 into pairs in more than one way (part-part-whole)
Number bonds to 9: Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)
Number bonds: Recall number bonds (addition and related subtraction facts) within 20
Adding and subtracting: Add and subtract one-digit and two-digit numbers to 20, including zero
Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
Addition and subtraction word problems: Solve addition and subtraction word problems within 10 using objects or drawings
Early Word Problems: Solve one-step word problems involving addition and subtraction to 20, including missing-number problems
Mental addition and subtraction (age 6+): Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations
Adding and subtracting tens mentally: Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations
Adding two two-digit numbers: Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods
Mental and written addition and subtraction: Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures
Fluent addition and subtraction: Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
Adding Three Small Numbers: Add three one-digit numbers using strategies including looking for pairs that make 10
Addition in any order: Understand and apply the commutative property of addition: addends can be added in any order
Inverse: addition undoes subtraction: Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems

2. Number - fractions

What Is a Half?: Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity
Finding halves and quarters (age 5+): Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity
Fractions of amounts: Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
Understanding fractions: Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2

3. Geometry - position and direction

Positional Language: Describe the position of objects using terms such as above, below, beside, in front of, behind, next to
Turns & Directions: Describe movement and direction, including whole, half, quarter, and three-quarter turns
Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences
Position, direction, and movement: Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)

4. Geometry - properties of shapes

2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
3-D shapes: Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)
2-D shapes (age 6+): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line
Edges, vertices, and faces: Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces
2-D faces on 3-D shapes: Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)
Sorting 2-D and 3-D shapes: Compare and sort common 2-D and 3-D shapes and everyday objects by their properties

5. Measurement

Comparing Lengths & Heights: Compare two objects directly by length or height and describe the difference using language such as long, short, tall, longer, shorter, taller, double, half
Ordering Events in Time: Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening
Days, Weeks, Months & Years: Recognise and use language relating to dates, including days of the week, weeks, months, and years
Comparing durations: Use comparative language for time: quicker, slower, earlier, later
Telling time to the minute: Measure and begin to record time in hours, minutes, and seconds
Telling Time: Hours and Half Hours: Tell the time to the hour and half past the hour, and draw clock hands to show these times
Measuring mass and weight (age 4+): Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than
Comparing Capacity: Compare and describe capacity and volume using language such as full, empty, more than, less than, half full
Measuring length and height (age 5+): Measure and begin to record lengths and heights using non-standard and standard units
Measuring mass and weight: Measure and begin to record mass/weight using non-standard and standard units
Capacity and volume: Measure and begin to record capacity and volume using non-standard and standard units
Coin Values: Recognise and know the value of different coins and notes
Choosing measurement units: Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit
Comparing and ordering measurements: Compare and order lengths, mass, and capacity and record results using >, <, and =
Pounds & Pence Notation: Recognise and use symbols for pounds (£) and pence (p) and combine amounts to make a particular value
Adding money and giving change: Find different combinations of coins that equal the same amount of money
Money Addition & Subtraction: Solve simple money problems involving addition and subtraction, including giving change
Sequence intervals of time: Compare and sequence intervals of time
Telling Time: Minutes: Tell and write the time to five minutes, including quarter past and quarter to, and draw clock hands to show these times
Number of minutes in an hour: Know the number of minutes in an hour and the number of hours in a day

6. Number - multiplication and division

Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)
Multiplication as repeated addition: Understand multiplication as repeated addition and grouping equal sets
Arrays for multiplication: Use arrays to represent multiplication and division situations
Odd and even numbers: Recognise odd and even numbers
Times tables: Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
Reading ×, ÷, and = Symbols: Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences
Commutative Multiplication: Understand and apply the commutative property of multiplication and recognise that division is not commutative
Multiplication as repeated addition (age 6+): Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts

7. Number - number and place value

Rote counting to 100: Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones
Counting in 2s: Count in multiples of 2, 5, and 10 (skip counting)
Reading and writing numbers to 20: Read and write numerals from 0 to 20
Reading and writing numbers to 100: Read and write numerals from 0 to 100
One More Each Time: Each successive counting number represents a quantity that is one larger than the previous number
Comparing groups: more or fewer: Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies
Representing numbers with objects: Represent numbers using objects, pictorial representations, and the number line
Number Words to Twenty: Read and write number words from one to twenty
Counting forwards and backwards: Count forwards and backwards in steps of 3 from 0
The two digits of a two-digit number: Understand that the two digits of a two-digit number represent amounts of tens and ones
Counting forwards and backwards (age 6+): Count forwards and backwards in tens from any number (not just multiples of 10)
Representing Numbers: Identify, represent, and estimate numbers using different representations including the number line
Comparing and ordering numbers: Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding
Number Words to 100: Read and write numbers to at least 100 in words
Place value understanding and number facts: Use place value understanding and number facts to solve problems

8. Statistics

Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables
Sorting Data into Categories: Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity
Sorting into categories (age 6+): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another