2nd Grade Math Checklist: What Your Child Should Know

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

Fluent adding and subtracting within 100

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

• Add two-digit numbers within 100 efficiently (e.g. 46 + 37 using place-value partitioning)
• Subtract two-digit numbers within 100 fluently (e.g. 83 − 25)
• Choose between strategies (decomposing, compensating, using known facts) based on the numbers involved

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)

Fluent adding and subtracting within 20

Fluently add and subtract within 20 using mental strategies; know from memory all sums of two one-digit numbers

• Answer any single-digit addition fact within 3 seconds
• Recall subtraction facts within 20 from memory (e.g. 15 − 8 = 7)
• Use known addition facts to derive related subtraction facts rapidly

Addition and subtraction within 1000

Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds

• Add two three-digit numbers using base-ten blocks or drawings, composing a ten or hundred when necessary
• Subtract three-digit numbers, decomposing a ten or hundred when necessary
• Relate the concrete/drawn strategy to a written method and explain why it works

Adding and subtracting (age 7+)

Add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction

• Set out a columnar addition correctly with digits aligned by place value
• Carry out columnar subtraction with exchange (borrowing) when needed
• Check the answer using the inverse operation or estimation

Estimating by rounding

Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning

• Round numbers to the nearest 10 or 100 to estimate a sum or difference before calculating
• Use addition to check a subtraction answer, or vice versa
• Identify when a calculated answer is unreasonable based on the estimate

Missing number problems (age 7+)

Solve addition and subtraction problems including missing-number problems, using number facts, place value, and more complex methods

• Solve a missing-number problem such as 245 + ? = 380
• Choose an appropriate method (mental, written, or combination) based on the numbers
• Solve multi-step problems combining addition and subtraction of three-digit numbers

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

Two-Step Word Problems

Solve one- and two-step word problems within 100 using addition and subtraction, with unknowns in all positions

• Solve a two-step word problem involving adding to and taking from
• Represent a word problem with an equation using a symbol for the unknown
• Solve comparison problems (how many more/fewer) within 100

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

Addition and subtraction strategies (age 7+)

Explain why addition and subtraction strategies work, using place value and the properties of operations

• Explain why adding tens and ones separately gives the correct total
• Describe why a compensation strategy works (e.g. 'I added 1 too many, so I subtract 1')
• Use place-value language to justify a written method step by step

Numbers on a number line

Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram

• Place whole numbers on a number line with equally spaced points
• Show an addition as a jump forward on the number line (e.g. 38 + 27 shown as jumps)
• Show a subtraction as a jump backward on the number line

Mental addition and subtraction (age 7+)

Mentally add and subtract a three-digit number and ones

• Calculate 345 + 7 mentally
• Calculate 462 − 5 mentally
• Explain that only the ones digit changes (unless bridging through a ten)

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 numbers

Add up to four two-digit numbers using strategies based on place value and properties of operations

• Add three or four two-digit numbers by grouping tens and ones
• Look for pairs that make multiples of 10 to simplify addition
• Explain the strategy used to combine multiple addends

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

Mentally adding hundreds to 3-digit numbers

Mentally add and subtract a three-digit number and hundreds

• Calculate 345 + 200 mentally
• Calculate 762 − 400 mentally
• Explain that only the hundreds digit changes

Mentally adding tens to 3-digit numbers

Mentally add and subtract a three-digit number and tens

• Calculate 345 + 40 mentally
• Calculate 462 − 30 mentally
• Explain that only the tens digit changes (unless bridging through a hundred)

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

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

Measuring length (age 7+)

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes

• Choose the most appropriate tool for measuring a given object
• Align the zero mark of a ruler with the end of the object and read the measurement
• Measure lengths in inches, feet, centimetres, and metres using the correct tool

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

Calculating with measurements

Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units

• Measure a length in centimetres and millimetres
• Weigh an object using grams and kilograms
• Add two measurements in the same unit (e.g. 250 ml + 400 ml = 650 ml)

Measuring Perimeters

Measure the perimeter of simple 2-D shapes

• Measure each side of a rectangle and add the lengths to find the perimeter
• Calculate the perimeter of a regular shape given the side length
• Explain that perimeter is the total distance around a shape

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

Time Units and Calendar Facts

Know the number of seconds in a minute and the number of days in each month, year, and leap year

• State that there are 60 seconds in a minute
• Name the months and state the number of days in each
• Explain that a leap year has 366 days and occurs every 4 years

Comparing Time Durations

Compare durations of events and calculate the time taken by particular events or tasks

• Calculate how long an activity lasted given start and end times
• Compare the duration of two events and identify which was longer
• Solve a problem such as 'The lesson starts at 10:15 and ends at 11:00. How long is it?'

