Chapter library

Chapter 1: Why order matters: multiply and divide first

• Can multiply and divide before adding and subtracting, so 2 + 1 × 3 = 5

Year 6 maths

Chapter 2: Multiply and divide first: step-by-step calculations

• Can multiply and divide before adding and subtracting, so 2 + 1 × 3 = 5

Year 6 maths

Chapter 3: Equal priority: working left to right

• Can work from left to right when operations have equal priority, such as 12 ÷ 3 × 2 = 8

Year 6 maths

Chapter 4: Brackets first: (2 + 1) × 3 = 9

• Can work out the part in brackets first, so (2 + 1) × 3 = 9

Year 6 maths

Chapter 5: All four operations with brackets

• Can add brackets to a calculation to make it give a target answer
• Can work out calculations with all four operations and brackets in the right order

Year 6 maths

Chapter 1: Split it up: the distributive law for 2-digit × 1-digit

• Can multiply a two-digit number by a one-digit number by splitting it into tens and ones (the distributive law)

Year 4 maths

Chapter 2: Formal written method: 2-digit × 1-digit (short multiplication)

• Can multiply a two-digit number by a one-digit number using the formal written method (short multiplication)

Year 4 maths

Chapter 3: Formal written method: 3-digit × 1-digit (short multiplication)

• Can multiply a three-digit number by a one-digit number using the formal written method (short multiplication)

Year 4 maths

Chapter 4: Scaling problems: 'times as many', then multiply and add

• Can solve scaling problems such as 'times as many' and 'times as long', and problems where you multiply and then add

Year 4 maths

Chapter 5: Correspondence problems: n objects connected to m objects

• Can solve correspondence problems, where each of n objects connects to m objects, such as counting outfits or meal choices

Year 4 maths

Chapter 1: Writing multiplication and division statements

• Can write and work out multiplication and division statements using the times tables they know, like 3 × 4 = 12 and 12 ÷ 3 = 4

Year 3 maths

Chapter 2: Using times-table facts: doubling and multiplying tens

• Can use times-table facts they know to work out new ones, by doubling (2s, 4s, 8s) and by multiplying tens, like 3 × 40 = 120

Year 3 maths

Chapter 3: Multiplying two-digit by one-digit numbers mentally (partitioning)

• Can multiply a 2-digit number by a 1-digit number in their head by splitting it into tens and ones

Year 3 maths

Chapter 4: Written method: multiplying two-digit by one-digit numbers in columns

• Can use a written column method to multiply a 2-digit number by a 1-digit number, exchanging 10 ones for a ten when needed

Year 3 maths

Chapter 5: Dividing two-digit numbers by one-digit numbers

• Can divide a 2-digit number by a 1-digit number by sharing the tens and then the ones, and check the answer by multiplying

Year 3 maths

Chapter 6: Missing number problems with multiplication and division

• Can find the missing number in multiplication and division facts, like □ × 4 = 20, by using the inverse

Year 3 maths

Chapter 7: Scaling problems: times as many, times as tall

• Can solve scaling problems, like 3 times as tall or 4 times as many, by multiplying, and work out how many times bigger by dividing

Year 3 maths

Chapter 8: Correspondence problems: 3 hats and 4 coats make 12 outfits

• Can solve correspondence problems, such as 3 hats and 4 coats make 12 outfits, and sharing problems, by multiplying or dividing

Year 3 maths

Chapter 1: Short multiplication: 4-digit numbers × 1-digit numbers

• Can multiply a 4-digit number by a 1-digit number using short multiplication

Year 5 maths

Chapter 2: Long multiplication: multiplying by a 2-digit number

• Can multiply numbers up to 4 digits by a 2-digit number using long multiplication

Year 5 maths

Chapter 3: Short division: dividing 4-digit numbers by 1 digit, with remainders

• Can divide a 4-digit number by a 1-digit number using short division, with remainders

Year 5 maths

Chapter 4: Remainders that make sense: round up, round down or left over

• Can decide whether to round up, round down or use the remainder in a division problem

Year 5 maths

Chapter 5: Mixed problems and the meaning of the equals sign

• Can solve two-step problems that combine addition, subtraction, multiplication and division
• Can explain that the equals sign means both sides have the same value, and find missing numbers

