Maths Year 3 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 Revision of 2x, 5x and 10x tables: x and ÷ (suggested as 3 days)

Objectives

Revision of 2x, 5x and 10x tables: multiplication and division
Unit 1: ID# 3307

National Curriculum
Mult/Div (ii)

Hamilton Objectives
15. Understand that multiplication is commutative, and write mathematical statements for multiplication and division.
16. Understand that division is the inverse of multiplication, e.g. ? x 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2x, 5x and 10x times tables, including division facts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use 5 jumps of 7 and 7 jumps of 5 along a 0-50 beaded line to show that these come to the same place. Then show an array of 5 rows of 7 cubes and turn it round to be 7 rows of 5 cubes. Stress commutativity.
Group Activities
-- Exploring arrays and writing corresponding number sentences.

Day 2 Teaching
Revise 2x table and focus on division, stressing that 12 x 2 = ? is one way of learning the fact and another is ? x 2 = 24: how many 2s in 24? Use ITP Number Grid; highlight multiples of 2, asking division questions.
Group Activities
Use the 'Make the Multiples' in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Finding out how many 2s are in a number using jumps and beaded lines as well as calculating.

Day 3 Teaching
Write 35, 24, 42, 95, 46, 50, 102, 105, 120 and 125 on the IWB on separate cards. Draw 3 intersecting sets labelled ‘multiples of 2’, ‘multiples of 5’ and ‘multiples of 10’. Discuss how to allocate each number.
Group Activities
-- Playing games exploring multiples of 2, 5, and 10 (as appropriate).

You Will Need

  • 0-50 beaded line
  • Arrays (see resources)
  • 100 bead bar
  • ITP: Number grid
  • 0-30 beaded lines (see resources)
  • 1-12 & 1-24 cards, 100 grid
  • 7 - 12 Dice

Mental/Oral Starters

Suggested for Day 1
Count in 5s and 10s to at least 100 (simmering skills)

Day 2
Count in 2s (pre-requisite skills)

Day 3
2, 5 and 10 times tables (pre-requisite skills)

Procedural Fluency

Day 1
Complete multiplication and division sentences for arrays and given numbers.

Day 2
Complete division sentences.

Day 5
Find multiples of 2.

Mastery: Reasoning and Problem-Solving

  • Write 4 number sentences to relate these 3 numbers: 5, 7 and 35.
  • We know 8 x 5 = 40. So what is 40 ÷ 5?
    We know 24 ÷ 2 = 12. So what is 12 x 2?
    Write a division with an answer of 5. Now write a different division using those same 3 numbers.
  • Explain in 1 sentence why you might prefer to do 5 x 9 as 9 lots of 5.


In-depth Investigation: Make the Multiples
Children draw on their knowledge of multiples of 2 and 5 to create these using digit cards 0 - 9.

Extra Support

Hops, Skips and Jumps
Counting in 2s from 0 to 20; Counting in 5s from 0 to 50

Unit 2 Multiplication/division facts: 3x and 4x (suggested as 2 days)

Objectives

Multiplication and division facts: 3x and 4x tables
Unit 2: ID# 3313

National Curriculum
Mult/Div (i) (ii)

Hamilton Objectives
16. Understand that division is the inverse of multiplication, e.g. ? x 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2x, 3x, 4x, 5x and 10x times tables, including division facts.
21. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show children 12 towers of 3 cubes and use these to demonstrate the multiplication and division facts for the 3 times table. As how many 3s in 24? Use cubes to help children answer.
Group Activities
-- Using multiples of 3 cards to create hops along a beaded line. Playing bingo with multiples of 3 to identify these.
Day 2 Teaching
Use a 12-section counting stick. Write 4, 8, 12… 48 under it. Together count in 4s along it. Repeat after rubbing out 4, 16, 24 and 36. Point to where 16 should be. What number goes here? How can we work it out? Point to 24, 36, etc. Record X and ÷ sentences.
Group Activities
Use the 'Mystery Age’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Using multiples of 4 cards to create hops along a beaded line. Challenge - writing multiplication and division sentences within 2 minutes using a timer.

