4th Grade Math Checklist: What Your Child Should Know

Fractions

Your child is exploring fractions, decimals, and percentages — understanding how they relate to each other, adding and subtracting fractions, and solving real-world problems involving these concepts.

• 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

• Fractions of a whole

  Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b

  • Given a shape divided into 5 equal parts, identify one shaded part as 1/5
  • Explain that 3/4 means 3 parts each of size 1/4
  • Draw a model showing 2/6 as 2 pieces of a whole cut into 6

• Equivalent fractions on a number line

  Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams

  • Use fraction strips to show 1/2 = 2/4 = 3/6
  • Verify on a number line that 2/3 and 4/6 land on the same point
  • Identify at least three fractions equivalent to 1/2 using diagrams

• Equivalent fractions (age 8+)

  Generate simple equivalent fractions and explain why they are equivalent using visual fraction models

  • Given 1/3, generate 2/6 as equivalent and show with area model
  • Simplify 4/8 to 1/2 and justify with a fraction strip
  • Complete equivalence chains: 1/4 = ?/8 = ?/12

• Equivalent fractions (age 9+)

  Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths

  • Use a fraction strip to show 2/3 = 4/6 = 6/9
  • Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged
  • Generate three fractions equivalent to 3/5 and verify with diagrams

• Fractions on a number line (age 8+)

  Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b

  • Partition a 0-to-1 number line into 4 equal parts and mark 1/4
  • Explain that each part on the line has size 1/b
  • Locate 1/3 and 1/6 on separate number lines

• Decimals for Tenths & Hundredths

  Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)

  • Rewrite 0.62 as 62/100
  • Write 3/10 as 0.3 and locate on a number line
  • Read 0.07 and express as 7/100

• Converting tenths to hundredths

  Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)

  • Rewrite 7/10 as 70/100
  • Calculate 3/10 + 4/100 = 34/100
  • Explain why 5/10 = 50/100 using a hundredths grid

• Decimal equivalents of tenths and hundredths

  Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)

  • Write 7/10 as 0.7 and vice versa
  • Convert 45/100 to 0.45
  • Place 0.3 and 3/10 at the same point on a number line

• Tenths (age 8+)

  Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10

  • Count from 3/100 to 12/100 in hundredths
  • Explain that 1/10 ÷ 10 = 1/100
  • Place several hundredths on a number line between 0 and 1/10

• Decimal & Percent Notation

  Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value

  • Read and write decimal numbers correctly, identifying the value of each digit (ones, tenths, hundredths)
  • Use the % symbol correctly and explain that per cent means 'out of 100'
  • Convert between simple fractions, decimals, and percentages (e.g. 1/2 = 0.5 = 50%) and explain why they are equal

• Tenths (age 9+)

  Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)

  • Write 0.025 as 25/1000
  • Explain that 1 tenth = 100 thousandths
  • Place 0.345 on a number line between 0.34 and 0.35

• Understanding fractions (age 9+)

  Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)

  • Express 5/8 as a sum of five copies of 1/8
  • Show on a number line how 4/3 is built by iterating 1/3 four times
  • Explain why 7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4

• Comparing Decimals

  Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <

  • Compare 0.45 and 0.405 and explain which is greater
  • Order 3.142, 3.14, 3.2 from smallest to largest
  • Justify that 0.7 = 0.70 = 0.700 using place-value reasoning

• Multiplying fractions

  Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)

  • Calculate 4 × 3/8 using repeated addition or the rule n × a/b = (n×a)/b
  • Multiply 2 1/3 × 3 and express as a mixed number
  • Use a visual model to show why 5 × 1/4 = 5/4

• Percentage and decimal equivalents

  Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25

  • State that 1/5 = 20% = 0.2 and use this to find 20% of 60
  • Convert 3/4 to 75% and to 0.75
  • A shop offers 25% off a £40 item — what is the sale price?

• Understanding Percentages

  Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal

  • Write 35% as 35/100 and as 0.35
  • Shade 40% of a 10×10 grid and write the fraction 40/100
  • Explain that 100% means the whole, 50% means half

• Fraction-Decimal Equivalents

  Recognise and write decimal equivalents of 1/4, 1/2, and 3/4

  • State that 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75
  • Match fractions to decimals in a sorting activity
  • Explain why 1/4 = 25/100 = 0.25 using a hundredths grid

• Decimal place value (age 8+)

  Compare numbers with the same number of decimal places up to two decimal places

  • Order 0.45, 0.54, 0.39 from smallest to largest
  • Compare 3.72 and 3.27 using place-value reasoning
  • Place three two-decimal-place numbers on a number line in order

• Adding fractions (different denominators)

  Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator

  • Calculate 1/3 + 1/6 by converting to sixths: 2/6 + 1/6 = 3/6 = 1/2
  • Calculate 3/4 − 1/8 by converting to eighths
  • Add 2/5 + 3/10 and simplify the answer

• Dividing by 10 and 100

  Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits as ones, tenths, and hundredths

  • Calculate 37 ÷ 10 = 3.7 and identify 3 as ones and 7 as tenths
  • Calculate 4 ÷ 100 = 0.04 and identify 4 as hundredths
  • Explain that dividing by 10 shifts each digit one place to the right

• Adding Fractions (Same Denominator)

  Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)

  • Calculate 3/5 + 4/5 = 7/5 and explain it equals 1 2/5
  • Subtract 2/6 from 5/6
  • Solve addition problems where the sum exceeds the whole: 7/8 + 3/8

• Comparing fractions (age 9+)

  Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models

  • Compare 3/8 and 5/12 by finding a common denominator of 24
  • Order 2/3, 3/5, and 7/10 from smallest to largest
  • Use the benchmark 1/2 to decide that 5/8 > 3/7

