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# Maths Year 3/4 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. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Rehearsing & understanding times tables (suggested as 3 days)

### Objectives

Rehearsing and understanding times tables
Unit 1: ID# 34254

Y3: Know × and ÷ facts for 2, 3, 4, 5 and 10× tables; understand that multiplication is commutative; recognise multiples of 2, 3, 4, 5 and 10.
Y4: Know 2, 3, 4, 5, 10× tables and associated division facts. Generate 6× and 8× table.

National Curriculum
Y3: Num/Mult/Div (i)
Y4: Num/Mult/Div (i)

Y3 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.
17. Know the 2×, 3×, 4×, 5×, and 10x times tables, including division facts.

Y4 Hamilton objectives
17. Know and recite times tables, including division facts, up to 12 × 12.

### Teaching and Group Activities for Understanding

Day 1
Quickly practise revising multiples of 5. Look at a 5 by 7 array; establish four connected multiplication and division facts. Repeat for 12 × 2, modelling groups on a bead bar.
Further teaching with Y4
Investigate multiplication and division facts using an interactive ‘function machine’.
Group activities: T with Y3
Y3 -- Identify the four number facts that an array describes. Play a tables facts game.
Y4 -- Create and solve function machine problems for the 2, 3, 4, 5 and 10 times tables.

Day 2
Model and derive 3 times table facts and corresponding divisions using 12 towers of 3 cubes.
Further teaching with Y4
Generate 6 times table facts by doubling the 3 times table.
Group activities: T with Y4
Y3 -- Find multiples of 3 by hopping on a beaded line. Play a 3 times table game.
Y4 -- Play a 3 times table and 6 times table game.

Day 3
Model 4 times table facts and the corresponding divisions using a 12-section counting stick.
Further teaching with Y4
Generate 8 times table facts by doubling the 4 times table.
Group activities: T with Y4
Use the in-depth problem-solving investigation for this unit ‘Mystery age’ as today’s group activity.
Or, use these activities:
Y3 -- Find multiples of 4 by hopping on a beaded line. Practise recall of the 4 times table.
Y4 -- Recall 4 times tables facts; double to find 8s. Play a 4 and 8 times table game.

### You Will Need

• ‘5 by 7 array’ and 'Arrays' (see resources)
• ITP: Function machine
• Sets of number cards (2, 5, 10 and 3–12)
• ‘2, 5 and 10 times tables’ (see resources)
• Coloured pencils and sticky notes
• ‘Mystery function machine’ (see resources)
• Cubes, number cards 1–12 and blank cards
• ‘0–40 beaded lines’ (see resources)
• Set of 1–12 cards and a coin per pair
• Set of 1–12 cards and set of 2–6 cards
• ‘Counting stick’ (see resources)
• ‘0–50 beaded lines’ (see resources)
• Multiples of 4 cards and 2-minute timer

### Short Mental Workouts

Day 1
Division facts: 5 times table

Day 2
Division facts: 2, 5 and 10 times tables

Day 3
Division facts: 3 and 6 times tables

### Procedural Fluency

Day 1
Y3: Recognise multiples of 2, 5 and 10.
Y4: Solve function machine problems using times tables facts.

Day 2
Y3: 3 times table practice.
Y4: 3 and 6 times tables practice.

Day 3
Y3: 4 times table practice.
Y4: 4 and 8 times tables practice.

### Mastery: Reasoning and Problem-Solving

Y3

• Write 4 number sentences to relate these 3 numbers: 5, 7 and 35.
• We know 8 × 5 = 40. So, what is 40 ÷ 5?
We know 24 ÷ 2 = 12. So, what is 12 × 2?
• Write a division with an answer of 5. Now write a different division using those same three numbers.
• Explain why you might prefer to do 5 × 9 as 9 lots of 5.
• Write the missing numbers:
☐ × 4 = 28
3 × ☐ = 21
36 ÷ ☐ = 4

Y4

• 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.
Answers in the 4 times table are even.
Answers in the 3 times table are also in the 6 times table.

In-depth Investigation: Mystery Age
Y3: Children use their knowledge of the 3, 4, and 5 times tables to work out mystery numbers.
Y4: Children use their knowledge of the 5, 6, and 8 times tables to work out mystery numbers.

