1st Grade Math Checklist: What Your Child Should Know

Subtraction as taking away or separating

Understand subtraction as taking away or separating from a group to find how many remain

• Model 'taking away' with physical objects and say how many remain
• Act out a 'take from' situation (e.g. 5 biscuits, eat 2, how many left?)
• Explain that subtraction means finding how many are left

Addition as combining or putting together two

Understand addition as combining or putting together two groups to find the total

• Model 'putting together' with physical objects and say the total
• Act out an 'add to' situation (e.g. 3 children arrive, then 2 more join)
• Explain that addition means finding how many altogether

Reading +, −, and = symbols

Read, write, and interpret the symbols +, −, and = in number sentences

• Read 3 + 2 = 5 aloud as 'three plus two equals five'
• Write a number sentence to match a concrete addition situation
• Interpret the = sign as 'is the same as' rather than just 'the answer is'

Number bonds to 9

Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)

• Given 7, respond '3' to make 10
• Use a ten-frame to find the complement to 10
• Record pairs that make 10 as equations (e.g. 6 + 4 = 10)

Numbers up to 10 into pairs

Decompose numbers up to 10 into pairs in more than one way (part-part-whole)

• Show that 5 = 1 + 4, 5 = 2 + 3, 5 = 0 + 5 etc.
• Use objects or drawings to find all pairs that make a given number
• Record decompositions as equations

Fluent adding and subtracting within 5

Fluently add and subtract within 5

• Answer 2 + 3 quickly without counting on fingers
• Answer 5 – 2 from recall or with minimal counting
• Complete a set of within-5 addition/subtraction facts accurately and quickly

Addition and subtraction within 20

Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts

• Solve 8 + 6 using making ten: 8 + 2 + 4 = 14
• Solve 13 − 4 by decomposing: 13 − 3 − 1 = 9
• Use a known fact (8 + 4 = 12) to derive 12 − 8 = 4

Fluent adding and subtracting within 10

Fluently add and subtract within 10

• Answer any addition fact within 10 quickly from memory
• Answer any subtraction fact within 10 quickly from memory
• Complete a timed set of within-10 facts with high accuracy

What the equals sign means

Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

• Explain that 6 = 6 is true because both sides are the same
• Determine that 4 + 1 = 5 + 2 is false
• Understand that = does not mean 'the answer comes next' — it means balance

Adding within 100

Add within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10

• Calculate 46 + 7 using place value (46 + 4 + 3 = 53)
• Calculate 38 + 40 = 78 using tens understanding
• Relate the strategy to a written method and explain the reasoning

Addition in any order

Understand and apply the commutative property of addition: addends can be added in any order

• Explain that 3 + 8 gives the same answer as 8 + 3
• Use commutativity to choose the larger number to count on from
• Demonstrate that subtraction is not commutative (5 − 3 ≠ 3 − 5)

Finding a missing number in addition

Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)

• Solve 10 − 8 by thinking 'what do I add to 8 to make 10?'
• Explain that subtraction can be thought of as a missing-addend problem
• Use known addition facts to solve related subtraction problems

Inverse: addition undoes subtraction

Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems

• Check 15 + 7 = 22 by calculating 22 − 7 = 15
• Use the inverse to solve: □ + 9 = 14, so □ = 14 − 9 = 5
• Explain that addition and subtraction 'undo' each other

Addition and subtraction word problems

Solve addition and subtraction word problems within 10 using objects or drawings

• Solve 'There are 6 apples, 2 are eaten, how many left?' using counters
• Solve 'add to' and 'take from' result-unknown problems
• Solve 'put together/take apart' problems with total unknown

Representing Addition and Subtraction

Represent addition and subtraction using objects, drawings, and mental images

• Use cubes or counters to show 3 + 2
• Draw a picture to represent a subtraction situation
• Use fingers to model an addition problem

