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# Maths Year 3 Summer 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 Counting in equal steps; sequences (suggested as 3 days)

### Objectives

Counting in equal steps; sequences
Unit 1: ID #3863

National Curriculum
Num/PV (i)
Mult/Div (i)

Hamilton Objectives
4. Count from 0 in 2s, 4s, 8s, 10s, 100s, and 50s.
21. Solve problems, including missing number (and scaling) problems.
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Count in 10s from 0 to 100 using the counting stick, then in 100s from 0 to 1000. Count in 100s from different numbers. Count in 50s to 500, then to 1000. Write: 4, 54, 104, 154; explain that 4 + 50 = 54, 54 + 50 = 104, 104 + 50 = 154. Repeat with 23, 73, 123.
Group Activities
Use the in-depth problem-solving investigation ‘Dog Chews’ as today’s group activity.
Or, use these activities:
-- Play ‘Ping Pong’, alternating between counting in 100s and 50s to 1000.
-- Play ‘Jump 50, Jump 100’, counting on a given number of 100s or 50s.

Day 2 Teaching
Count in steps of 4 from 4 to at least 100, noting that the numbers are all even. Count in 8s to 96. Observe that these are also even. Explain how we find the digital root of a number; find digital roots of numbers in the 4x table.
Group Activities
-- Find the digital roots of numbers in the 4 and 8 times table and beyond.
-- Play the compound leaves game, counting in 4s and 8s.

Day 3 Teaching
Show the first three numbers of a sequence: 28, 24, 20. Children describe the rule for this sequence and write the next three numbers. Discuss how sequences can decrease as well as increase. Show a sequence starting at 2, e.g. 2, 6, 10. Can children write the next three terms? Children create their own sequences, then extend: 2, 4, 8, 16.
Group Activities
-- Play sequences card game, challenging a partner to spot the rule of a sequence and write the next three numbers.
---Play sequences game, identifying the rule for a given sequence of numbers.

### You Will Need

• Counting stick
• Mini-whiteboards and pens
• Bean bags
• ‘Count in steps of 100’ sheet (see resources)
• ‘Jump 50, Jump 100’ cards (see resources)
• 0-9 Dice
• Internet access
• ‘Counting patterns’ (see resources)
• Additional activity sheets (see resources)
• 1–12 dice

### Mental/Oral Maths Starters

Day 1
Count in 100s (pre-requisite skills)

Suggested for Day 2
Odd and even numbers (simmering skills)

Suggested for Day 3
Count back in 3s (simmering skills)

### Procedural Fluency

Day 1
Complete missing numbers in a 10 to 1000 grid, counting in steps of 10 and 100.
Fill the missing numbers in sequences that count in 50s or 100s.

Day 2
Fill the missing numbers in sequences that count in 4s or 8s.

Day 3
Complete the sequences and state the counting rule.

### Mastery: Reasoning and Problem-Solving

• Write the next four numbers in these sequences:
4, 8, 12, ,…
13, 63, 113, …
8, 16, 24, …
100, 96, 92, …
341, 441, 541, …
601, 551, 501, …
• Create a sequence of ten numbers where you count on in 8s from an odd number.
• Harry says, ‘If I count in 4s, starting at 3, I won’t say 30, but I will say 303.’ Do you agree? Explain your ideas.

In-depth Investigation: Dog Chews
Children ﬁnd a multiple of 50 and a multiple for 4 with a given total.

### Extra Support

Ladders to Success
Counting in steps of 50 from 0 to 1000

## Unit 2 Revise multiplication and division facts (suggested as 2 days)

### Objectives

Revise multiplication and division facts
Unit 2: ID #3877

National Curriculum
Mult/Div (i)

Hamilton Objectives
17. Know the 2, 3, 4, 5, 8 and 10 times tables, including division facts.
15. Understand that multiplication is commutative, and write mathematical statements for multiplication and division.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a partially completed multiplication grid. Explain how it works, model with 2 × 5, writing 10 in the corresponding space. This grid has lots of spaces! Point to some; ask children to write in the answers. Point out how we can use facts we know to find other facts, such as 7 × 5 to find 5 × 7.
Point to 21. How many threes are in 21? Follow rows and columns to find the answer 7. Discuss number sentences using 3, 7 and 21… Scribe: 7 x 3 = 21; 3 x 7 = 21, then the divisions: 21 ÷ 3 =7; 21 ÷ 7 =3. Point to other multiples of 3, 4, or 8. Can you write a division number sentence that starts with that number?
Group Activities
-- Ring certain times table numbers on a 1–50 grid and say the associated division fact.
-- Play division facts bingo for the 2, 3, 4, 5, 6, 8 and 10 times tables.