You Will Need

  • Cubes
  • 1-12 & 1-24 cards
  • 0-40 beaded line (see resources)
  • Counting stick (see resources)
  • 0-50 beaded lines (see resources)
  • 7-12 dice

Mental/Oral Starters

Day 1
Count in 3s from 3 to at least 36 (pre-requisite skills)

Day 2
Count in 4s to at least 48 (pre-requisite skills)

Procedural Fluency

Day 1
Complete timed bronze, silver and gold x3 times table challenge.

Day 2
Complete timed bronze, silver and gold x4 times table challenge.

Mastery: Reasoning and Problem-Solving

  • Write the missing numbers:
    ☐ x 4 = 28
    3 x ☐ = 21
    36 ÷ ☐ = 4
  • Write 8 x 4 = 32 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 sentences using this central fact. (Hint: Some may involve the number 2 rather than 4.)
  • Always true, sometimes true or never true?
    6 x 4 is the same as 4 x 3 x 2.
    Multiplying a number by 3 gives an odd number.
    If a number divides equally by 4, it is even.


In-depth Investigation: Mystery Age
Children use their knowledge of the 3, 4 and 5 times tables to work out mystery numbers using a series of logical clues.

Extra Support

Monster Multiplications
Counting in 3s - 'clever counting' and multiplication

Unit 3 Division using facts and remainders (suggested as 3 days)

Objectives

Division using facts including remainders
Unit 3: ID# 3323

National Curriculum
Mult/Div (i) (iii)


Hamilton Objectives
16. Understand that division is the inverse of multiplication, e.g. ? x 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2x, 3x, 4x, 5x and 10x times tables, including division facts.
21. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Draw an array for 3 rows of 4 spots. This shows 3 lots of 4. Write 3 x 4 = 12 What else do we know from this? How many 4s in 12? 3. Write the division. Rotate the array to show 4 lots of 3. Children write 4 x 3 = 12. How many 3s in 12? Write the division. Use a 2 x 5 array to repeat.
Group Activities
-- Investigating all the possible array formations that can be made from 24 and 36.
Day 2 Teaching
Write □ x 5 = 20. How many 5s in 20? Write 20 ÷ 5 and discuss. Write 21 ÷ 5. Discuss what happens now. Launch the ITP Grouping; choose 21 ÷ 5 as the calculation. Model division with remainders.
Group Activities
Use the ‘Divide it Out’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Exploring how to calculate and record left overs when dividing by 5.
Day 3 Teaching
Write 15 ÷ 5. Ask children what this means. Read as 15 divided into groups of 5. How many groups? Are any left over? Why not? Model on ITP Grouping to confirm. Then divide 15 by 4, by 3 and by 2. Repeat for 22 ÷ 5.
Group Activities
-- Creating a range of number stories that show how groups can be formed from different numbers of children (including with left overs).

You Will Need

  • Whiteboards & pens
  • Counters
  • ITP: Grouping
  • 0-50 beaded lines (see resources)
  • Cubes
  • Story cards & group images (see resources)

Mental/Oral Starters

Day 1
Division facts for 2 times table (pre-requisite skills)

Day 2
Division facts for 5 times table (pre-requisite skills)

Suggested for Day 3
Division facts for 10 times table (simmering skills)

Procedural Fluency

Day 1
Practise bronze, silver, gold multiplication/division pairs.
Day 2
Divide by 3, 4, and 5 with remainders.
Day 3
Divide by 2, 3, 4, 5, and 10 with remainders.

Mastery: Reasoning and Problem-Solving

  • Write 3 pairs of numbers which give a product of 24 when multiplied.
  • Write the missing numbers:
    ☐ x 3 = 36
    8 x ☐ = 32
    14 ÷ ☐ = 7
  • What is the remainder when 34 divides by 4?
  • Divide 29 by 2 then by 3, then by 4, then by 5. What will the remainder be if you divide it by 10?
  • What number will divide 34 and leave a remainder of 4?


