Maths Year 4 Autumn Multiplication and Division

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents.

Unit 1 Double and halve 2- and 3-digit numbers (suggested as 2 days)

Objectives

Double and halve 2-digit and 3-digit numbers
Unit 1: ID# 4327

National Curriculum
Mult /Div (iii) (v)

Hamilton Objectives
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display 26 and model how to draw a jotting to partition:

Double 26
/ \
40 12
40 + 12 = 52

Demonstrate how the same jotting will help us partition a number to halve it. Repeat with other numbers.
Group Activities
Use the ‘Doubling Forever’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Find double and half of odd and even 2-digit numbers.

Day 2 Teaching
Write 226 and draw a partitioning jotting to show children how to double this number. The same process can be modelled for halving. Demonstrate how the jotting is crucial (we use it to partition the numbers).
Group Activities
Use doubling to check halving answers.
Double and halve 3-digit numbers.

You Will Need

  • Place value dice or 0–9 digit cards
  • Whiteboards
  • Flipchart
  • Place value equipment

Mental/Oral Starters

Day 1
Double the numbers 1 to 20 and find the corresponding halves (pre-requisite skills)

Day 2
Double and halve multiples of 100 (pre-requisite skills)

Procedural Fluency

Day 1
Use bar models to find pairs of doubling and halving facts.

Day 2
Double and halve 3-digit numbers.

Mastery: Reasoning and Problem-Solving

  • Write two sentences to relate these three numbers: 37, 74 and 148.
  • Use a jotting to double these numbers:
    a) 216
    b) 327
    c) 438
    Look at the pattern in the answers.
  • We know double 30 is 60 and double 8 is 16.
    So what half of 76?
  • Explain in one sentence why the jotting helps us find half of 318.


In-depth Investigation: Doubling forever
Children double numbers up to 20 and look for duplicate sequences.

Extra Support

Double or Halve?
Doubling and halving 2-digit numbers using partitioning (whole number answers only)

Unit 2 Multiplication and division facts (suggested as 3 days)

Objectives

Multiplication and division facts
Unit 2: ID# 4337

National Curriculum
Mult/Div (i) (ii)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and multiply and divide by 1.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.

Teaching and Group Activities for Understanding

Day 1 Teaching
Revise the 4 times table, giving multiplication facts and asking children to write matching divisions. Then double the products to generate the 8 times table. Revise division facts here as well.
Group Activities
Multiply by 4 and by 8 to revise the times table facts.

Day 2 Teaching
Remind children how we used the 4 times table to generate the 8 times table. Show how we can use the 3 times table to generate the 6 times table. Revise division facts in both tables.
Group Activities
Multiply by 3 and use this to multiply by 6.

Day 3 Teaching
Launch ITP Function Blocks. Use this to generate division by 3. Can children work out the function? Repeat with the functions ÷ 4, ÷ 5, ÷ 6 and ÷ 8.
Group Activities
Use the in-depth problem-solving investigation ‘Function Machines’ from NRICH as today’s group activity. Or, use these activities:
Find hidden functions to multiply and divide by 3, 4, 5, 6 and 8.

You Will Need

  • 0–12 cards
  • Coins
  • Flipchart
  • 24 cards
  • ITP: Function Blocks
  • Post-it notes
  • ‘Mystery Function Machines’ (see resources)

Mental/Oral Starters

Day 1
4 times table (pre-requisite skills)

Day 2
3 times table, division facts (pre-requisite skills)

Day 3
6 times table (pre-requisite skills)

Procedural Fluency

Day 1
Use 4 times table multiplication and division facts to find 8 times table multiplication and division facts.

Day 2
Double 3 times table facts to find 6 times table facts.

Day 3
Complete function machines for the 3, 4, 5, 6 and 8 times tables.

Mastery: Reasoning and Problem-Solving

  • Write 48 in the middle of a space and circle it. Draw 10 spider legs out from it. Write 10 multiplication or division sentences using this number, e.g. 48 ÷ 6 = 8.
  • What times table is this? Explain what number ‘a’ stands for.
    6 × a = 20 + a
    8 × a = 30 + half of a
  • Always true, sometimes true or never true?
    -- In one times table, there are only 2 possible ones digits in the answers.
    -- 3 times a number is an odd number.
    -- All answers in the 4 times table are even.
    -- Answers in the 3 times table are also in the 6 times table.