Day 2 Teaching
Play a game with class into 2 teams. Write 4 × 6 = ___ and agree the product (24). Each child writes a related tables fact on a whiteboard, e.g. 6 × 4 = 24, 4 × 12 = 48, 2 × 6 = 12, 3 × 8 = 24. On a count of 3, children show their facts. Award points and record team totals. Repeat with another fact, e.g. 5 x 8 = 40.
Group Activities
Use the in-depth problem-solving investigation ‘Ordering cards’ from NRICH as today’s group activity.
Or, use these activities:
-- Play multiplication/division ‘Ping Pong’ by writing a multiplication or division from the 2, 3, 4, 5, 8 or 10 times tables, followed by a partner who writes a related x or ÷, and so on…
-- Practise multiplication and division facts using online games.

### You Will Need

• ‘Partially completed multiplication grid’ (see resources)
• ‘1–50 grid’ and ‘1–100 grid’ (see resources)
• Mini-whiteboards and pens
• Internet access

### Mental/Oral Maths Starters

Day 1
3 and 4 times table (pre-requisite skills)

Day 2
5 and 8 times table (pre-requisite skills)

### Procedural Fluency

Day 1
Fill in the incomplete multiplication grid for the 1, 2, 3, 4, 5, 8 and 10x tables.
Fill in the incomplete grid for all tables facts to 10 x 10.

Day 2
Write multiplication and division facts that relate to a given fact.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers.
☐ × 8 = 32
6 × ☐ = 48
9 = 36 ÷ ☐
☐ × 4 = 48
5 = ☐ ÷ 8
• Write 8 × 6 = 48 in the middle of a space and circle it. Draw 8 spider legs out from it. Write 8 related number sentences using this central fact.
• Always true, sometimes true or never true?
6 × 8 is the same as 4 × 12.
Dividing a number by 3 gives an odd answer.
Even numbers divide by 8 to leave no remainder.

In-depth Investigation: Ordering Cards
Children use their knowledge of times table facts to find the order of a set of loop cards. Ordering Cards from nrich.maths.org.

### Extra Support

Multiplication/division ‘Ping Pong'
Adapt this Group Activity from Day 2 to revise multiplication/division facts for 2-, 3-, 4-, 5- and 10-times tables.

## Unit 3 Partition to double, halve and multiply (suggested as 4 days)

### Objectives

Partition 2-digit numbers to double, halve and multiply using grid
Unit 3: ID #3889

National Curriculum
Mult/Div (ii) (iii)

Hamilton Objectives
20. Partition to double and halve numbers.
19. Multiply a 1-digit number by a 2-digit number using partitioning.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use the ITP Place value to show 20 and 7 = 27. Children work in pairs: one doubles 10s, the other doubles 1s. They add their answers. So, double 27 = 54. We worked it out using partitioning. Show 47, with the cards not split. Children repeat the process. Repeat for 2-digit numbers >50.
Group Activities
-- Play a 4-in-a-row grid game, doubling 2-digit numbers.
-- Play an online game to practise doubling using partitioning as a method.

Day 2 Teaching
Ask two children to make 48 using 10s and 1s cards. They partition the number. One child halves 40 and the other halves 8, then they add their answers. Record half of 48 is 24. Repeat with 56, then with 45. Remind children how to halve 5 to give 2¹/2. Repeat with 75. Create number chains.
Group Activities
-- Play a chain game, halving even numbers and adding 1 when numbers are odd.
-- Play an online game to practise halving using partitioning as a method.

Day 3 Teaching
Show a grid used to do 2 × 14. Point out that we do not need the grid but it is very useful to show partitioning. Use the grid to do 3 × 14. Then 6 × 14. Explain that grid method helps us keep track of the steps in multiplying.
Group Activities
-- Describe stepping stones in developing use of the grid method. Rehearse use of preferred image(s) to begin using the grid method.
--Practise multiplying teen numbers by single digit numbers.
--Play a multiplication game using the grid method.

Day 4 Teaching
Discuss solving 3 × 24 with the grid method. Children use the grid method to multiply 24 by 1, 2, 3, 4 … 9 so that they create the 24 times table.
Group Activities
Use the in-depth problem-solving investigation ’18 times table – wow!’ as today’s group activity.
Or, use these activities:
-- Investigate multiplying odd and even 2-digit numbers by 1-digit numbers using the grid method.