Number bonds

Recall number bonds (addition and related subtraction facts) within 20

• Quickly recall that 8 + 5 = 13
• Given 13 – 5, respond 8 using knowledge of related addition fact
• Know all pairs of single-digit numbers that sum to numbers up to 20

Adding and subtracting

Add and subtract one-digit and two-digit numbers to 20, including zero

• Calculate 14 + 5 = 19
• Calculate 17 – 3 = 14
• Add or subtract 0 and explain the result stays the same

Early Word Problems

Solve one-step word problems involving addition and subtraction to 20, including missing-number problems

• Solve 'I have 12 sweets and eat 4, how many left?'
• Solve missing number: 7 = [ ] – 9
• Solve problems using concrete objects and pictorial representations

Mental and written addition and subtraction

Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures

• Solve a two-step problem: 'I had 35p, spent 12p, then found 5p. How much now?'
• Choose an appropriate method (mental or written) for a given problem
• Solve problems involving measures, e.g. 'a ribbon is 45cm, I cut off 18cm'

Adding two two-digit numbers

Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods

• Calculate 34 + 27 using base-ten blocks or column addition
• Calculate 63 − 28 using a number line or partitioning
• Explain a strategy for adding or subtracting two two-digit numbers

Mental addition and subtraction (age 6+)

Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations

• Calculate 36 + 7 = 43 using objects or mentally
• Calculate 52 − 4 = 48 using a number line or mentally
• Explain bridging through 10 when adding ones to a two-digit number

Unknown in Addition & Subtraction

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

• Solve 8 + ? = 11 and write 3
• Solve 5 = □ − 3 and write 8
• Solve 6 + 6 = □ and write 12

Fluent addition and subtraction

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

• Rapidly recall 7 + 8 = 15 and 15 − 8 = 7
• Use 6 + 4 = 10 to derive 60 + 40 = 100
• Derive 35 + 5 = 40 from knowledge that 5 + 5 = 10

Adding and subtracting tens mentally

Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations

• Calculate 45 + 30 = 75 mentally
• Calculate 82 − 40 = 42 mentally
• Explain that only the tens digit changes when adding/subtracting tens

Subtracting multiples of 10

Subtract multiples of 10 (10–90) from multiples of 10 using place value strategies

• Calculate 70 − 30 = 40
• Use base-ten blocks to show 80 − 50 = 30
• Explain that subtracting tens is like subtracting the tens digits

Adding Three Small Numbers

Add three one-digit numbers using strategies including looking for pairs that make 10

• Calculate 5 + 7 + 3 by first adding 7 + 3 = 10, then 5 + 10 = 15
• Add any three single-digit numbers correctly
• Identify useful pairs within three addends to make the calculation easier

Grouping numbers to add

Understand and apply the associative property of addition: when adding three numbers, any two can be added first

• Solve 2 + 6 + 4 by first adding 6 + 4 = 10, then 2 + 10 = 12
• Explain that grouping addends differently gives the same total
• Choose which two numbers to add first to make the calculation easier

Addition and subtraction strategies

Use counting on and counting back as strategies for addition and subtraction

• Add 8 + 3 by starting at 8 and counting on 3 (9, 10, 11)
• Subtract 12 − 3 by counting back 3 from 12 (11, 10, 9)
• Explain that counting on is a way to add

Measurable Attributes of Objects

Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)

• Identify that a pencil has length and can be measured
• Describe multiple attributes of one object (e.g. a bottle has height, weight, and capacity)
• Use words like 'long', 'heavy', 'full' to describe objects

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

• Measure the length of a table in centimetres using a ruler
• Weigh an object in grams using a scale
• Measure the capacity of a container in millilitres using a measuring jug

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

• Stand two children back-to-back and say who is taller/shorter
• Directly compare the heights of two towers and describe one as taller
• Use 'longer' and 'shorter' to compare two ribbons placed side by side

Measuring length and height (age 5+)

Measure and begin to record lengths and heights using non-standard and standard units

• Measure the length of a table using cubes and record the result
• Begin to use a ruler to measure in centimetres
• Record a measurement as a number with a unit

Comparing Capacity

Compare and describe capacity and volume using language such as full, empty, more than, less than, half full

• Compare two containers and say which holds more/less
• Use 'half full' and 'quarter full' to describe a container
• Solve practical problems like 'Which cup has more water?'