Year 5 maths

Chapter 6: Scaling by simple fractions and simple rates

• Can scale amounts by whole numbers and simple fractions, and solve problems with simple rates

Year 5 maths

Chapter 1: Count it! Tally charts

• Can collect data with tally marks, count them quickly in fives and write the totals in a table

Chapter 2: Picture it! Pictograms

• Can read and draw pictograms where one picture stands for 2, 5 or 10, including half pictures

Chapter 3: Build it! Bar charts

• Can read and draw bar charts whose scale counts in 2s, 5s or 10s, including bars that stop between the lines

Chapter 4: Sort it! Tables

• Can read tables and two-way tables using rows, columns and totals, and fill in missing numbers

Chapter 5: Solve it! Data detective

• Can answer 'how many more?' and 'how many fewer?' questions in one or two steps using charts and tables

Chapter 1: Discrete and continuous data: counting or measuring?

• Can tell discrete data (counted) from continuous data (measured) and choose a bar chart or a time graph to show it

Year 4 maths

Chapter 2: Reading bar charts with different scales

• Can read bar charts with different scales, including bars that stop halfway between two lines

Year 4 maths

Chapter 3: Presenting data: drawing bar charts with a good scale

• Can present data in a bar chart by choosing a scale that fits, adding a title and labels, and drawing each bar accurately

Year 4 maths

Chapter 4: Pictograms and tables: comparison, sum and difference

• Can solve comparison, sum and difference problems (how many more, how many fewer, how many altogether) using charts, pictograms, tables and graphs

Year 4 maths

Chapter 5: Time graphs: reading and drawing change over time

• Can read and draw time graphs that show something changing over time, by plotting points and joining them
• Can solve comparison, sum and difference problems (how many more, how many fewer, how many altogether) using charts, pictograms, tables and graphs

Year 4 maths Year 4 maths

Chapter 6: Solving problems with bar charts and time graphs: comparison, sum and difference

• Can read and draw time graphs that show something changing over time, by plotting points and joining them
• Can solve comparison, sum and difference problems (how many more, how many fewer, how many altogether) using charts, pictograms, tables and graphs

Year 4 maths

Chapter 1: Parts of a line graph: axes, scales and plotting points

• Can read values from a line graph by using the scale, including values between gridlines

Year 5 maths

Chapter 2: Reading values from a line graph, including between gridlines

• Can read values from a line graph by using the scale, including values between gridlines

Year 5 maths

Chapter 3: Finding differences: how many more, rises and falls

• Can use a line graph to find how many more, how much something rose or fell, and the difference between two values

Year 5 maths

Chapter 4: Finding totals by adding values from a line graph

• Can use a line graph to find how many more, how much something rose or fell, and the difference between two values
• Can add values read from a line graph to find a total, and knows when a question needs adding or subtracting

Year 5 maths

Chapter 5: Comparing two lines and finding the biggest change

• Can compare two lines on a line graph and find where a line rises or falls the most
• Can use a line graph to find how many more, how much something rose or fell, and the difference between two values

Year 5 maths

Chapter 6: Solving two-step problems with line graphs

• Can compare two lines on a line graph and find where a line rises or falls the most
• Can use a line graph to find how many more, how much something rose or fell, and the difference between two values
• Can add values read from a line graph to find a total, and knows when a question needs adding or subtracting

Year 5 maths

Chapter 1: Reading line graphs: scales, axes and values between points

• Can read values from a line graph, including scales that go up in 2s, 5s or 10s and values between the plotted points

Year 6 maths

Chapter 2: Drawing line graphs: choosing an even scale and plotting points

• Can draw a line graph from a table, choosing an even scale, plotting points, labelling the axes and knowing when a line graph is the right choice
• Can read values from a line graph, including scales that go up in 2s, 5s or 10s and values between the plotted points

Year 6 maths

Chapter 3: Solving problems with line graphs: two lines and conversion graphs

• Can use line graphs, including graphs with two lines and conversion graphs, to compare values and work out differences