• Fraction Addition Concepts

  Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way

  • Show that 3/8 = 1/8 + 1/8 + 1/8 and also 3/8 = 1/8 + 2/8
  • Write two different decompositions of 5/6
  • Use a visual model to justify a decomposition of 2 1/8 into whole-number and fraction parts

• Comparing fractions (age 8+)

  Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols

  • Compare 3/8 and 3/4: same numerator, larger denominator means smaller pieces so 3/8 < 3/4
  • Compare 5/6 and 2/6: same denominator so 5/6 > 2/6
  • Justify a comparison using a visual model and explain why both fractions must refer to the same whole

• Decimals to three places

  Solve problems involving numbers with up to three decimal places

  • Calculate the total of three measurements: 1.234 m + 0.567 m + 2.199 m
  • A bottle holds 1.5 litres; 0.375 l is poured out — how much remains?
  • Find two numbers with 3 d.p. that add to make 1

• Mixed numbers and improper fractions

  Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)

  • Convert 11/4 to 2 3/4
  • Convert 3 2/5 to 17/5
  • Write 6/5 + 4/5 = 10/5 = 2 as both improper fraction and whole number

• Fractions of a whole (age 8+)

  Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6)

  • Write 5 as 5/1 and explain why
  • Locate 4/4 and 1 at the same point on a number line
  • Identify which fractions from a list equal a whole number: 6/3, 8/4, 5/2

• Adding and subtracting mixed numbers

  Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations

  • Calculate 2 3/5 + 1 4/5 and express as a mixed number
  • Subtract 3 1/4 from 5 3/4
  • Solve 4 2/6 − 1 5/6 by regrouping the whole number

• Addition and subtraction word problems

  Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations

  • A jug contains 3/4 litre of juice; 2/4 litre is poured out — how much remains?
  • Two pieces of ribbon are 2 3/8 and 1 5/8 inches — what is their total length?
  • Draw a fraction model to represent and solve a fraction word problem

• Fractions of amounts (harder)

  Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number

  • Find 3/5 of 20
  • Calculate 2/3 of 18 and explain the two-step process (divide then multiply)
  • Solve: A bag has 24 sweets, 3/8 are red — how many red sweets?

• Decimals and fractions

  Solve simple measure and money problems involving fractions and decimals to two decimal places

  • Calculate 1/4 of £3.20
  • A rope is 2.5 m long; how much is left after cutting 0.75 m?
  • Find 3/10 of 1 kg and express the answer in grams and as a decimal of a kg

• Decimal place value

  Round decimals with one decimal place to the nearest whole number

  • Round 3.7 to 4 and 3.2 to 3
  • Place 6.5 on a number line between 6 and 7 and decide it rounds to 7
  • Round a set of one-decimal-place numbers and explain the rounding rule

• Decimal place value (age 9+)

  Round decimals with two decimal places to the nearest whole number and to one decimal place

  • Round 3.47 to the nearest whole number (3) and to 1 d.p. (3.5)
  • Round 12.95 to 1 d.p. (13.0) and explain the boundary case
  • Estimate 4.83 + 2.17 by rounding each to the nearest whole number

• Fractions of a whole (age 9+)

  Solve word problems involving multiplication of a fraction by a whole number using visual models and equations

  • Each person eats 3/8 of a pizza and there are 5 people — how many pizzas are needed?
  • A ribbon is cut into pieces of 2/3 metre; how long are 4 pieces altogether?
  • Between what two whole numbers does 6 × 3/4 lie?

• Fractions as parts of shapes

  Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole

  • Partition a rectangle into 6 equal-area parts and label each 1/6
  • Show two different ways to partition a square into 4 equal parts
  • Given a pre-partitioned shape, write the unit fraction for one part

Multiplication & Division

Your child is mastering more complex multiplication and division — working with larger numbers, understanding factors and multiples, solving multi-step problems, and beginning to use formal written methods.

• What Multiplication Means

  Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)

  • Explain that 4 × 6 means 4 groups of 6 objects
  • Draw a picture or array to represent a multiplication expression
  • Match a multiplication expression to a word problem involving equal groups

• All times tables to 12×12

  Recall multiplication and division facts for multiplication tables up to 12 × 12

  • Recall any fact from the 1–12 times tables rapidly
  • Recall the corresponding division fact for any multiplication fact
  • Use known facts to check or derive answers in calculations

• Long multiplication

  Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models

  • Calculate 2,347 × 6 using formal written layout
  • Calculate 34 × 27 using long multiplication
  • Draw an area model for 45 × 23 and connect to the written method

• Written Multiplication

  Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

  • Set out and solve 47 × 6 using short multiplication
  • Set out and solve 234 × 5 using short multiplication with carrying
  • Check the answer using estimation (e.g. 234 × 5 ≈ 200 × 5 = 1000)

• Properties of Operations

  Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide

  • Use commutativity: if 6 × 4 = 24 then 4 × 6 = 24
  • Use the distributive property: 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56
  • Use associativity to multiply three numbers: 2 × 3 × 5 = 6 × 5 = 30

• Fluent multiplication and division facts

  Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division

  • Answer any single-digit multiplication fact within 3 seconds
  • Answer any related division fact within 3 seconds
  • Use known facts to derive unknown facts (e.g. 9 × 7 from 10 × 7 − 7)

• Division as Unknown Factor

  Understand division as an unknown-factor problem (e.g. find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8)

  • Explain that 32 ÷ 8 = ? is the same as 8 × ? = 32
  • Use a known multiplication fact to find a division answer
  • Describe the relationship between multiplication and division as inverse operations