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

• Heft two objects and say which is heavier/lighter
• Use a simple balance to compare the weight of two objects
• Describe one object as 'heavier than' another

Capacity and volume

Measure and begin to record capacity and volume using non-standard and standard units

• Measure capacity by counting how many cups fill a container
• Begin to use litres as a unit of capacity
• Record capacity measurements with a number and unit

Measuring mass and weight

Measure and begin to record mass/weight using non-standard and standard units

• Use a balance to compare masses of two objects
• Measure mass using non-standard units (e.g. 'this book weighs 5 cubes')
• Begin to read a simple scale for mass

Ordering Events in Time

Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening

• Order three daily events using 'first', 'next', 'last'
• Use 'yesterday', 'today', 'tomorrow' correctly
• Describe an event as happening in the 'morning' or 'afternoon'

Days, Weeks, Months & Years

Recognise and use language relating to dates, including days of the week, weeks, months, and years

• Name the seven days of the week in order
• Name the twelve months of the year in order
• Understand that a year is made up of months and weeks

Measuring length (age 6+)

Measure the length of an object using same-size length units laid end to end with no gaps or overlaps

• Measure a book by laying paper clips end to end and counting them
• Understand that the length measurement is the number of units that span the object
• Avoid gaps and overlaps when placing units

Measuring length

Order three objects by length and compare the lengths of two objects indirectly using a third object

• Put three ribbons in order from shortest to longest
• Use a piece of string to compare the heights of two objects that cannot be placed side by side
• Explain that if A is longer than B and B is longer than C, then A is longer than C

Comparing and ordering measurements

Compare and order lengths, mass, and capacity and record results using >, <, and =

• Measure two objects and write 45cm > 32cm
• Order three containers by capacity after measuring each
• Use = when two measurements are the same

Comparing durations

Use comparative language for time: quicker, slower, earlier, later

• Compare two events and say which was quicker/slower
• Use 'earlier' and 'later' correctly to describe daily events
• Solve practical problems like 'Who finished first?'

Telling time to the minute

Measure and begin to record time in hours, minutes, and seconds

• Use a sand timer or stopwatch to time an activity
• Begin to understand that 1 minute = 60 seconds
• Record a duration in simple terms (e.g. 'it took about 2 minutes')

Number of minutes in an hour

Know the number of minutes in an hour and the number of hours in a day

• State that there are 60 minutes in an hour
• State that there are 24 hours in a day
• Use these facts to solve simple time problems

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

• Read an analogue clock showing 3:25
• Write 'quarter past 9' or '9:15'
• Draw clock hands to show twenty to four

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

• Read an analogue clock showing 3 o'clock
• Read an analogue clock showing half past 7
• Draw the hour and minute hands on a blank clock face to show a given o'clock or half-past time

Coin Values

Recognise and know the value of different coins and notes

• Identify 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2 coins
• Know that a £2 coin is worth more than a 50p coin
• Recognise £5 and £10 notes

Sequence intervals of time

Compare and sequence intervals of time

• Order three events by how long they took
• Compare the duration of two activities (e.g. 'the race took longer than the walk')
• Sequence intervals on a timeline

Money Addition & Subtraction

Solve simple money problems involving addition and subtraction, including giving change

• Calculate the total cost of two items priced in pence
• Work out change from 50p after buying an item costing 35p
• Solve 'How much more money do I need?' problems

Adding money and giving change

Find different combinations of coins that equal the same amount of money

• Show that 50p can be made with 2×20p + 1×10p, or 5×10p, or 1×50p
• Systematically find multiple coin combinations for a given total
• Explain why different coin sets give the same total