### Extra Support

Y3
Hops, Skips and Jumps

Counting in 2s from 0 to 20 and counting in 5s from 0 to 50

and/ or

Monster Multiplications
Counting in 3s - 'Clever Counting' and multiplication

Y4
Clever Counting

3 and 4 times tables. Linking multiplication and division

## Unit 2 Partitioning in multiplication and division (suggested as 3 days)

### Objectives

Partitioning in multiplication and division
Unit 2: ID# 34270

Y3: Multiply by 4 by doubling twice; Divide by 4 by halving twice; Writing division facts to go with multiplications.
Y4: Use grid method to multiply a 2-digit number by a 1-digit number.

National Curriculum
Y3: Num/Mult/Div (i) (ii) (iii)
Y4: Num/Mult/Div (i) (ii) (iv)

Y3 Hamilton objectives
20. Partition to double and halve numbers.

Y4 Hamilton objectives
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
Identify and reason about patterns across the 1, 2 and 4 times tables. Use this as a basis for modelling multiplying by 4 by doubling twice, using the strategy of partitioning, doubling and recombining.
Further teaching with Y4
Introduce the grid method for multiplying 2-digit by 1-digit numbers, beginning with comparison of partitioning/recombining and grid for 23 × 2.
Group activities: T with Y4
Use the in-depth problem-solving investigation ‘Doubling forever’ as today’s group activity.
Or, use these activities:
Y3 -- Multiply a range of 2-digit numbers by 4.
Y4 -- Multiply 23 by 1-digit numbers using the grid method. Some children will find the 36 times table using the grid method.

Day 2
Model dividing by 4 by halving twice, linking with Day 1’s strategy of multiplying by 4 by doubling twice.
Further teaching with Y4
Use grid multiplication with larger 2-digit numbers.
Group activities: T with Y4
Y3 -- Divide numbers on cards by 4 by halving twice.
Y4 -- Use grid multiplication to find which arrangement of digits produces the greater answer.

Day 3
Year 4 explain grid multiplication to Y3, for 6 × 13, then 7 × 14.
Further teaching with Y3
Look at the multiplication and division facts that an array describes.
Group activities: T with Y3 or Y4
Y3 -- Investigate arrays.
Y4 -- Investigate grid multiplication, finding different numbers that produce the same products.

### You Will Need

• ‘Multiples of 1, 2 and 4’ (see resources)
• Set of 2–9 cards and sets of 1–10 cards
• ‘Multiplying and Dividing by 4’ (see resources)
• ‘Multiples of 4 number cards’ (see resources, 1 set per pair)
• Calculators
• Place value cards (arrow cards): tens (10–50) and ones (1–9)
• 1–6 dice and counters

### Short Mental Workouts

Day 1
4 and 8 times tables

Day 2
3 and 6 times tables

Day 3
Multiply and divide by 10

### Procedural Fluency

Day 1
Y3: Multiply by 4 by doubling twice.
Y4: Complete multiplication grids for multiplying 2-digit by 1-digit numbers.

Day 2
Y3: Halve twice to divide by 4.
Y4: Grid method multiplication.

Day 3
Y3: Linking multiplication and division within tables.
Y4: Matching grids – find different multiplications with the same partial products.

### Mastery: Reasoning and Problem-Solving

Y3

• 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 these diagrams:
Diagram 1:
 36 36

Diagram 2:

 52 ? ?
• What mistake has Fred made in his work?
13 × 4 = 26
21 × 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?

Y4

• Use the grid method to complete each of these:
24 × 6 = ☐
☐ = 3 × 48
Say why the missing numbers are the same.
• Write the missing numbers:
 x 30 4 24 = ☐
• Say how much bigger the answer to (ii) will be than the answer to (i). Answer both using the grid method to find out if you were right.
(i) 6 × 43
(ii) 5 × 43

In-depth Investigation: Doubling Forever
Children double numbers up to 10 (Y3) or 20 (Y4) and look for duplicate sequences.