• Division with remainders

  Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation

  • 52 children go on a trip in minibuses holding 9 each — how many minibuses are needed? (interpret remainder)
  • A shop sells packs of 6 pencils for £1.50 each — how much do 5 packs cost?
  • Represent a two-step problem with an equation using n for the unknown

• What Division Means

  Interpret whole-number quotients (e.g. 56 ÷ 8 as the number of objects in each share or the number of equal groups)

  • Explain that 56 ÷ 8 can mean sharing 56 into 8 equal groups or making groups of 8
  • Draw a picture to represent a division expression
  • Match a division expression to a word problem involving equal sharing or grouping

• Arrays for multiplication (age 9+)

  Divide numbers up to four digits by a one-digit number using short division (and place-value/array strategies); interpret remainders appropriately for the context

  • Calculate 4,932 ÷ 6 using short division
  • Solve 125 ÷ 8 and interpret: 15 remainder 5 means 15 full bags with 5 left over
  • Use the multiplication–division relationship to check a division answer

• Multiply & Add Problems

  Solve problems involving multiplying and adding, including using the distributive law, integer scaling problems, and harder correspondence problems

  • Use the distributive law to solve 14 × 6 as 10 × 6 + 4 × 6
  • Solve a scaling problem (e.g. 'A tower is 3 times as tall as a 15 m building')
  • Solve a correspondence problem (e.g. '3 types of bread, 4 types of filling — how many different sandwiches?')

• Factor Pairs & Commutativity

  Recognise and use factor pairs and commutativity in mental calculations

  • List all factor pairs of a given number (e.g. 24: 1×24, 2×12, 3×8, 4×6)
  • Use commutativity to reorder a multiplication for easier mental calculation
  • Explain what a factor pair is and how commutativity helps

• Factors, multiples, and primes

  Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems

  • List all factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6)
  • State the first five multiples of 7
  • Find the common factors of 24 and 36

• Multiplying and dividing

  Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

  • Calculate 3.45 × 100 = 345
  • Calculate 72 ÷ 1000 = 0.072
  • Explain that multiplying by 10 shifts each digit one place to the left

• Multiplicative Comparison

  Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations

  • Explain that '4 times as many' means multiply by 4
  • Write an equation for: Sarah has 3 times as many stickers as Tom, who has 8 stickers
  • Distinguish multiplicative comparison from additive comparison in word problems

• Patterns in Times Tables

  Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations

  • Notice that all products of 5 end in 0 or 5 and explain why
  • Observe that the sum of two even numbers is always even
  • Identify a pattern in the multiplication table and explain it using commutativity or the distributive property

• Shape patterns

  Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

  • Given 'start at 1, add 3', generate terms and notice they alternate odd/even
  • Given a shape pattern, predict the next three terms and describe the rule
  • Explain why starting at 2 and adding 4 always gives even numbers

• Understanding fractions

  Solve problems involving scaling by simple fractions and problems involving simple rates

  • A recipe for 4 people needs 200 g of flour — how much for 6 people?
  • If 3 kg costs £12, how much does 5 kg cost?
  • Scale a shape by a factor of 1/2 and find the new dimensions

• Multiplying by Tens

  Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations

  • Calculate 7 × 30 = 210 by reasoning 7 × 3 tens = 21 tens = 210
  • Explain why multiplying by a multiple of 10 adds a zero to the product
  • Use this skill to estimate products of larger numbers

• Mental multiplication and division

  Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers

  • Calculate 40 × 6 = 240 mentally using place value
  • Explain why any number × 0 = 0 and any number × 1 = the number itself
  • Multiply three numbers mentally by choosing a useful pair first (e.g. 2 × 7 × 5 = 2 × 5 × 7 = 70)

• Factors, multiples, and primes (age 9+)

  Solve problems involving multiplication and division using knowledge of factors, multiples, squares, and cubes

  • Is 156 a multiple of 6? Explain how you know
  • Find two square numbers that add to make 100
  • Use factor pairs to simplify 24 × 25 as 6 × (4 × 25) = 6 × 100 = 600

• Mental multiplication and division (age 9+)

  Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments

  • Calculate 40 × 60 mentally by using 4 × 6 = 24 then appending zeros
  • Derive 7 × 15 by calculating 7 × 10 + 7 × 5
  • Calculate 360 ÷ 9 mentally using 36 ÷ 9 = 4

• Prime numbers

  Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19

  • Explain that a prime number has exactly two factors: 1 and itself
  • Determine whether 51 is prime or composite and justify the answer
  • List all prime numbers up to 19 from memory

• Multiplicative Comparison

  Solve word problems involving multiplicative comparison using drawings and equations with a symbol for the unknown number

  • A blue ribbon is 3 times as long as a red ribbon of 7 cm — how long is the blue ribbon?
  • 36 is 4 times a number — what is the number?
  • Explain why 'Sam has 5 more' is additive but 'Sam has 5 times as many' is multiplicative

• Multiplication and Division Word Problems

  Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities

  • Solve an equal-groups word problem using multiplication
  • Solve a measurement division problem (e.g. 'How many 4-cm pieces from a 28-cm ribbon?')
  • Solve an array/area word problem using multiplication

• Square and cube numbers

  Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

  • Identify 49 as 7² and explain that 7 × 7 = 49
  • Calculate 4³ = 64 and explain it means 4 × 4 × 4
  • List the first ten square numbers

• Unknown in Multiplication & Division

  Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)

  • Find the missing factor in 7 × ? = 63
  • Find the missing dividend in ? ÷ 5 = 9
  • Explain the strategy used (e.g. using the related multiplication fact)

Geometry

Your child is learning to measure and work with angles using protractors, classify shapes by their properties, and understand transformations like reflections and translations while exploring how angles relate to each other.