Pounds & Pence Notation

Recognise and use symbols for pounds (£) and pence (p) and combine amounts to make a particular value

• Write £1.50 or 150p correctly
• Combine coins to make a given total, e.g. 50p + 20p + 5p = 75p
• Read prices written with £ and p symbols

3-D shapes

Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)

• Name a cube, sphere, cylinder, and cone when shown them
• Identify 3-D shapes in the environment (e.g. a tin is a cylinder)
• Recognise a cuboid and a pyramid among a set of solid shapes

2-D shapes

Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)

• Name a triangle, circle, rectangle, and square when shown them
• Identify a shape correctly regardless of its size or orientation
• Pick out all the triangles from a mixed set of shapes

3-D shapes (age 5+)

Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes

• Count the sides and corners of a shape
• Compare a triangle and a rectangle by number of sides
• Describe a cube as having 'square faces' and 'corners'

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

• Count the number of sides of a given 2-D shape
• Identify whether a 2-D shape has a vertical line of symmetry
• Use properties (number of sides, symmetry) to describe and distinguish between shapes

Angles in triangles (age 6+)

Distinguish defining attributes of shapes (e.g. triangles are closed and three-sided) from non-defining attributes (e.g. colour, orientation, overall size)

• Build and draw shapes that possess defining attributes
• Identify that a shape remains a triangle regardless of its size, colour, or orientation
• Explain why a given shape is or is not a particular type based on its defining properties

Turns & Directions

Describe movement and direction, including whole, half, quarter, and three-quarter turns

• Follow instructions to move forward, backward, turn left/right
• Demonstrate a whole turn, half turn, and quarter turn with their body
• Describe a route using directional language

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)

• Use terms such as clockwise, anti-clockwise, quarter turn, half turn, three-quarter turn
• Describe a right angle as a quarter turn
• Give and follow directions involving straight-line movement and turns

Positional Language

Describe the position of objects using terms such as above, below, beside, in front of, behind, next to

• Describe a toy as being 'on top of' the table
• Follow instructions like 'put the cube behind the box'
• Use 'left' and 'right' in simple contexts

Edges, vertices, and faces

Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces

• Count the edges, vertices, and faces of common 3-D shapes
• Use the terms edge, vertex (vertices), and face correctly
• Describe a 3-D shape by its properties (e.g. a cube has 6 faces, 12 edges, 8 vertices)

Sorting 2-D and 3-D shapes

Compare and sort common 2-D and 3-D shapes and everyday objects by their properties

• Sort a collection of 2-D shapes by number of sides
• Sort 3-D shapes by number of faces or whether faces are flat/curved
• Explain criteria used to sort a group of shapes

Building & Drawing Shapes

Model shapes by building from components (e.g. sticks and clay balls) and by drawing

• Build a triangle from three sticks and three clay balls
• Draw a recognisable rectangle
• Construct a cube from straws and connectors

Combining Simple Shapes

Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)

• Join two triangles to make a rectangle or larger triangle
• Use pattern blocks to fill a hexagon outline
• Create a picture or design by combining basic shapes

Building with 3-D Shapes

Compose three-dimensional shapes (cubes, right rectangular prisms, right circular cones, right circular cylinders) and create composite shapes; build new shapes from component shapes

• Stack cubes and prisms to build towers or structures
• Combine 3-D shapes to make a new solid (e.g. cone on top of cylinder)
• Describe a composite 3-D shape in terms of its component shapes

Composing Shapes

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape

• Combine two triangles to form a rectangle or larger triangle
• Put together half-circles and quarter-circles to form circles or new shapes
• Decompose a composite shape and describe which simpler shapes make it up

Flat vs Solid Shapes

Distinguish two-dimensional (flat) shapes from three-dimensional (solid) shapes

• Sort shapes into 'flat' and 'solid' groups
• Explain that a circle is flat but a sphere is solid
• Identify whether a given shape is 2-D or 3-D

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)