### Extra Support

Y3

Doubling 2-digit numbers (answers less than 100)

and/or

Fair Friends
Halving even 2-digit numbers, with even 10s digits

Y4

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

and/or

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

## Unit 3 Strategies for division (suggested as 4 days)

### Objectives

Strategies for division
Unit 3: ID# 34286

Y3: Dividing using multiplication facts, with remainders.
Y4: Divide numbers above the 10th multiple using chunking/written method.

National Curriculum
Y3: Num/Mult/Div (i) (ii) (iii)
Y4: Num/Mult/Div (i) (ii) (iv)

Y3 Hamilton objectives
16. Understand that division is the inverse of multiplication.
17. Know the 2×, 3×, 4×, 5× and 10× times tables, including division facts.

Y4 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.

### Teaching and Group Activities for Understanding

Day 1
Explore division by 5 by grouping. Use numbers that facilitate introduction of remainders, e.g. 21 ÷ 5.
Further teaching with Y4
Division on an Empty Number Line (no remainders)
Group activities: T with Y3 or Y4
Y3 -- Explore how to calculate and record ‘left overs’ when dividing by 5.
Y4 -- Make a poster showing how to divide using ‘chunking’ on a number line.

Day 2
Y4s show Y3s how they use an Empty Number Line for solving division questions.
Further teaching with Y3
Divide by 3, 4, 5 and 10 using the Grouping ITP.
Group activities: T with Y3
Y3 -- Create a range of number stories that show how groups can be formed from different numbers of children (including with left overs).
Y4 -- Improve fluency with dividing by chunking.

Day 3
Consider how to tell if a division question will have a remainder; check division by multiplication.
Further teaching with Y4
Model vertical layout for division.
Group activities: T with Y3 or Y4
Use the in-depth problem-solving investigation ‘Rocking remainders’ as today’s group activity.
Or, use these activities:
Y3 -- Divide a range of 2-digit numbers by 3, 4, 5 and 10; check division by multiplication.
Y4 -- Divide 2-digit numbers to give answers with remainders.

Day 4
Use multiples of 10 times the divisor to estimate answers to divisions. Reason about which will have the largest/smallest answer.
Further teaching with Y3
Estimating answers to divisions, which will have the largest/smallest answer? (further examples).
Group activities: T with Y3 or Y4
Y3/ Y4 -- Play a game to create divisions of 2-digit numbers, resulting in answers within a given range and with a remainder.

### You Will Need

• ITP: Grouping
• ‘0–50 beaded lines’ (see resources)
• Cubes, poster paper and pens
• ‘Story cards’ (see resources)
• ‘Images to use for grouping’ (see resources)
• Sticky notes
• ‘Chunking Champ’ division cards (see resources)
• Blank cards, bag and stopwatch
• ‘3×, 4× and 5× tables’ (see resources)
• Mini whiteboards and pens
• 1–6 dice and 0–9 dice (or spinners)

### Short Mental Workouts

Day 1
Multiplication patterns

Day 2
I spy a 3 times table fact

Day 3
Doubles and halves

Day 4
Division facts: 3 and 6 times tables

### Procedural Fluency

Day 1
Y3 Dividing by 3, 4, and 5 with remainders.
Y4 Use chunking on a number line to divide by 3, 4, 5, 6 and 8 with no remainders.

Day 2
Y3 Dividing by 2, 3, 4, 5, and 10 with remainders.
Y4 Use chunking on a number line to divide by 3, 4, 5, 6 and 8 with no remainders.

Day 3
Y3 Reason about remainders; check division by multiplication.
Y4 Divide 2-digit numbers by 1-digit numbers - beyond tables - with remainders.

Day 4
Y3 Odd one out: Division with remainders.
Y4 Use division in real-life contexts to solve word problems.

### Mastery: Reasoning and Problem-Solving

Y3

• 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 into 34 and leave a remainder of 4?
• Which number between 30 and 40 can be divided by the most numbers leaving no remainders?

Y4

• 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 calculation where we divide by 5.

In-depth Investigation: Rocking Remainders
Children divide 11, 22, 33 ... 99 by 3, 4, 5... and look for patterns in the remainders.

### Extra Support

Y3: Beads and Rings
Dividing by 3, 5 and 10

Y4: Chunky Divisions
Using 'chunking' to divide numbers just beyond the times tables