• Types of angles

  Identify acute and obtuse angles; compare and order angles up to two right angles by size

  • Classify given angles as acute, right, or obtuse
  • Order four angles from smallest to largest by visual comparison
  • Identify all acute and obtuse angles in a given triangle or quadrilateral

• Types of angles (age 8+)

  Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown values

  • Mark a right angle with a small square symbol in a diagram and explain what it means
  • Use tick marks to show equal lengths in a shape and double tick marks for a second pair of equal sides
  • Read and interpret angle notation (e.g. angle ABC) and identify the angle being referred to in a diagram

• Degrees and turns

  Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees

  • Explain that a full turn is 360° and a right angle is 90°
  • Describe what 'one degree' means in terms of a fraction of a circle
  • State that an angle of 45° has turned through 45 one-degree angles

• What Is an Angle?

  Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes

  • Identify the vertex and arms of an angle in a diagram
  • Find examples of angles in the classroom (e.g. open door, clock hands)
  • Explain why two rays meeting at a point form an angle

• Measuring angles

  Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure

  • Measure an angle with a protractor and read 47°
  • Draw an angle of 135° using a protractor
  • Identify which scale on the protractor to use for an obtuse angle

• Lines, Rays & Angles

  Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures

  • Draw a pair of perpendicular lines and a pair of parallel lines
  • Identify all pairs of parallel sides in a trapezoid
  • Mark a right angle, an acute angle, and an obtuse angle in a given figure

• Understanding angles (age 8+)

  Understand that shapes in different categories may share attributes defining a larger category; classify quadrilaterals (rhombuses, rectangles, squares) and draw examples of quadrilaterals not in those subcategories

  • Explain that a square is a special rectangle and also a special rhombus
  • Sort shapes into a Venn diagram: quadrilaterals vs rectangles vs squares
  • Draw a quadrilateral that is not a rectangle, rhombus, or square

• Angle Sum Rules

  Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles

  • State that two angles on a straight line add to 180°
  • Explain that four right angles at a point make 360°
  • Identify 270° as three right angles

• Regular and irregular polygons

  Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles

  • Classify a set of polygons as regular or irregular
  • Explain that a regular pentagon has 5 equal sides and 5 equal angles
  • Identify that a rectangle is irregular (equal angles but not all equal sides) unless it is a square

• First Quadrant Coordinates

  Describe positions on a 2-D grid as coordinates in the first quadrant

  • Read the coordinates of a point on a grid as (3, 5)
  • Explain that the first number is the horizontal distance and the second is the vertical distance
  • Identify the coordinates of all vertices of a shape plotted on a grid

• Measuring angles (age 9+)

  Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown

  • Two angles on a straight line are 65° and x°; find x = 115°
  • An angle is decomposed into 35° and 40°; state the whole angle is 75°
  • Solve: angles at a point are 120°, 90°, and x°; find x = 150°

• Estimating Angles

  Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size

  • Estimate an angle as approximately 130° and classify it as obtuse
  • Identify a reflex angle in a diagram and estimate it as about 270°
  • Order four angles from smallest to largest by estimation before measuring

• Classifying shapes by line properties

  Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category

  • Sort a set of quadrilaterals into those with parallel sides and those without
  • Identify which triangles in a set are right triangles
  • Classify shapes that have both perpendicular and parallel sides

• Understanding angles (age 9+)

  Use the properties of rectangles to deduce related facts and find missing lengths and angles

  • Given one side of a rectangle is 8 cm and the perimeter is 28 cm, find the other side
  • Explain that all angles in a rectangle are 90°
  • Find a missing side of a rectangle given its area and one side length

• Coordinates (age 8+)

  Plot specified points on a coordinate grid and draw sides to complete a given polygon

  • Plot points (1,1), (1,4), (5,4), (5,1) and join to make a rectangle
  • Given three vertices of a square, plot the fourth vertex
  • Complete a triangle by plotting the third vertex at given coordinates and drawing sides

• 3-D shapes (age 9+)

  Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

  • Identify a cuboid from its net
  • Name the 3-D shape shown in an isometric drawing
  • Match 2-D representations to the correct 3-D shape

• Transformations on a Grid

  Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed

  • Reflect a triangle in a vertical mirror line on a coordinate grid and state the new coordinates
  • Translate a shape 3 units right and 2 units up and describe the movement
  • Explain that a reflected/translated shape is congruent to the original

• Transformations on a grid

  Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

  • Reflect a shape in a given mirror line on a grid and label the new coordinates
  • Translate a shape by a given number of squares horizontally and vertically and describe the movement
  • Rotate a shape 90° or 180° about a given centre on a grid and check the image is congruent to the original

• Nets of 3-D Shapes

  Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net

  • Draw the net of a cube, cuboid, or triangular prism and fold it mentally to identify which faces connect
  • Build a 3-D shape from its net and check that all faces, edges, and vertices match
  • Identify which of several given nets will fold into a specific 3-D shape and explain why the others won't

• Describing Movements

  Describe movements between positions as translations of a given unit to the left/right and up/down

  • Describe moving from (2,3) to (5,3) as 3 units to the right
  • Translate a shape 4 units right and 2 units up and state the new coordinates
  • Predict where a point will be after a given translation

• 2-D shapes (age 8+)

  Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

  • Find all lines of symmetry in a rectangle, square, and equilateral triangle
  • Determine whether a given shape has a line of symmetry when rotated
  • Identify which shapes in a set have exactly one line of symmetry

• Lines of symmetry

  Complete a simple symmetric figure with respect to a specific line of symmetry

  • Given half a butterfly shape and a mirror line, complete the other half on a grid
  • Complete a symmetric pattern on squared paper with a vertical line of symmetry
  • Check a completed figure by folding along the mirror line

Measurement

Your child is mastering advanced measurement skills — calculating area and perimeter of shapes, working with fractions in measurements, converting between different units, and solving real-world problems involving distance, time, and volume.