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 to the minute (age 7+)

Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation

• Read the time to five minutes on an analogue clock face
• Write the time using digital notation (e.g. 3:25)
• Distinguish between a.m. and p.m. and relate to daily events

Estimating answers (age 7+)

Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours

• Read an analogue clock to the nearest minute
• Estimate how long an activity takes in minutes or seconds
• Compare two durations and determine which is longer

Addition and subtraction word problems

Solve word problems involving lengths within 100, using addition and subtraction with drawings and equations

• Solve 'The rope is 45 cm long. I cut off 18 cm. How long is it now?'
• Draw a diagram (e.g. a ruler drawing) to represent a length word problem
• Write an equation with a symbol for the unknown to represent the problem

Measuring & Plotting Lengths

Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot

• Measure the lengths of several objects and record the data
• Create a line plot with a horizontal scale marked in whole-number units
• Interpret a line plot to answer questions about the data

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

Halves and quarters (age 7+)

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately

• Determine the total value of a collection of coins
• Solve a word problem about making change with US currency
• Use $ and ¢ symbols correctly in answers

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

Comparing lengths by measuring

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit

• Measure two objects and calculate the difference in length
• Express the difference using the correct unit (e.g. '7 cm longer')
• Solve a comparison problem: 'How much taller is the bookshelf than the desk?'

Giving Change

Add and subtract amounts of money to give change, using both £ and p in practical contexts

• Calculate the total cost of two or three items priced in pounds and pence
• Work out the change from £5 or £10
• Record money calculations using £ and p notation correctly (e.g. £3.47)

Estimating Lengths

Estimate lengths using units of inches, feet, centimetres, and metres

• Estimate the length of a classroom object before measuring it
• Use a known reference (e.g. width of a finger ≈ 1 cm) to make reasonable estimates
• Check estimates by measuring and evaluate how close they were

Measuring with different units

Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen

• Measure a desk in both centimetres and inches and compare the two numbers
• Explain that measuring with a smaller unit gives a larger number
• Predict whether a measurement in centimetres will be greater or less than in inches

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

A Hundred Is Ten Tens

Understand that 100 can be thought of as a bundle of ten tens — called a 'hundred'

• Explain that 10 groups of 10 ones make 100
• Bundle ten tens sticks into one hundred and describe what happened
• Represent 100 using base-ten blocks showing 10 tens

The three digits of a three-digit number

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

• State the value of each digit in a three-digit number (e.g. in 362, the 3 represents 3 hundreds)
• Partition a three-digit number into hundreds, tens, and ones (e.g. 485 = 400 + 80 + 5)
• Explain why 706 has 7 hundreds, 0 tens, and 6 ones

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

Ordering Numbers to 1000

Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding

• Compare two three-digit numbers by examining hundreds first, then tens, then ones
• Use >, =, and < correctly to record comparisons of three-digit numbers
• Order a set of numbers up to 1000 from smallest to largest

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

The multiples of 100

Understand that the multiples of 100 (100–900) each represent a number of hundreds with 0 tens and 0 ones

• Identify that 300 means 3 hundreds, 0 tens, 0 ones
• Place multiples of 100 on a number line to 1000
• Read and write multiples of 100 and explain their place-value structure

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

Reading and writing numbers to 1000

Read and write numbers to 1000 in numerals, number names, and expanded form

• Read a three-digit numeral aloud correctly
• Write a three-digit number in words (e.g. 'three hundred and forty-two')
• Write a number in expanded form (e.g. 600 + 30 + 7)

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

10 or 100 More or Less

Find 10 or 100 more or less than a given number up to 1000

• Given a three-digit number, state what is 10 more and 10 less
• Given a three-digit number, state what is 100 more and 100 less
• Explain the strategy using place-value understanding (e.g. only the tens/hundreds digit changes)

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

Place Value to 1000

Solve number problems and practical problems involving place value of numbers up to 1000

• Solve a problem that requires identifying how many hundreds, tens, or ones are in a number
• Apply place-value knowledge to a practical context (e.g. counting money in pounds)
• Explain the strategy used to solve a place-value problem