Year 6 maths

Chapter 4: Reading pie charts: using fractions of the total

• Can work out how many each slice of a pie chart stands for, using fractions of the total

Year 6 maths

Chapter 5: Reading pie charts with percentages and angles

• Can use percentages and angles to work out amounts from a pie chart, knowing the whole pie is 100% and 360° and that two pie charts can have different totals

Year 6 maths

Chapter 6: Drawing pie charts: working out angles and using a protractor

• Can draw a pie chart by working out each slice's angle out of 360° and measuring it with a protractor

Year 6 maths

Chapter 1: Tally charts: sorting and counting in fives

• Can count how many are in each group and sort the groups from most to fewest
• Can make tally marks, closing a gate at every five, and read a tally chart by counting in fives

Year 2 maths Year 2 maths

Chapter 2: Simple tables: counting, sorting and totals

• Can count how many are in each group and sort the groups from most to fewest
• Can turn tallies into numbers in a table and read numbers from a simple table
• Can answer 'altogether' questions by adding and 'how many more or fewer' questions by finding the difference

Year 2 maths Year 2 maths Year 2 maths

Chapter 3: Block diagrams: building and reading towers

• Can build a block diagram with one block for each thing and read a tower using the numbers up the side
• Can count how many are in each group and sort the groups from most to fewest

Year 2 maths Year 2 maths

Chapter 4: Pictograms: reading and making them with a key

• Can count how many are in each group and sort the groups from most to fewest
• Can read a pictogram using its key, and make pictograms where one picture stands for 1, 2, 5 or 10, including half pictures

Year 2 maths Year 2 maths

Chapter 5: Totalling and comparing: altogether, how many more and fewer

• Can count how many are in each group and sort the groups from most to fewest
• Can answer 'altogether' questions by adding and 'how many more or fewer' questions by finding the difference

Year 2 maths Year 2 maths

Chapter 1: The mean as a fair share: levelling out

• Can explain that the mean is the fair share everyone gets when amounts are levelled out

Year 6 maths

Chapter 2: Calculating the mean: add up, then divide

• Can calculate the mean by adding all the values and dividing by how many values there are

Year 6 maths

Chapter 3: Interpreting the mean: what it tells you and comparing groups

• Can calculate the mean by adding all the values and dividing by how many values there are
• Can explain what a mean tells you, use means to compare groups and work back from a mean to a total

Year 6 maths

Chapter 1: Simplifying fractions using common factors

• Can simplify fractions by dividing the numerator and denominator by a common factor, and write fractions in their simplest form

Year 6 maths

Chapter 2: Using common multiples to give fractions the same denominator

• Can use common multiples to give two fractions the same denominator

Year 6 maths

Chapter 3: Comparing and ordering fractions, including fractions greater than 1

• Can compare and order fractions, including fractions greater than 1

Year 6 maths

Chapter 4: Adding and subtracting fractions with different denominators

• Can add and subtract fractions with different denominators, using equivalent fractions

Year 6 maths

Chapter 5: Adding and subtracting mixed numbers

• Can add and subtract mixed numbers, using equivalent fractions

Year 6 maths

Chapter 1: Multiplying fractions: finding a fraction of a fraction

• Can multiply two proper fractions, like 1/4 × 1/2, by multiplying the numerators and multiplying the denominators

Year 6 maths

Chapter 2: Multiplying fractions and writing the answer in its simplest form

• Can multiply two proper fractions, like 1/4 × 1/2, by multiplying the numerators and multiplying the denominators
• Can write the answer to a fraction multiplication in its simplest form, by dividing the top and bottom by a common factor

Year 6 maths

Chapter 3: Dividing a proper fraction by a whole number

• Can divide a proper fraction by a whole number, like 1/3 ÷ 2 = 1/6, and explain why the answer is smaller

Year 6 maths

Chapter 4: Fractions as division: 3/4 is the same as 3 ÷ 4

• Can explain that a fraction is a division, like 3/4 = 3 ÷ 4, and use it to share things equally

Year 6 maths

Chapter 5: Fractions to decimals: dividing to find 3/8 = 0.375

• Can change a fraction into a decimal by dividing, like 3/8 = 3 ÷ 8 = 0.375

Year 6 maths