• Point out a circular face on a cylinder or cone
• Identify triangular faces on a pyramid
• Recognise that the faces of 3-D shapes are 2-D shapes

Patterns & Sequences

Order and arrange combinations of mathematical objects in patterns and sequences

• Continue a repeating pattern of shapes or colours
• Describe the rule for a given sequence of objects
• Create own patterns and sequences using mathematical objects

Explaining Mathematical Reasoning

With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words

• Explain a solution strategy using a drawing or number sentence (e.g. 'I made ten first, then added the rest')
• Justify why an answer is correct by showing an alternative method that gives the same result
• Identify and explain an error in a worked example or a peer's solution

Showing Your Working

Show and tell how a mathematical answer was found using objects, drawings, and spoken words

• Use objects or drawings to demonstrate how an addition or subtraction was solved
• Respond to 'how do you know?' by pointing to objects or a drawing and describing what was done
• Listen to a peer's explanation and say whether they agree or disagree

Guided Multi-Step Problem Solving

With teacher guidance, make sense of multi-step and more complex problems by planning a pathway to the solution, identifying relevant information, and choosing appropriate operations

• When given a word problem within 20 or 100, identify the known information and what needs to be found
• Try a strategy (drawing, number line, known fact) and switch approach if the first attempt stalls
• Check the reasonableness of an answer using estimation or a different method

Making Sense of Problems

Make sense of a problem by identifying what is being asked, choosing concrete objects or pictures to represent the situation, and explaining a pathway to the solution

• When given a word problem within 10, explain what the problem is asking before attempting to solve
• Choose objects, fingers, or drawings to represent a problem situation
• After finding an answer, check it makes sense (e.g. re-count objects to verify a total)

Connecting maths to real life

Represent real-world problems with number sentences, bar models, or diagrams, and interpret the mathematical result back in context

• Choose and write an appropriate number sentence for a measurement or money word problem
• Draw a bar model or diagram to represent a two-step or comparison problem
• Interpret the numerical answer in context (e.g. '15 cm means the ribbon is 15 centimetres long')

Numbers on a number line

Select and use appropriate tools and representations (number lines, hundred squares, rulers, part-whole models) to support problem-solving

• Choose a number line or hundred square to support adding or subtracting two-digit numbers
• Select a ruler when a problem requires measuring length
• Explain why one representation (e.g. a number line vs cubes) is more helpful for a particular problem

Generalising Patterns

Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts

• Use a known doubles fact to derive a near-doubles answer (e.g. 6 + 7 = 6 + 6 + 1 = 13)
• Notice that subtracting 10 from any two-digit number always reduces the tens digit by 1
• Describe a rule for a pattern and use it to extend or predict (e.g. 'each time we add 5, the ones digit alternates between 0 and 5')

Precise Maths Communication

Communicate with mathematical precision: use correct vocabulary, specify units, and use symbols accurately

• Use the = sign correctly to mean 'is the same as' rather than 'the answer is'
• Include units when giving a measurement answer (e.g. '12 cm' not just '12')
• Use precise terms such as 'edge', 'vertex', 'face' when describing 3-D shapes, and 'greater than', 'less than' when comparing numbers

Connecting Representations

Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)

• Write a number sentence (e.g. 14 + 5 = 19) to match a word problem and explain the connection
• Draw a bar model or part-whole diagram to represent a problem, then solve using the diagram
• Translate between a concrete model and a symbolic equation, describing what each number represents

Shape patterns

Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently

• Use the commutative property deliberately (e.g. reorder 3 + 9 as 9 + 3 to count on from the larger number)
• Use place-value structure to add or subtract tens (e.g. 47 + 10 = 57 because only the tens digit changes)
• Recognise structural similarities between shapes (e.g. rectangles and squares both have 4 sides and 4 right angles)

Using objects to model real problems

Use objects, drawings, or simple number sentences to represent a real-world situation (early mathematical modelling)