In-depth Investigation: Function Machines
Can you work out the three processes in the function machine? Function Machines from nrich.maths.org.

Extra Support

Clever Counting
3 and 4 times tables. Linking multiplication and division

Unit 3 Grid multiplication using tables facts (suggested as 3 days)

Objectives

Grid multiplication using tables facts
Unit 3: ID# 4349

National Curriculum
Mult/Div (i) (iii) (v)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and multiply and divide by 1.
19. Multiply 1-digit numbers by 2-digit or 'friendly' 3-digit numbers mentally or using grid method (i.e. using the distributive law).

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 24 × 3 on the board. Model solving this using a grid. Explain that a grid is another way of writing a jotting like the one we used for doubling. It helps us to partition the larger number and then multiply it. Repeat to model 22 × 6 and 55 × 3.
Group Activities
-- Use place value equipment to multiply 2-digit by 1-digit numbers.
-- Accurately draw and complete multiplication grids.

Day 2 Teaching
Display the ITP Multiplication Grid. Children copy the grid and then complete it. Remind children how the grid helps us partition the bigger number before we multiply. Reveal each square at a time and discuss. Repeat with 52 × 5 and 13 × 2. Ask children to use known number facts to estimate the answer first.
Group Activities
Use the ‘Magical Nines’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Understand how to fill in each square of a multiplication grid and use it to find an answer.
-- Pick tens and ones cards to generate a 2-digit number. Throw a dice to get a 1-digit number. Use the grid method to multiply these together.

Day 3 Teaching
Play ‘What’s wrong? as a whole class. Discuss answers each time and encourage children to work out the multiplications themselves.
Group Activities
Investigate why some multiplication grids have different numbers but give the same answers.

Mental/Oral Starters

Day 1
Count in steps of 30 (pre-requisite skills)

Day 2
6 times table (pre-requisite skills)

Day 3
Division facts for the 8 times table (pre-requisite skills)

Procedural Fluency

Day 1
Use a multiplication grid to multiply 2-digit numbers by 1-digit numbers.

Day 2
Draw and use multiplication grids.

Day 3
Create multiplication grids that generate the same answers.

Mastery: Reasoning and Problem-Solving

  • Use the grid method to complete each of these:
    24 × 6 = ☐
    48 × 3 = ☐
    Say why the answers are the same.
  • Write the missing numbers:

x30
424=
  • Say how much bigger the answer to (i) will be than the answer to (ii).
    Do both using the grid method to find out if you were right.
    (i) 5 × 43
    (ii) 6 × 43


In-depth Investigation: Magical Nines
Children look for patterns when multiplying ‘nearly numbers’ by 9 using mental multiplication strategies.

Extra Support

Double Trouble
Doubling 2-digit numbers using partitioning (including answers over 100)

Unit 4 Division using efficient chunking (suggested as 2 days)

Objectives

Division using efficient chunking
Unit 4: ID# 4357

National Curriculum
Mult/Div (ii) (v)

Hamilton Objectives
17. Know and recite times tables, including division facts, up to 12 × 12; multiply by 0 and multiply and divide by 1.
20. Know how to use ‘efficient chunking’ for division above the range of the tables facts, e.g. 84 ÷ 6 = ?

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 96 ÷ 6 and read it, reminding children that it asks us how many 6s in 96? Draw an empty number line and model finding 10 lots of 6 and then 6 lots (see download).
Point out that 10 + 6 is 16 so we know there are 16 lots of 6 in 96. Ask children to show 78 ÷ 6 and 72 ÷ 4.
Group Activities
-- Make a poster showing how to divide using chunking on a number line.

