# Maths Year 3/4 Spring Multiplication and Division

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Times tables and factors (suggested as 4 days)

### Objectives

Times tables and factors
Unit 1: ID# 34588

Y3: Double the 4 times table to get the 8 times table; double ×3 to get ×6. Recall of times tables and associated division facts. Finding factors.
Y4: 7, 9, 11 and 12 times tables and associated division facts. Finding factors.

National Curriculum
Y3: Multiplication and Division (i) (iii)
Y4: Multiplication and Division (i) (iii)

Y3 Hamilton objectives
16. Understand that division is the inverse of multiplication, e.g. ? × 3 = 21 ≡ 21 ÷ 3 = ?
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.

Y4 Hamilton objectives
17. Know and recite times tables, including division facts, up to 12 × 12.
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.

### Planning and Activities

Day 1
Find 8 times table facts by doubling 4 times table. Model this, using partitioning for doubling.
Further Teaching with Y4
Derive 9 times table facts: count on in 9s on a counting stick, use ‘finger trick’ to calculate 9s, show patterns of 9s on a 100-square and discuss digital roots of answers.
Group Activities: T with Y4
Y3 -- Play games to explore the 8 times table.
Y4 -- Explore the 9 times table, including division facts: dice and card games.

Day 2
Find 6 times table facts by doubling 3 times a number. Using multiplication facts children write/say corresponding division facts.
Further Teaching with Y4
Explore the 7 times table – count in 7s on a counting stick and ‘add 10 subtract 3’; discuss patterns (or lack of them) compared to 9s.
Group Activities: T with Y3
Y3 -- Play a card game to rehearse spotting and writing 6 times table multiplication and division facts.
Y4 -- Explore multiplication and division facts for the 7 times table.

Day 3
Complete multiplication grids with missing products, drawing on previous lessons to make links between times tables.
Further Teaching with Y4
Explore 11 and 12 times tables, drawing on knowledge of other tables, and beginning to use partitioning to derive facts, e.g. 7 × 12 = 7 × 10 + 7 × 2.
Group Activities: T with Y4
Y3 -- Multiplication target boards – timed challenge.
Y4 -- Explore multiplication facts for the 12 and/or 11 times table.

Day 4
Find factors of numbers (up to 40). Start with a 6 × 4 array of counters and discuss other rectangular arrangements. Define factors. Repeat for 21, then 16 counters.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Multiples Grid’ from NRICH as today’s group activity.
Or, use these activities:
Y3/Y4 Whole class investigation: find factors of numbers up to 40.

### You Will Need

• ‘Fill in the missing numbers from the 4 and 8 times tables’ (see resources)
• Counting stick
• ITP Number Grid
• Number cards 1–12, 1–12 dice
• Picture of a dog
• 24 blank cards (these can be pieces of thick paper or thin card)
• Interlocking cubes
• 1-minute and 2-minute IWB or sand timers
• Stopwatches
• ‘Blank multiplication grid’ (see resources)
• Dice with handwritten stickers for 2, 3, 4, 5, 6, 8
• ‘Target boards 1 and 2’ (see resources)
• 0–9 dice

### Short Mental Workouts

Day 1
4 times table

Day 2
Multiplication Ping Pong

Day 3
3 times table division facts bingo

Day 4

### Procedural Fluency

Day 1
Y3: Multiply by 8, to 12 × 8.
Y4: Multiply by 9, to 12 × 9; associated division facts.

Day 2
Y3: Multiply by 3, then 6, to 12 × _.
Y4: Multiply and divide by 7; explain patterns of multiples in number grids.

Day 3
Y3: Practise 2, 3, 4, 5, 6, 6 and 10× tables; extend to 11 and 12×.
Y4: Multiply by 11; derive the 12× table.

Day 4
Y3: Find factors of numbers to 30.
Y4: Find factors of numbers to 50. Find factors of numbers to 84.

### Mastery: Reasoning and Problem-Solving

Y3

• Use number cards 2, 3, 4 and 8. How many multiplication and division sentences can you create?
• Put these numbers in ascending order, according to the number of factors each has: 21, 30, 43, 25.

Y4

• Which of these numbers are multiples of 9?
28, 108, 126, 49, 153, 891
How do you know?
• Which of these numbers are multiples of 7?
84, 79, 32, 63, 56, 140, 133
How do you know?
• Complete this grid in less than 1 minute:
 x 7 9 12 5 7 8
• Poppy says, ‘The biggest number in a group always has the most factors, so 73 will have more factors than the other numbers in this list: 42, 60, 73, 36.’
Do you agree with her?

In-depth investigation: Multiples Grid
What do the shaded numbers on a 100 square have in common? Children apply knowledge of tables facts and divisibility. Multiples Grid from nrich.maths.org.

### Extra Support

Y3/Y4
Fantastic Facts
Know the 2, 3, 4, 5 and 10 times tables by heart.

## Unit 2 Partitioning in multiplication (suggested as 4 days)

### Objectives

Partitioning in multiplication
Unit 2: ID# 34602

Y3: Multiplying by 10s; doubling 2-digit numbers; multiplication and division word problems.
Y4: Multiplying by 10s and 100s; multiplying 3-digit numbers by 1-digit numbers using grid and ladder method.