• Draw a picture or use objects to represent a simple real-world situation involving counting or comparing
• Write or dictate a number sentence to describe a real-world situation (e.g. 'I had 5 apples and ate 2')
• Use the model to answer a question about the situation

Spotting mathematical patterns

Notice simple patterns and structures: spot that changing order doesn't change the total, and recognise how numbers relate to each other

• Notice that 3 + 2 gives the same answer as 2 + 3 (early commutativity)
• Recognise that teen numbers are 'ten and some more' (e.g. 14 is 10 and 4)
• Spot a pattern in a sequence of objects or numbers and predict what comes next

Early Maths Vocabulary

Use mathematical words carefully when counting, comparing, and describing shapes and positions

• Use 'more than', 'fewer than', and 'the same as' correctly when comparing groups
• Name shapes correctly and describe their features using words like 'sides' and 'corners'
• Use positional words (above, below, next to) precisely to describe where objects are

Real-World to Maths Connections

Move between a real-world situation and a mathematical representation using concrete objects, drawings, diagrams, tables, number sentences, or bar models

• Given a story about combining groups, represent it with counters or cubes and find the total
• Given a set of objects, tell a simple addition or subtraction story to match
• Connect a physical action (putting together, taking away) to the matching operation

Finding efficient methods

Notice when a calculation or pattern repeats and use this to count more efficiently or predict results

• Notice that skip counting by 2s follows a repeating odd/even pattern
• Recognise that adding 1 to any number always gives the next counting number
• Use a repeated pattern (e.g. +10 on a hundred chart always moves down one row) to predict answers

Hands-On Problem Solving

Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problem

• Choose cubes, counters, or fingers to help solve an addition or subtraction problem
• Use a ten frame to organise objects for counting or comparing
• Explain why a particular tool (e.g. cubes rather than fingers) was chosen for a given problem

Reading and writing numbers to 20

Read and write numerals from 0 to 20

• Read any numeral 0–20 when shown it
• Write numerals 0–20 legibly from dictation
• Represent a number of objects with the correct written numeral

The teen numbers

Understand that the teen numbers (11–19) are composed of ten ones and some further ones (early place value)

• Compose 14 as a group of ten and four ones using objects
• Decompose 17 into 10 + 7 and record as an equation
• Explain that 13 is 'one ten and three ones'

A Ten Is Ten Ones

Understand that 10 can be thought of as a bundle of ten ones — called a 'ten'

• Group 10 single cubes into one rod of 10 and explains why
• Explain that 10 ones is the same as 1 ten
• Exchange 10 ones for a single tens block

The two digits of a two-digit number

Understand that the two digits of a two-digit number represent amounts of tens and ones

• Explain that in 47, the 4 represents 4 tens (40) and the 7 represents 7 ones
• Use base-ten blocks to show a two-digit number as tens and ones
• Identify the tens digit and ones digit in any two-digit number

Comparing and ordering numbers

Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding

• Correctly place > or < between 34 and 43
• Order a set of two-digit numbers from smallest to largest
• Explain a comparison by referring to the tens digit first, then ones

Representing Numbers

Identify, represent, and estimate numbers using different representations including the number line

• Place a two-digit number on a 0–100 number line in approximately the right position
• Estimate 'about how many' objects are in a set of 30–50 without counting
• Represent the same number using base-ten blocks, a number line, and a drawing

10 More or 10 Less

Mentally find 10 more or 10 less than a given two-digit number without counting

• Given 56, quickly say 66 is 10 more and 46 is 10 less
• Explain that adding 10 increases the tens digit by 1
• Answer '10 more than 73' without using fingers or counting on

Number Words to 100

Read and write numbers to at least 100 in words

• Read 'fifty-seven' and write the numeral 57
• Write 'eighty-three' when shown the numeral 83
• Read and write all decade words (twenty, thirty … ninety) correctly

Number Words to Twenty

Read and write number words from one to twenty

• Read the word 'twelve' and identify it as 12
• Write the word form of a given number 1–20
• Match numeral cards to number word cards