• Area (age 8+)

  Measure areas by counting unit squares (square cm, square m, square in, square ft)

  • Count unit squares to find the area of an L-shaped figure
  • Measure the area of a book cover using square-centimetre tiles
  • Compare areas of two shapes by counting their unit squares

• Understanding Area

  Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps

  • Identify a unit square and state its area is 1 square unit
  • Explain why a figure covered by 12 unit squares has area 12 square units
  • Distinguish between area and perimeter as different measurements

• Area by Tiling

  Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths

  • Tile a 4×6 rectangle and count 24 squares, then verify 4×6=24
  • Explain why the number of rows times the number in each row gives the area
  • Draw a rectangle on squared paper, tile it, and write the multiplication

• Understanding angles (age 8+)

  Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas

  • Calculate the area of a 7 cm × 9 cm rectangle as 63 cm²
  • Draw a rectangle with area 36 square units and label its side lengths
  • Solve: A garden is 8 m by 5 m — what is its area?

• Area and the distributive property

  Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property

  • Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2
  • Use an area model to compute 6×13 as 6×10 + 6×3
  • Draw an area model showing 5×(7+3) = 5×7 + 5×3

• Fractions on a number line

  Solve word problems involving distances, time intervals, liquid volumes, masses, and money using the four operations with fractions or decimals; represent with diagrams including number lines

  • A 2.5 kg bag of flour is split equally into 4 portions — what does each weigh?
  • A journey takes 1 hr 45 min; what time do you arrive if you leave at 09:20?
  • Three ribbons of 0.75 m, 1.2 m, and 0.95 m — what is the total length?

• Converting measurement units

  Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)

  • Convert 3 km to 3000 m
  • State 2 hours = 120 minutes
  • Convert 5 weeks to 35 days

• Telling time to the minute (age 9+)

  Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)

  • Convert 3 hours 25 minutes to 205 minutes
  • A programme lasts 150 seconds — express in minutes and seconds
  • How many days are in 8 weeks and 3 days?

• Converting measurement units (age 9+)

  Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables

  • Convert 3.5 km to 3,500 m
  • Complete a conversion table for cm and mm: (1,10), (2,20), (3,30)...
  • Express 2 kg 350 g as 2,350 g

• Perimeters of polygons

  Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)

  • Calculate the perimeter of a rectangle with sides 8 cm and 5 cm
  • Find the missing side of a pentagon with perimeter 30 cm and four known sides
  • Draw two rectangles both with perimeter 24 cm but different areas

• Estimating answers (age 9+)

  Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes

  • Find the width of a room given area = 48 m² and length = 8 m
  • Calculate the area of a square with side 7.5 cm
  • Estimate the area of an irregular pond drawn on a cm² grid

• Measurement Line Plots

  Make a line plot to display measurement data in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using line plot data

  • Create a line plot of seed growth measurements in 1/8-inch increments
  • Use a line plot to find the difference between the longest and shortest specimens
  • Calculate the total length of all items in a line plot by adding the fractional measurements

• Metric & Imperial Conversion

  Understand and use approximate equivalences between metric units and common imperial units (inches, pounds, pints)

  • State that 1 inch ≈ 2.5 cm and use this to estimate length in inches
  • Know that 1 kg ≈ 2.2 pounds and estimate a person's weight in pounds
  • Convert approximately between litres and pints (1 litre ≈ 1.75 pints)

• Numbers on a number line

  Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line

  • A film starts at 2:15 and lasts 47 minutes — when does it end?
  • Calculate how many minutes between 9:20 and 10:05
  • Use a number line to show the elapsed time between two events

• Halves and quarters (age 8+)

  Generate measurement data by measuring lengths to the nearest half and quarter inch; display the data on a line plot with a scale marked in whole numbers, halves, and quarters

  • Measure five objects to the nearest 1/4 inch
  • Create a line plot showing the lengths of classmates' pencils in half-inches
  • Read a line plot and answer questions about the data

• Telling time to the minute (age 8+)

  Tell and write time to the nearest minute using analogue and digital clocks

  • Read 7:43 from an analogue clock face
  • Write 11:06 on a digital display given a clock with hands
  • Match analogue and digital times to the nearest minute

• Perimeter of Compound Shapes

  Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

  • Find the perimeter of an L-shaped figure by identifying all side lengths
  • Calculate the perimeter of a composite shape where some sides must be deduced
  • Draw a composite rectilinear shape with a perimeter of 40 cm

• Estimating and comparing money

  Estimate, compare, and calculate different measures including money in pounds and pence

  • Estimate the length of the classroom in metres
  • Compare 1.5 kg and 1200 g and identify which is heavier
  • Calculate the total cost of 3 items at £2.45, £1.30, and £0.75

• Measuring Liquids & Masses

  Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume

  • Estimate the mass of a textbook in grams or kilograms
  • Read a scale to measure liquid volume in litres
  • Solve: 3 bags weigh 250 g each — what is the total mass?

• Estimating volume

  Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water

  • Build a cuboid from 1 cm³ blocks and state its volume
  • Estimate how many cm³ blocks would fill a given box
  • Estimate the capacity of a jug by comparing to known litre measures

• Area of compound shapes

  Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas

  • Decompose an L-shape into two rectangles, find each area, and add them
  • Find the area of a floor plan shaped like a T by splitting into rectangles
  • Solve: A room is L-shaped (3m×5m plus 2m×4m) — what is the total area?