National Curriculum
Y3: Multiplication and Division (i) (ii) (iii)
Y4: Multiplication and Division (i) (ii) (iv) (v)

Y3 Hamilton objectives
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
18. Multiply 2-digit numbers by 10 or 1-digit numbers by 100; divide multiples of 10 or 100 by 10 or 100. Understand the effect of × or ÷ by 10 or 100.
20. Partition to double and halve numbers.

Y4 Hamilton objectives
18. Use known facts, place value, factors and commutativity to multiply and divide mentally.
19. Multiply 1-digit numbers by 2-digit or 'friendly' 3-digit numbers mentally or using grid method.

### Planning and Activities

Day 1
Multiply by multiples of 10 and 100, using times table facts and place value digit shifts. Use Number dials ITP to look at the relationship between the 3 and 30 times tables, then 6 and 60. Also use counting stick – count in 4s, then GO LARGE for 40s, then create MEGA tables facts for the 400s.
Group Activities: TA with Y3
Y3 -- Multiply by multiples of 10 dice activity.
Y4 -- Multiply multiples of 10 and 100 by 1-digit numbers using times table facts. Write inverse division sentences.

Day 2
Multiply by multiples of 10 and 100, using times table facts and place value digit shifts – recap from Day 1.
Further Teaching with Y4
Revise grid method for 3-digit by 1-digit multiplication, model setting this out including partitioning 3-digit number and using multiples of 10 and 100 to complete the grid.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Round and Round the Circle’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Creating ‘mega’ times tables, e.g. 40 and 60 times tables, using knowledge of 4 and 6 times tables. Write inverse division facts.
Y4 -- Using grid method for 3-digit by 1-digit multiplication. Some children explore deliberate errors.

Day 3
Revise doubling larger 2-digit numbers by partitioning and using multiplication facts, e.g. double 27 by doubling 20 then 7 then recombining.
Further Teaching with Y4
Introduce ‘ladder’ method for 3-digit by 1-digit multiplication. Compare with the grid method. Discuss advantages/disadvantages of each.
Group Activities: T with Y4
Y3 -- Double numbers by partitioning and recombining.
Y4 -- Investigate products of a 3-digit numbers by 1-digit multiplication.

Day 4
Quick recap of ‘ladder method’ for multiplication: Y4 demonstrate for Y3.
Further Teaching with Y3
Multiplication and division word problems – model examples of each – (see resources), encouraging children to identify the correct operation.
Group Activities: T with Y3
Y3 -- Create multiplication and division word problems.
Y4 -- Investigate digital roots of 3-digit × 1-digit multiplications.

### You Will Need

• Number Dials ITP; Place value ITP
• ‘4-digit place value grid’ (see resources)
• Counting stick
• 0–9 dice, 1–12 dice, 1–6 dice
• ‘Ladders of 10s’ (see resources)
• ‘Target numbers’ (see resources)
• ‘Using the grid method’ (see resources)
• 100s, 10s and 1s place value cards
• ‘Doubling numbers’ sheets 1 and 2 (see resources)
• ‘Multiplication and division word problems’ (see resources)
• Sets of number cards: 2, 3, 4, 5, 8 and 10
• Blank A6 cards

### Short Mental Workouts

Day 1
2, 4 and 8 times tables

Day 2
Division facts for 10 times table

Day 3
Multiplying and dividing by 10

Day 4
6 and 60 times tables

### Procedural Fluency

Day 1
Y3: Multiply by multiples of 10.
Y4: Multiply by multiples of 10 and 100.

Day 2
Y3: Multiply by multiples of 10; spot patterns.
Y4: Use the grid method to multiply a 3-digit number by a 1-digit number.

Day 3
Y3: Double numbers to 44 and beyond. Double numbers to 73 and beyond.
Y4: Use the grid method to multiply a 3-digit number by a 1-digit number.

Day 4
Y3: Solve multiplication and division word problems.

### Mastery: Reasoning and Problem-Solving

Y3

• Complete these LARGE and MEGA multiplications:
8 × 50 = 
210 =  7
40 ×  = 320
3000 =  × 600
 × 800 = 4800
• Double:
19, 24, 36, 48
• Halve:
84, 52, 78, 96
• Write a multiplication word problem with the answer 240 for your teacher to solve. Remember you must have found the correct answer!

Y4

• Jimmy writes: 40 × 5 = 2000.
Is he correct? What might he not understand yet?
• Write the missing numbers and find the final product.
 x 300 4 160 24
• Ola used the ladder method to find 424 × 6 and 3 × 848. Can you suggest why she was surprised with her answers?

In-depth investigation: Round and Round the Circle
Adapt to show multiples of 10 around the circle. What happens if you join every second point on the circle? Try with different steps and see if you can predict what will happen. Round and Round the Circle from nrich.maths.org.

### Extra Support

Y3
Doubles and Halves
Double multiples of 5; halve multiples of 10.