In-depth Investigation: Divide it Out
What is the lowest number that leaves a remainder of 1 when divided by any number from 2 to 10? Create a low-threshold for this problem by reducing the number of divisors. Divide it Out from nrich.maths.org

Unit 4 Double nos <51; halve even nos <101 (suggested as 2 days)

Objectives

Doubling (numbers < 51) and halving (even numbers < 101)
Unit 4: ID# 3331

National Curriculum
Mult/Div (iii)


Hamilton Objectives
20. Partition to double and halve numbers.
21. Solve problems, including missing number problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Find double 23 and 34 using the ITP Place value to help (make 2 of each number). Record as 23 + 23 = 46 and double 23 is 46. Children double 25 using PV cards. Record:
Double 25
/ \
40 10
40 + 10 = 50
Children work in pairs using this strategy to double 42 and record. Repeat.
Group Activities
-- Making 2-digit numbers with a spinner and then doubling them.
-- Doubling the value of recipe ingredients to increase baking batches.

Day 2 Teaching
Show pictures of chocolate bars. Pick one with an odd 10s digit. Model as below:
Half of 54p
/ \
25 2
25 + 2 = 27p
Repeat for another chocolate bar with an odd 10s digit.
Group Activities
Use the ‘Doubling Fives’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Halving given prices for a half-price chocolate bar sale.

Mental/Oral Starters

Day 1
Doubles to double 15, doubles of multiples of 10 (pre-requisite skills)

Day 2
Halve even numbers to 30, halve even multiples of 10 (pre-requisite skills)

Procedural Fluency

Day 1
Double numbers (parts A & B).
Day 2
Halve even numbers to 50 and spot patterns.

Mastery: Reasoning and Problem-Solving

  • Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? Repeat, starting at 4. How many this time?
  • Write the missing numbers in this diagram:
?
3636
  • Write the missing numbers in this diagram:
52
??
  • How many double/half pairs (e.g. 8 and 16) between 1 and 50 have 1s digits of 7 and 4?

In-depth Investigation: Doubling Fives
Spot patterns when doubling multiples of 5. Doubling Fives from nrich.maths.org

Extra Support

Doubles and Halves
Doubling multiples of 5; halving multiples of 10

Unit 5 Mental strategies for x and ÷ (suggested as 2 days)

Objectives

Mental strategies for multiplication and division
Unit 5: ID# 3343

National Curriculum
Mult/Div (ii) (iii)

Hamilton Objectives
16. Understand that division is the inverse of multiplication, so halving is the inverse of doubling.
20. Partition to double and halve numbers.
21. Solve problems, including missing number and scaling problems.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children write x2 table on left hand side of w/bs. Children now write the corresponding 4x table on right hand side. Note that in order to work out x4 a number, you can double it twice. Model for larger numbers. 13 x 4 ≡ double 26.
Group Activities
-- Practising multiplying by 4.
Day 2 Teaching
Ask children how to multiply a number by 4. Agree you can double twice. We use this to divide by 4. Show example on IWB, reminding children that halving is the inverse of doubling. So we can divide by 4 by halving twice.
Group Activities
Use the ‘Does It or Not?’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Practising dividing by 4.

You Will Need

  • 4 times table (see resources)
  • x2 & x4 times tables (see resources)
  • 1-24 number cards
  • Multiplying & dividing by 4 (see resources)
  • Multiple of 4 cards (see resources)

Mental/Oral Starters

Day 1
Double 2-digit numbers (pre-requisite skills)

Day 2
Halve even 2-digit numbers (pre-requisite skills)

Procedural Fluency

Day 1
Multiply by 4: differentiated sets.

Day 2
Divide by 4: colour coded questions.

Mastery: Reasoning and Problem-Solving

  • Multiply 26 by 4. WOW!
  • Write 4 sentences to link the numbers 24, 4 and 96.
  • What mistake has Fred made in his work?
    13 x 4 = 26
    21 x 4 = 42
    56 ÷ 4 = 28
    64 ÷ 4 = 32
  • Divide 128 by 4.
    Can you divide the answer by 4?
    Can you divide that answer by 4?