• 12-hour and 24-hour time

  Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks

  • Convert 3:45 pm to 15:45 in 24-hour time
  • Read 19:30 and state the 12-hour equivalent as 7:30 pm
  • Match a set of 12-hour and 24-hour times

Mathematical Thinking

Your child is developing advanced problem-solving skills, learning to choose the best mathematical tools and methods for complex problems, and communicating their mathematical reasoning clearly.

• Complex Multi-Step Problems

  Make sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning multi-step strategies, and evaluating reasonableness through estimation and inverse operations

  • Break a three-step problem involving unit conversion and multiplication into sub-problems and solve systematically
  • Estimate 4,832 × 7 as roughly 5,000 × 7 = 35,000 to check a calculated answer of 33,824
  • Identify that a percentage answer over 100% doesn't make sense in context

• Precise Maths Vocabulary

  Communicate with mathematical precision: use correct vocabulary for primes, factors, multiples, angle types, and polygon regularity; specify units including cm², m³, °; use notation for squares/cubes and percentages accurately

  • Distinguish 'factor' from 'multiple' in a written explanation
  • Write an area answer as 48 cm² (not just 48) and a volume estimate as approximately 60 cm³
  • Use 5² notation correctly and read it as 'five squared'

• Understanding fractions (age 9+)

  Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods

  • Prove that 3/4 > 2/3 using a common denominator argument and a visual model
  • Find and explain an error in a long multiplication where a partial product was misaligned
  • Present a chain of reasoning to show that angles in a triangle sum to 180° by tearing and arranging

• Real-World Maths Modelling

  Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context

  • Model a recipe-scaling problem with multiplication and fractions, then interpret the answer in grams
  • Represent a room-carpet problem by drawing a scale diagram and applying the area formula
  • Use a percentage bar model to find a sale price and explain the answer in £

• Choosing representations strategically

  Select and use tools and representations strategically: choose between mental methods, formal written methods, protractors, fraction strips, and diagrams based on the demands of the problem

  • Choose mental multiplication for 25 × 40 but long multiplication for 347 × 26
  • Select a protractor to verify an estimated angle rather than relying on visual inspection alone
  • Choose a common-denominator approach vs. benchmark comparison for ordering fractions, and explain why

• Mathematical Precision

  Communicate with mathematical precision: use correct fraction/decimal vocabulary, name angle types accurately, specify units in measurement and money, and use notation (=, <, >, ÷, ×) correctly

  • Distinguish between 'three fourths' and 'three quarters' and use both correctly
  • State an answer in the correct unit: '63 square centimetres' not just '63'
  • Write 15:45 in 24-hour notation and explain the distinction from 3:45 pm

• Multi-Step Problem Solving

  Make sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress

  • Break a two-step word problem into parts and explain a plan before calculating
  • Choose between drawing a diagram or writing equations for a perimeter problem
  • Check a fraction-of-quantity answer by estimating: 3/5 of 20 must be more than half of 20

• Fractions on a number line (age 9+)

  Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations

  • Represent a scaling problem as both a bar model and a multiplication equation
  • Show how 0.35, 35/100, and 35% all represent the same quantity on a hundredths grid
  • Translate a line-graph reading into a subtraction equation to find the difference

• Justifying mathematical reasoning (age 8+)

  Construct and present multi-step mathematical arguments; critique the reasoning of others and explain clearly why a method works or fails

  • Explain why 1/3 > 1/5 using the idea that more parts means smaller pieces
  • Find and explain an error in a peer's column subtraction with exchanges
  • Present a chain of reasoning: since 6×8=48 and 6×2=12, then 6×10=60 so 6×8=60−12=48

• Reasoning with Equivalences

  Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

  • Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why
  • Describe the general rule for a sequence and predict the 20th term
  • Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number

• Choosing mathematical tools

  Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task

  • Decide to use mental multiplication for 25×4 but a written method for 167×3
  • Choose fraction strips rather than a number line to compare 3/8 and 1/4
  • Use a ruler and squared paper to verify area by counting squares after calculating l×w

• Modelling with multiplication and fractions

  Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context

  • Model a tiling/area problem with an array and write the corresponding multiplication
  • Represent a recipe-scaling problem as a fraction calculation and interpret the answer in grams
  • Use a bar model to set up a unit conversion problem (metres to centimetres)

• Fractions, Decimals & Percentages

  Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically

  • Use the structure 25 × 16 = 25 × 4 × 4 = 100 × 4 = 400 by exploiting factor pairs
  • Recognise that 0.75 = 3/4 = 75% and use whichever form is most efficient for the problem
  • Use the fact that angles on a straight line sum to 180° as a structural tool to find missing angles

• Times tables (age 8+)

  Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently, describe general rules

  • Notice that all fractions equivalent to 1/2 have a numerator that is half the denominator
  • Use the pattern 3×4=12, 3×40=120, 3×400=1200 and explain the generalisation
  • Derive 8×7 from 8×5=40 plus 8×2=16 and describe the strategy as a general approach

• Fractions on a number line

  Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows

  • Represent a sharing problem as both a fraction diagram and a division equation
  • Explain how a bar model for 4 × 23 connects to the area model and the written method
  • Translate a decimal on a number line into a fraction and explain the equivalence

• Using Mathematical Structure

  Look for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction equivalence to compare and compute, use shape properties to classify quadrilaterals

  • Decompose 7×13 into 7×10 + 7×3 using the distributive property
  • Explain why multiplying by 10 shifts digits one place left using place-value structure
  • Use the fact that a square is a special rectangle to reason about quadrilateral properties

Number Representation & Place Value

Your child is working with larger numbers up to 1 million — understanding place value, rounding to different levels of accuracy, and beginning to work with negative numbers in everyday contexts.