Day 2 Teaching
Show the posters made yesterday. Ask children to share how we use a number line to help us divide. First, we find 10 times the divisor, then we work out how many more lots we need. Model 102 ÷ 6 as 10 × 6 and 7 × 6 on a number line. Repeat for 72 ÷ 4 and 54 ÷ 3.
Group Activities
Use the in-depth problem-solving investigation ‘Growing Garlic’ from NRICH as today’s group activity.
Or, use these activities:
-- Divide using chunking as quickly as possible.

You Will Need

  • Chunking posters
  • ‘Chunking Champ’ division cards (see resources)
  • 3, 4 and 5 times tables sheet (see resources)

Mental/Oral Starters

Day 1
Division facts for the 6 times table (pre-requisite skills)

Day 2
Multiplication and division facts (pre-requisite skills)

Procedural Fluency

Days 1 and 2
Use chunking on a number line to divide by 3, 4, 5, 6 and 8 with no remainders.

Mastery: Reasoning and Problem-Solving

  • Correct Amit’s number line divisions. He has made the same mistake twice. Explain what the mistake is. Show the correct calculations (see download).
  • What is similar about these two calculations
    57 ÷ 3 = ?
    76 ÷ 4 = ?
    Challenge! Write a similar one where we divide by 5.

In-depth Investigation: Growing Garlic
Plant up to 100 garlic bulbs into rows of different lengths to explore remainders. Growing Garlic from nrich.maths.org.

Extra Support

Chunky Divisions
Using 'chunking' to divide numbers just beyond the times tables

Unit 5 Larger divisions with remainders (suggested as 2 days)

Objectives

Division using efficient chunking with remainders
Unit 5: ID# 4363

National Curriculum
Mult/Div (ii) (v)

Hamilton Objectives
20. Know how to use ‘efficient chunking’ for division above the range of the tables facts, e.g. 84 ÷ 6 = ? Begin to extend this to 3-digit numbers.
21. Solve single-step problems; begin to solve multi-step problems, including multiplication/division.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 44 ÷ 3 and draft an empty number line from 0 to 44. Discuss how we first find 10 lots of 3, then work out how many more lots are needed. Point out that 3 does not divide exactly into 14. We do 4 × 3 = 12 to 42. Show on the line the remainder of 2. Show a vertical written way of recording this.
Group Activities
-- Divide 2-digit numbers to get answers with remainders, and check answers using multiplication.
-- Use grid multiplication to work out a division calculation for a partner to solve.

Day 2 Teaching
Write 42 ÷ 3, 78 ÷ 4, 85 ÷ 5 on the flipchart and ask children to say which will have an answer closest to 20 or closest to 10. Then model finding answers using the vertical written recording method used yesterday. Repeat to ensure children understand that dividing by a smaller number gives a larger answer.

Group Activities
Use the in-depth problem-solving investigation ‘The Remainders Game’ from NRICH as today’s group activity.
Or, use these activities:
-- Create divisions of 2-digit numbers to get answers within a given range.

You Will Need

  • Flipchart
  • Tables sheet with 3, 4 and 5 times tables (see resources)
  • Whiteboards
  • Post-it notes

Mental/Oral Starters

Day 1
Divide with tables to give answers with remainders (pre-requisite skills)

Day 2
Recognise multiples of 2, 3, 4 and 5 (pre-requisite skills)

Procedural Fluency

Day 1
Divide 2-digit numbers by 1-digit numbers to get answers with remainders.

Day 2
Use division in real-life contexts to solve word problems.

Mastery: Reasoning and Problem-Solving

  • Use a number line to solve these two divisions.
    (i) 84 ÷ 6
    (ii) 108 ÷ 6
    What is the relation between the 2nd hop on the two lines?
  • Look at the remainders in each of these divisions. Compare the remainder with the divisor.
    a) 56 ÷ 3
    b) 75 ÷ 4
    c) 94 ÷ 5
    Can you write a division where you divide by 6 and the remainder is 5?


In-depth Investigation: The Remainders Game
Can you work out the computer's mystery number? Choose a divisor and the computer will give you some information about the number. The fewer divisions you require, the more points you get! The Remainders Game from nrich.maths.org.

Extra Support

Left Overs
Dividing by 3, 4, 5 and 10 to give remainders