In-depth Investigation: Does It or Not?
Children find numbers between 50 and 100 which they can divide by 4. They halve each number twice to find out.

Extra Support

This unit has no separate Extra Support activities.

Unit 6 Times tables; multiplication/division (suggested as 5 days)

Objectives

2x, 3x, 4x, 5x, 8x, 10x tables: multiplication and division, including remainders
Unit 6: ID# 3347

National Curriculum
Mult/Div (i) (ii)

Hamilton Objectives
15. Understand that multiplication is commutative, and write mathematical statements for multiplication and division.
16. Understand that division is the inverse of multiplication, e.g. ? x 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2x, 3x, 4x, 5x, 8x and 10x times tables, including division facts.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children write the 4x table down the left hand side of a whiteboard. Children now write 8x table on right hand side. Note that in order to multiply a number by 8, you can times number by 4 then double it. Model with different questions.
Group activities
-- Multiplying by 8 card game. Ping Pong: multiplying by 8.

Day 2 Teaching
Show a blank multiplication grid. Model filling it: I know 6 x 4 is 24 so I write 24 here. Give each child their own blank grid and ask them to complete it.
Group activities
-- Complete a range of multiplication target boards.

Day 3 Teaching
Display multiplication grid. Children think, pair, share how this helps with division. Revise this: 3 x 6 is 3 lots of 6 are 18. So 18÷ 6 is how many 6s make 18? ☐ x 6 is 18.
Group activities
Use the ‘Crack the Code’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Times table division card game.

Day 4 Teaching
Display blank divisions table. Cover all but first 2 rows. Model division within tables with remainders (÷2, 3, 4, 5, 8 and 10).
Group activities
-- Complete a division investigation that looks for patterns.

Day 5 Teaching
Remind children that we have practised multiplying and dividing. Today we’ll choose one of these to find answers to word problems. Reveal word problems one by one. Discuss and complete.
Group activities
Use the ‘Crack the Code’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Creating multiplication and division word problems.

You Will Need

  • 8 times table (see resources)
  • Incomplete x4 and x8 list (see resources)
  • 1-12 cards
  • Cubes
  • Blank multiplication grid (see resources)
  • 2, 3, 4, 5, 8, 10 dice (hand written)
  • Target boards (see resources)
  • Multiplication grid (see resources)
  • Number cards (between 10 and 100)
  • 2, 3, 4, 5, 8, 10 dice (hand written)
  • Blank divisions table (see resources)
  • Large multiplication grid
  • Divisions tables (see resources)
  • Word problems (see resources)

Mental/Oral Starters

Day 1
4 times table (pre-requisite skills)

Day 2
2, 4 and 8 times tables (pre-requisite skills)

Day 3
Division facts for 2 times table (pre-requisite skills)

Day 4
Division facts for 3 times table (pre-requisite skills)

Day 5
Division facts for 4 times table (pre-requisite skills)

Procedural Fluency

Day 1
Multiply by 8: ‘orderly’ and ‘disorderly’ sheets.

Day 2
Multiply by 2, 3, 4, 5, 8, and 10.

Day 3
Divide by 2, 3, 4, 5, 8, and 10.

Day 4
Use division machines (colour coded).

Day 5
Complete multiplication and division word problems.

Mastery: Reasoning and Problem-Solving

  • Divide 36 by 4. Divide the answer by 2.
    Divide 36 by 8. What fraction of 8 is the remainder?
  • Use number cards 2, 3, 4 and 8. How many multiplication and division sentences can you create?
  • Mystery number
    Which ONE number makes this sentence true?
    ☐ ÷ 6 = 24 ÷ ☐
  • Which number between 30 and 40 can be divided by the most numbers leaving no remainders?
  • Write a word problem involving division for your teacher to solve. Remember you must have worked out the correct answer!


In-depth Investigation: Crack the Code
Children work together to reason and think logically to crack a code. They practise mental multiple and division strategies.

Extra Support

This unit has no separate Extra Support activities.