Place value understanding and number facts

Use place value understanding and number facts to solve problems

• Use knowledge that 34 = 30 + 4 to help add 34 + 20 = 54
• Solve 'I think of a number, add 10, and get 45. What was my number?'
• Apply partitioning to solve a problem in an unfamiliar context

The multiples of 10

Understand that the multiples of 10 (10, 20, 30 … 90) represent one to nine tens and 0 ones

• Explain that 30 means 3 tens and 0 ones
• Represent 50 using 5 tens rods and no unit cubes
• Match decade numbers to their tens representation

Reading and writing numbers to 100

Read and write numerals from 0 to 100

• Read two-digit numerals up to 100 correctly
• Write any number 0–100 as a numeral from dictation

Reading and writing numbers to 120

Count to 120 starting at any number less than 120; read and write numerals to 120

• Count from 47 to 120 without errors
• Read the numeral 108 correctly
• Write the numeral for one hundred and fifteen

One-to-one counting

One-to-one correspondence when counting objects: each object is paired with exactly one number name

• Point to or touch each object exactly once while saying number names
• Do not skip objects or double-count when counting a set
• Recognise an error when someone counts an object twice

How Many in Total?

Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order counted

• After counting a set, answer 'how many?' with the last number stated
• Understand that rearranging objects does not change the count
• Understand that counting in a different order gives the same total

Rote counting to 100

Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones

• Recite the number sequence 1–100 without skipping or repeating
• Count backward from 20 to 0
• Count forward starting from a number other than 1 (e.g. 'start at 23')

Counting in 2s

Count in multiples of 2, 5, and 10 (skip counting)

• Count 2, 4, 6, 8 … up to at least 20
• Count 5, 10, 15, 20 … up to at least 50
• Count 10, 20, 30 … up to 100

Counting objects to 20

Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)

• Accurately count up to 20 objects in a line
• Count up to 10 scattered objects without losing track
• Given a number 1–20, count out that many objects from a larger set

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

• Use one-to-one matching to compare two groups
• State which group has more/fewer after counting both
• Use the language 'equal to', 'more than', 'less than', 'fewer', 'most', 'least'

Two written numerals between 1 and 10

Compare two written numerals between 1 and 10 to determine which is greater or less

• Given two written numerals (e.g. 4 and 7), identify which is greater
• Correctly use > and < or 'greater than' / 'less than' to compare single-digit numerals

Representing numbers with objects

Represent numbers using objects, pictorial representations, and the number line

• Show a given number using counters, cubes, or fingers
• Draw a pictorial representation of a quantity (e.g. tally marks, dots)
• Locate a number on a number line

One More Each Time

Each successive counting number represents a quantity that is one larger than the previous number

• Given a set of 5, know that adding one object makes 6
• Explain that 8 is one more than 7
• Given a number, identify one more and one less

Counting forwards and backwards (age 6+)

Count forwards and backwards in tens from any number (not just multiples of 10)

• Count 7, 17, 27, 37 … from a non-multiple starting point
• Count backwards in tens from 83
• Explain the pattern of adding/subtracting 10

Counting forwards and backwards

Count forwards and backwards in steps of 3 from 0

• Count 3, 6, 9, 12, 15 … up to at least 30
• Count backwards in 3s from 30
• Identify the next number in a sequence of multiples of 3

Division as equal sharing

Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)

• Share 10 counters equally between 2 plates
• Group 12 objects into sets of 3 and count 4 groups
• Use concrete objects to solve 'How many groups of 2 in 8?'