• Place value of each digit

  Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

  • State the value of each digit in a four-digit number (e.g. in 7,345 the 7 represents 7 thousands)
  • Partition a four-digit number into thousands, hundreds, tens, and ones
  • Compose a four-digit number from given place-value parts (e.g. 3000 + 400 + 50 + 2 = 3,452)

• Place Value × 10 Pattern

  Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)

  • Explain that the 3 in 3,000 is ten times the 3 in 300
  • Complete: 700 ÷ 70 = __ and explain using place-value reasoning
  • State how many times greater the value of the 5 in 50,000 is than the 5 in 5,000

• Reading and writing numbers (age 9+)

  Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding

  • Write 403,072 in words and in expanded form
  • Compare 548,301 and 543,801 using < and explain the reasoning
  • Order four six-digit numbers from smallest to largest

• Comparing Large Numbers

  Order and compare numbers beyond 1000

  • Compare two four-digit numbers using >, <, and = by examining digits from the highest place value
  • Order a set of numbers up to 10,000 from smallest to largest
  • Justify the ordering using place-value reasoning

• Negative Numbers

  Count backwards through zero to include negative numbers

  • Count backwards from 5 through zero: 5, 4, 3, 2, 1, 0, −1, −2 …
  • Place negative numbers on a number line
  • Understand that negative numbers are less than zero and use them in context (e.g. temperature)

• Negative numbers in context

  Interpret negative numbers in context (temperature, sea level, bank balance); count forwards and backwards with positive and negative whole numbers, including through zero

  • Place –3, –1, 0, 2, 5 on a number line
  • The temperature is –4°C and rises by 7 degrees — what is the new temperature?
  • Count backwards from 3 in ones: 3, 2, 1, 0, –1, –2

• Rounding to 10, 100, 1000

  Round any number to the nearest 10, 100, or 1000

  • Round 4,367 to the nearest 10 (4,370), 100 (4,400), and 1000 (4,000)
  • Explain the rounding rule using a number line (which multiple is closer)
  • Apply rounding to estimate calculations

• Rounding Large Numbers

  Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding

  • Round 456,782 to the nearest 10,000 (460,000)
  • Round 950,500 to the nearest 100,000 and explain the boundary case
  • Use rounding to estimate the sum of 387,412 + 214,560

• Numbers to 10,000

  Identify, represent, and estimate numbers up to 10,000 using different representations

  • Represent a four-digit number on a place-value chart or with base-ten materials
  • Estimate where a number falls on a 0–10,000 number line
  • Match different representations of the same number (e.g. expanded form, place-value counters, numeral)

• Working with Large Numbers

  Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000

  • What is the largest six-digit number with digits summing to 15?
  • A stadium holds 67,450 people. Round to the nearest thousand for a news report
  • Order the populations of five cities and find the difference between the largest and smallest

• Place Value Problem-Solving

  Solve number and practical problems involving place value with increasingly large positive numbers

  • Solve a problem requiring rounding, comparing, or ordering numbers beyond 1000
  • Apply place-value knowledge in a practical context (e.g. population figures, distances)
  • Explain the strategy used, referencing place-value understanding

• Counting forwards and backwards (age 9+)

  Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000

  • Count on in 10,000s from 462,000
  • Count back in 100,000s from 800,000
  • Identify the next three terms: 375,000; 475,000; 575,000; ...

• 1000 More or Less

  Find 1000 more or less than a given number

  • Given 4,562, state that 1000 more is 5,562 and 1000 less is 3,562
  • Explain using place value that only the thousands digit changes
  • Apply this skill to numbers beyond 10,000

• Roman numerals to 100

  Read Roman numerals to 100 (I to C) and understand that the numeral system changed over time to include zero and place value

  • Read and write Roman numerals I, V, X, L, C and combinations up to 100
  • Convert between Roman numerals and Hindu-Arabic numerals (e.g. XLIV = 44)
  • Explain that Roman numerals have no zero and no place-value system

• Roman numerals to 1000

  Read Roman numerals to 1000 (M) and recognise years written in Roman numerals

  • Read MCMXCIX as 1999
  • Write 2024 in Roman numerals (MMXXIV)
  • Explain the subtractive principle: IV = 4 not IIII

Addition & Subtraction

Your child is mastering mental arithmetic with large numbers and using formal written methods for complex calculations, while learning to choose the most efficient method for different types of problems.

• 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

• Two-Step Equations

  Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity

  • Solve a two-step problem that combines addition/subtraction with multiplication/division
  • Write an equation using a letter for the unknown (e.g. 3 × n + 5 = 26)
  • Assess the reasonableness of the answer using estimation and mental computation

• Adding and subtracting (age 9+)

  Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

  • A school collects 12,450 bottles in Week 1 and 8,372 in Week 2; their target is 25,000 — how many more do they need?
  • Choose between mental and written methods for each step and explain why
  • Solve a three-step problem involving addition and subtraction of five-digit numbers

• Checking Answers by Rounding

  Use rounding to check answers to calculations and determine appropriate levels of accuracy in context

  • Check 47,832 + 23,156 ≈ 48,000 + 23,000 = 71,000 to verify the exact answer 70,988
  • Decide whether to round to the nearest 100 or 1,000 for a given estimation context
  • Identify that a calculated answer of 3,421 cannot be correct because the estimate gives approximately 50,000

• Adding and subtracting (age 8+)

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

  • Set out and solve a columnar addition with up to four-digit numbers
  • Set out and solve a columnar subtraction with exchange across multiple columns
  • Check the answer using estimation or inverse operations