Y4
Grid Genius
Use the grid method to multiply 2-digit numbers by 1-digit numbers.

Moving multiplications
Multiply by 20, 30, 40 and 50 using times tables and place value.

## Unit 3 Division (suggested as 4 days)

### Objectives

Division
Unit 3: ID# 34618

Y3: Connecting multiplication and division facts; remainders; finding unit and non-unit fractions.
Y4: Division using vertical layout; finding unit and non-unit fractions.

National Curriculum
Y3: Multiplication and Division (i) (ii) (iii); Fractions (ii)
Y4: Multiplication and Division (i) (iii); Fractions (iii)

Y3 Hamilton objectives
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
23. Recognise, find and write unit and non-unit fractions of 'convenient' amounts, e.g. 1/10 of 100 or 1/3 of 60.

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.
24. Use times tables to find unit and non-unit fractions of amounts, e.g. 1/6 of 48, 3/8 of 64.

### Planning and Activities

Day 1
Model using multiplication grid to find division facts including remainders, i.e. by tracing along 3s row to find 18 ÷ 3 then 20 ÷ 3.
Further Teaching with Y4
Divide 47 ÷ 3 using an ENL then using a vertical layout. Discuss links between the methods; then repeat for further examples, e.g. 68 ÷ 5, 67 ÷ 3 and 91 ÷ 4.
Group Activities: T with Y4
Y3 -- Division card game, using dice to generate random divisors.
Y4 -- Play a game or investigate dividing 2-digit numbers by 1-digit numbers (with remainders). Reason about patterns of remainders.

Day 2
Recap of vertical division layout – Y4 model for Y3, show how it draws on division facts.
Further Teaching with Y3
Complete blank divisions table – dividing numbers from 19 upwards by 2, 3, 4, 5, etc. and looking for patterns.
Group Activities: T with Y4
Y3 -- Complete blank divisions table, exploring patterns.
Y4 -- Divide 2-digit numbers by 1-digit numbers (with remainders). Some children will divide 3-digit numbers by 1-digit numbers.

Day 3
Find unit fractions. Use a visual model using a strip of 12 objects to find a half, a quarter and a third of 12. Make the connection to division facts then record as a bar model.
Group Activities: T with Y3
Y3 -- Find quarters or eighths using times table facts.
Y4 -- Find unit fractions of quantities using division facts including larger numbers.

Day 4
Recap from previous day then extend to non-unit fractions, i.e. if 1/3 of 18 is 6 what is 2/3? Use a visual model of a 5 × 5 grid of stars to find fifths and also record in a bar model. Also for eighths of 24.
Group Activities: T with Y3
Use the in-depth problem-solving investigation ‘Andy's Marbles’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Write multiplication, division and fraction sentences about arrays.
Y4 -- Using bar models, write fraction sentences to go with multiplication sentences for 24 and 40. Some children create a poster to explain how to find non-unit fractions.

### You Will Need

• ‘Multiplication grid’ (see resources)
• Number cards 1–100
• 1–6 dice, labelled with handwritten stickers 2, 3, 4, 5, 8, 10
• 1-100 grid
• Day 2 Y4 practice sheets
• Counters, Cubes
• Large multiplication grid
• ‘Blank divisions table 1’ and ‘Blank divisions table 2’ (see resources)
• ‘Strips of 12 objects’ (see resources)
• ‘Bar models’ (see resources)
• ‘Finding non-unit fractions 1’ and ‘Finding non-unit fractions 2’ (see resources)

### Short Mental Workouts

Day 1
Division facts for 3 times table

Day 2
Place value subtraction chains

Day 3
Practise the 8 times table

Day 4
Finding fractions of numbers

### Procedural Fluency

Day 1
Y3: Divide 2-digit numbers by 2, 3, 4, 5, 8, and 10.
Y4: Divide 2-digit numbers to give remainders.

Day 2
Y3: Function machines to divide by 2, 3, 4, 5, 8, and 10.
Y4: Divide 2- and 3-digit numbers by 1-digit numbers.

Day 3
Y3: Find unit fractions, using a bar model for support. Find unit fractions of numbers to 40.
Y4: Find unit fractions of 3-digit multiples of 10.

Day 4
Y3: Find unit, then non-unit fractions of numbers. Find non-unit fractions of numbers.
Y4: Find non-unit fractions of 2-digit numbers; then 3-digit multiples of 10.

### Mastery: Reasoning and Problem-Solving

Y3

• 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?

Y4

• Find 1/8, then 3/8 and then 5/8 of 24.
• Write the missing numbers.
___ of 15 is 5
2/3 of ___ = 14
3/5 of 20 = ____
___ of 10 = 4
• Which is bigger, 2/5 of 35 or 3/8 of 32?

In-depth investigation: Andy's Marbles
Calculate fractions of numbers to help Andy work out how many of his marbles have been lost or given away. Andy's Marbles from nrich.maths.org.

### Extra Support

Y3
Fruit Strips
Find 1/4 of numbers by folding strips.

Y4
Leftovers
Use ‘chunking’ to divide numbers just beyond the times tables, including with remainders.