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 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

Odd or Even

Determine whether a group of objects (up to 20) has an odd or even number of members

• Pair objects and determine whether there is one left over (odd) or not (even)
• Count a group by 2s to determine if the total is even
• Write an equation to express an even number as a sum of two equal addends (e.g. 8 = 4 + 4)

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

Multi-Step Problem Solving

With teacher support, make sense of multi-step problems involving larger numbers or mixed operations by breaking them into parts, choosing strategies, and checking answers for reasonableness — children at this stage are developing the habit with guidance; independent strategy evaluation comes later

• Break a two-step word problem within 1000 into sub-problems and solve each part
• Estimate an answer before calculating to set a reasonableness benchmark
• Check an answer using a different method or inverse operation and revise if needed

Understanding fractions (age 7+)

Communicate with mathematical precision: use correct place-value and fraction vocabulary, specify units in measurement answers, and use notation accurately

• Consistently specify units in measurement answers (e.g. '35 cm' not '35')
• Use fraction vocabulary precisely (numerator, denominator, equivalent)
• Write equations with correct notation including £/p, >, <, = and fraction symbols

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

Justifying mathematical reasoning

Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work

• Explain step by step why a columnar addition method gives the correct answer
• Find and explain an error in a worked example (e.g. incorrect regrouping)
• Construct a simple argument for why a general statement is true (e.g. 'adding two even numbers always gives an even number')

Working with money

Model real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context

• Choose whether to use a bar model, number line, or equation for a measurement problem
• Model a multi-step money problem with equations and interpret the final answer as change or total cost
• Create a line plot from measurement data and use it to answer questions about the real-world situation

Understanding fractions

Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents

• Write an equation with three-digit numbers to match a measurement or money word problem
• Draw a bar model to represent a fraction problem and use it to solve
• Explain how a number line diagram relates to the quantities in a word problem

Choosing the right strategy

Select and use appropriate tools and representations strategically, including choosing between mental methods, jottings, formal algorithms, and calculators for arithmetic with multi-digit numbers, decimals, and fractions

• Choose a mental method for 345 + 200 but a written method for 345 + 278
• Select a ruler vs a metre stick based on the object being measured
• Decide when a number line is more useful than base-ten blocks for a given problem

Shape patterns (age 7+)

Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape properties to classify

• Use the structure of place value to explain why adding hundreds only changes the hundreds digit
• Use commutativity and the relationship between multiplication and division to derive unknown facts
• Classify shapes by their structural properties (number of sides, right angles, parallel lines)

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')

Extending Table Patterns

Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences

• Notice that all multiples of 4 are even and use this to check answers
• Derive 8 × 7 from 8 × 5 + 8 × 2 by spotting the pattern
• Describe a rule for a growing pattern (e.g. 'add 50 each time') and use it to predict the next terms

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)

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

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

Right Angles & Turns

Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turn

• Use a right-angle checker to identify right angles in shapes and the environment
• Classify angles as right angles, less than a right angle, or greater than a right angle
• Explain that 4 right angles make a full turn (360°)

Understanding angles

Recognise angles as a property of shape or a description of a turn

• Identify angles at the corners of 2-D shapes
• Describe a turn (e.g. quarter turn, half turn) in terms of the angle made
• Explain that an angle measures the amount of turn between two lines meeting at a point

Parallel and perpendicular lines

Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

• Point out horizontal and vertical lines in shapes and real-world contexts
• Identify a pair of parallel lines (lines that never meet and are always the same distance apart)
• Identify perpendicular lines (lines that meet at a right angle)

Angles in triangles (age 7+)

Recognise and draw shapes having specified attributes (e.g. a given number of angles or equal faces); identify triangles, quadrilaterals, pentagons, hexagons, and cubes

• Draw a shape with exactly 5 sides (pentagon)
• Identify all quadrilaterals in a set of mixed shapes
• Name and draw a hexagon, explaining it has 6 sides and 6 angles

2-D shapes (age 7+)

Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

• Draw a triangle, rectangle, pentagon, or hexagon accurately
• Construct a cube or cuboid from modelling materials (e.g. straws and connectors)
• Recognise a 3-D shape (e.g. a pyramid) when it is rotated or seen from a different angle

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 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