• Two-step addition and subtraction problems

  Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

  • Identify the two steps needed to solve a contextual problem
  • Choose between mental and written methods for each step based on the numbers
  • Explain why the chosen operations and methods are appropriate

• Fluent addition and subtraction (age 9+)

  Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm

  • Calculate 34,567 + 28,945 using columnar addition
  • Calculate 500,000 − 234,178 using columnar subtraction with multiple exchanges
  • Add three five-digit numbers in a single column layout

• Mental addition and subtraction (age 9+)

  Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts

  • Mentally calculate 45,000 + 8,000
  • Mentally subtract 3,200 from 10,000 by counting up
  • Use near-doubles: 2,500 + 2,600 = 5,100

• Fluent adding and subtracting within 1000

  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction

  • Add two three-digit numbers fluently using an efficient method
  • Subtract three-digit numbers fluently, including with regrouping
  • Choose the most efficient strategy based on the numbers involved

Data & Statistics

Your child is learning to work with data — reading timetables and graphs, and solving problems by interpreting the information presented in charts and line graphs.

• 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

• Representing numbers with objects (age 8+)

  Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables

  • Draw a bar graph where each square represents 5 pets
  • From a scaled pictogram, answer: how many more children chose football than tennis?
  • Solve a two-step problem: how many votes in total for the top two choices?

• Reading tables

  Complete, read, and interpret information in tables, including timetables

  • Read a bus timetable to find the departure time for a particular stop
  • Complete a two-way table from given data about favourite sports by gender
  • Calculate how long a train journey takes using a timetable

• Bar graphs

  Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

  • Read a time graph showing temperature changes over a day
  • Present data about plant growth over weeks as a time graph
  • Explain the difference between a bar chart (discrete) and a time graph (continuous)

• Reading and Comparing Bar Graphs

  Solve comparison, sum, and difference problems using information presented in a bar graph

  • Read a line graph of temperature over a week and identify the warmest day
  • Find the difference in rainfall between two months from a line graph
  • Explain what a rising/falling line means on a time-series graph

• Statistical Analysis Vocabulary

  Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes

  • Correctly define and calculate the mean, median, mode, and range of a small data set
  • Use 'outlier' correctly to identify a value that doesn't fit the pattern, and explain its effect on the mean
  • Use 'correlation' correctly when describing the relationship shown in a scatter graph

Probability

• Probability as a Fraction

  Describe the probability of simple equally-likely outcomes using unit fractions: the probability of rolling a 6 on a fair die is 1/6, flipping heads is 1/2, picking one specific colour from three equally represented colours is 1/3; place these fractional probabilities on a 0-to-1 probability scale

  • State that the probability of rolling a 6 on a fair die is 1/6 and explain why
  • Express the probability of picking a red card from a standard deck as 26/52 or 1/2
  • Write the probability of a simple event as a fraction: favourable outcomes over total outcomes

• Simple Chance Experiments

  Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes

  • Flip a coin 20 times, record heads and tails in a tally chart, and describe what they notice about the results
  • Roll a die 30 times and compare how often each number came up with what they expected
  • Pull counters from a bag, record results, and explain whether the outcomes matched their prediction

• Likelihood Language

  Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible

  • Place five everyday events (e.g. 'the sun will rise tomorrow', 'it will snow in July', 'I'll flip heads') on a scale from impossible to certain
  • Use 'likely', 'unlikely', 'certain', 'impossible', and 'even chance' correctly to describe different events
  • Explain why pulling a red ball from a bag of mostly red balls is 'likely' but not 'certain'

• Equally Likely Outcomes

  Understand that 'equally likely' means every outcome has exactly the same chance of occurring; identify whether a given situation has equally likely outcomes (a fair coin, a fair die, a spinner with equal sections) or unequally likely outcomes (a bag with more of one colour, a spinner with unequal sections)

  • Explain that a fair coin has equally likely outcomes because heads and tails each have the same chance
  • Identify whether a spinner with unequal sections has equally likely outcomes or not, and explain why
  • Give an example of a situation with equally likely outcomes and one without, explaining the difference

• Ordering Likelihoods

  Compare the likelihood of different events and order them from least to most likely — including situations with unequal outcomes such as a bag with more of one colour than another, or a spinner with sections of different sizes — and explain reasoning using informal language

  • Order four or more events from least likely to most likely and justify each placement
  • Compare likelihoods when outcomes are not equally likely — e.g. 'Drawing red from a bag with 7 red and 3 blue is more likely than drawing blue'
  • Explain why some events are closer to 'even chance' and others are closer to 'certain' or 'impossible'

Ratio & Proportion

• Bar Models for Ratios

  Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer

  • Draw a bar model to represent a ratio problem — e.g. sharing £20 in the ratio 3:2 by drawing 5 equal blocks
  • Use a bar model to solve a proportion problem and explain each step
  • Compare bar models with other representations (tables, double number lines) and explain when each is most useful

• Percentages (age 9+)

  Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)

  • Explain the difference between a 'ratio' and a 'proportion' using a concrete example like mixing paint
  • Use 'per cent' correctly and convert between fractions, decimals, and percentages in context
  • Define 'scale factor' and use it to describe how a shape has been enlarged or reduced

Counting & Cardinality

Your child is practicing skip-counting in larger number patterns, building fluency with multiples of 6, 7, 9, 25, and 1000.

• Counting in 6s

  Count in multiples of 6, 7, 9, 25, and 1000

  • Recite the multiples of 6 from 0 to at least 72
  • Recite the multiples of 7 from 0 to at least 84
  • Count in steps of 25 from 0 to 1000 and in steps of 1000 up to 10,000