Multiplication as repeated addition

Understand multiplication as repeated addition and grouping equal sets

• Explain that 3 groups of 2 is the same as 2 + 2 + 2
• Use objects to make equal groups and count the total
• Recognise an array as showing equal rows

Times tables

Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables

• Quickly answer 5 × 3 = 15 from memory
• Quickly answer 20 ÷ 5 = 4 from memory
• Recite the 2, 5, and 10 times tables fluently

Arrays for multiplication

Use arrays to represent multiplication and division situations

• Build an array of 3 rows of 4 objects to show 3 × 4
• Read an array and state the total
• Use an array to solve a simple division problem (e.g. 12 objects in rows of 4 → 3 rows)

Reading ×, ÷, and = Symbols

Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences

• Read 3 × 4 = 12 aloud as 'three times four equals twelve'
• Write a multiplication sentence to match an array
• Read 12 ÷ 3 = 4 aloud correctly

Commutative Multiplication

Understand and apply the commutative property of multiplication and recognise that division is not commutative

• Explain that 3 × 5 = 5 × 3 and show this with an array rotated
• Use commutativity to choose the easier calculation
• Demonstrate that 12 ÷ 3 ≠ 3 ÷ 12

Multiplication as repeated addition (age 6+)

Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts

• Solve 'There are 5 bags with 2 apples in each. How many apples?' using repeated addition or known fact
• Solve 'Share 15 sweets equally among 3 children' using grouping
• Draw an array to solve a multiplication problem in context

Odd and even numbers

Recognise odd and even numbers

• Identify whether a given number is odd or even
• Explain that even numbers can be divided into 2 equal groups
• Spot the pattern: even numbers end in 0, 2, 4, 6, or 8

What Is a Half?

Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity

• Fold a shape into two equal parts and identify each as 'a half'
• Find half of 8 objects by sharing into 2 equal groups
• Identify whether a shape has been divided into halves or not (equal vs unequal parts)

Finding halves and quarters (age 5+)

Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity

• Fold a shape into four equal parts and identify each as 'a quarter'
• Find a quarter of 12 objects by sharing into 4 equal groups
• Identify whether a shape has been divided into quarters (four equal parts)

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

• Find 1/3 of 12 objects by sharing into 3 equal groups
• Shade 3/4 of a rectangle that has been divided into 4 equal parts
• Identify 1/4 of a length on a number line or ruler

Fraction Notation

Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole

• Point to and name the numerator and denominator in any given fraction and explain what each tells you
• Correctly classify fractions as unit, proper, improper, or mixed number with an example of each
• Explain in own words why 2/4 and 1/2 are equivalent fractions

Decomposing a shape into more equal shares

Understand that decomposing a shape into more equal shares creates smaller shares

• Explain that a quarter of a pizza is smaller than a half of the same pizza
• Demonstrate that fourths are smaller pieces than halves
• Compare the size of halves and quarters of the same shape

Halves & Quarters of Shapes

Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters

• Divide a circle into two equal halves
• Divide a rectangle into four equal quarters
• Describe the whole as 'two halves' or 'four quarters'

Understanding fractions

Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2

• Write 1/2 of 10 = 5
• Explain that 2/4 is the same as 1/2 using a diagram
• Calculate simple unit fractions of quantities and write the result

Sorting into categories

Classify objects into given categories, count the number in each category, and sort the categories by count

• Sort a set of shapes by colour and count how many in each group
• Sort objects by size (big/small) and state how many in each category
• Identify which category has the most/fewest after sorting and counting

Sorting Data into Categories

Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity

• Sort a set of objects into 2-3 given categories and count each group
• Create a simple table or list showing category names and counts
• Order categories from most to fewest or fewest to most

Pictograms and tally charts (age 6+)

Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data

• Correctly label the axes of a bar chart including a title, axis labels, and scale
• Distinguish between discrete data (counted) and continuous data (measured) with an example of each
• Use 'tally', 'frequency', and 'pictogram' correctly when describing how to record and display data

Pictograms and tally charts

Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

• Read a pictogram where each symbol represents one item
• Construct a tally chart from collected data
• Draw a block diagram to represent data from a survey

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

• Answer 'how many?' for each category in a data set
• Calculate the total number of data points across all categories
• Compare two categories using 'how many more/fewer' language