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

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

Tenths

Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10

• Count: one tenth, two tenths, three tenths … up to ten tenths (one whole)
• Show that dividing a shape into 10 equal parts gives tenths
• Explain that 3 ÷ 10 = 3/10

Fractions on a number line

Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line

• Place 1/2, 1/4, 3/4 on a number line from 0 to 1
• Identify that 1/3 lies between 0 and 1/2 on the number line
• Understand that a fraction is a single number, not just 'part of a shape'

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'

Splitting shapes into equal parts (age 7+)

Partition circles and rectangles into two, three, or four equal shares; describe shares as halves, thirds, and fourths; recognise that equal shares of identical wholes need not have the same shape

• Partition a circle into 3 equal parts and label each 'a third'
• Partition a rectangle into 4 equal shares in more than one way
• Explain that two different-looking shares can still be equal in size

Equivalent fractions

Recognise and show, using diagrams, equivalent fractions with small denominators

• Show that 1/2 = 2/4 using a diagram of equal parts
• Use a fraction wall or bar model to find equivalent fractions
• Explain why two fractions are equivalent by comparing the shaded areas

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

Simple Fraction Sums

Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

• Calculate 2/5 + 2/5 = 4/5
• Calculate 6/8 − 3/8 = 3/8
• Explain that when denominators are the same, you add/subtract the numerators

Comparing fractions

Compare and order unit fractions, and fractions with the same denominator

• Order 1/2, 1/3, 1/4, 1/5 from largest to smallest
• Explain that a larger denominator means smaller unit fractions
• Compare 2/5 and 4/5 and explain that 4/5 is larger because it has more fifths

Unit fractions

Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

• Find 1/4 of 12 objects by dividing into 4 equal groups
• Find 3/4 of 12 objects
• Write the fraction of a set that is shaded or selected

Comparing fractions (age 7+)

Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison

• Solve a word problem requiring finding a fraction of a quantity
• Solve a problem that requires comparing or ordering fractions
• Choose and apply appropriate fraction knowledge to a multi-step problem

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

Times tables (age 7+)

Recall and use multiplication and division facts for the 3, 4, and 8 multiplication tables

• Recall 3 × 1 through 3 × 12 and corresponding division facts
• Recall 4 × 1 through 4 × 12 and corresponding division facts
• Recall 8 × 1 through 8 × 12 and corresponding division facts

Arrays for multiplication (age 7+)

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and 5 columns; write an equation to express the total as a sum of equal addends

• Count objects in a 3×4 array and write 4 + 4 + 4 = 12
• Explain that each row has the same number of objects so the total can be found by repeated addition
• Draw a rectangular array to model a given repeated-addition equation

Written Multiplication & Division

Write and calculate mathematical statements for multiplication and division using known tables, including two-digit × one-digit, using mental and progressing to formal written methods

• Calculate 23 × 4 using partitioning (20 × 4 + 3 × 4)
• Calculate 96 ÷ 8 using known table facts
• Begin to use a formal written layout for short multiplication

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

Multi-Step Multiply & Divide

Solve problems involving multiplication and division, including scaling problems and correspondence problems where n objects are connected to m objects

• Solve a scaling problem (e.g. 'the ribbon is 3 times as long')
• Solve a correspondence problem (e.g. '4 shirts and 3 trousers — how many outfits?')
• Solve a missing-number multiplication or division problem

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

Rows & Columns in Rectangles

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them

• Divide a rectangle into equal rows and columns of unit squares
• Count the total number of squares using repeated addition or skip counting
• Relate the rows-and-columns structure to a rectangular array

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

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

Skip Counting (4s, 8s, 50s, 100s)

Count from 0 in multiples of 4, 8, 50, and 100

• Recite the multiples of 4 from 0 to at least 48
• Recite the multiples of 8 from 0 to at least 96
• Count in steps of 50 and 100 from 0 to 1000

Counting Within 1,000

Count within 1000, including skip-counting by 5s, 10s, and 100s

• Count forwards and backwards within 1000 from any starting number
• Skip-count by 5s from any multiple of 5 to 1000
• Skip-count by 100s from any number (e.g. 150, 250, 350 …)

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

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

Picture & Bar Graphs

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph

• Draw a picture graph with a symbol representing one unit for each data point
• Draw a bar graph with labelled axes and a single-unit scale
• Use a bar graph to answer comparison questions (e.g. 'How many more votes did cats get than dogs?')

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