### You Will Need

• ITP: Place Value
• ‘Doubling numbers’ sheets 1 and 2 (see resources)
• Coloured pencils
• Place value cards
• Internet access
• Mini-whiteboards and pens
• ‘Steps towards using the grid method for 14 x 5’ sheets 1 and 2 (see resources)
• ‘Using the grid method’ sheet (see resources)
• Squared paper
• Number cards 12–15, 22–25 and 32–35
• 1–6 dice
• Counters
• Number cards 1-9, 11-30 and 21-40
• ITP: Number Dials

### Mental/Oral Maths Starters

Day 1
Multiply 1-digit numbers by 20 (pre-requisite skills)

Day 2
30 times table (pre-requisite skills)

Suggested for Day 3
Add 1-digit numbers to 2-digit numbers (simmering skills)

Suggested for Day 4
× and ÷ by 10 and 100 (simmering skills)

### Procedural Fluency

Day 1
Double given numbers using partitioning.

Day 2
Halve given numbers using partitioning.

Day 3
Multiply teens numbers by 1-digit numbers using the grid method.
Multiply numbers 18 to 39 by 1-digit numbers using the grid method.

Day 4
Choose a series of grid multiplications to complete:
numbers 13 to 19 x 1-digit numbers, or
numbers 18 to 39 x 1-digit numbers, or
numbers 26 to 45 x 1-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers in each diagram.
Diagram 1:
 ? 56 56

Diagram 2:

 74 ? ?

Diagram 3:

 95 ? ?
• How many odd numbers between 50 and 100, when halved, give an answer ending 4¹/2?
• Write the missing numbers in this grid.

 x 30 6 4
• Now complete the addition to find the total of the partial products.
☐ + ☐ = ☐

In-depth Investigation: 18 Times Table – Wow!
Children use the grid method to work out the 18 times table and look for patterns in the answers.

### Extra Support

Doubles Decisions
Doubling numbers up to 50

Harder Halves
Halving even numbers to 100

## Unit 4 Solve scaling problems (suggested as 2 days)

### Objectives

Solve scaling problems
Unit 4: ID #3907

National Curriculum
Mult/Div (iii)

Hamilton Objectives
21. Solve problems, including (missing number and) scaling problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write a list of ingredients for a flapjack recipe. This is enough to make one tray. We need lots of flapjacks for the cake sale. What do we need to do? Together, multiply each measure by 4 by doubling twice. Repeat with a lemonade recipe, scaling it up by a factor of 10.
Group Activities
-- Scale up recipes by 4x and 10x.
-- Scale up drawings (rectangles and triangles) by 4x and 10x.

Day 2 Teaching
Show a life-size outline drawing of yourself with measurements that are all multiples of 10cm. Explain that we will make a scale drawing of this picture, scaling each measurement down to 1/10 of its original length. My height is 170cm, so what will the height be on your piece of paper…?
Group Activities
Use the in-depth problem-solving investigation ‘Follow the numbers’ from NRICH as today’s group activity.
Or, use these activities:
-- Scale down a drawing by a factor of 10.
-- Scale down Lego houses to 1/4 of their original number of bricks.

### You Will Need

• ‘Scaling up’ sheets 1 and 2 (see resources)
• cm2 paper
• To-scale drawing of person (prepare in advance)
• Poster paper
• Lego bricks
• Rulers

### Mental/Oral Maths Starters

Day 1
Double numbers to 50 (pre-requisite skills)

Day 2
Halve even numbers to 100 (pre-requisite skills)

### Procedural Fluency

Day 1
Help a caterer work out how to cater for parties 4 times and 10 times the size of a standard party.

Day 2
Draw shapes according to instructions then scale them down by a factor of 4.

### Mastery: Reasoning and Problem-Solving

• The postcards in the art gallery measure 15cm by 10cm.
One is of a painting which is 4 times bigger.
One is of a painting which is 10 times bigger.
One is of a painting which is 5 times bigger.
Write the measurements of each painting.
• A painting in the museum measures 160cm by 100cm. The gift shop sells posters of the painting at 1/4 full size and postcards at 1/10 full size. How big are posters and postcards?

In-depth Investigation: Follow the Numbers
Adapt this investigation to find the digital root and multiply by 4 or 10. Keep following this rule and see what happens. Investigate the patterns when you start with different numbers. Follow the Numbers from nrich.maths.org.

### Extra Support

Double Double
Multiplying by 4 by doubling twice; Dividing by 4 by halving twice

## Unit 5 Divide numbers just beyond times tables (suggested as 3 days)

### Objectives

Divide numbers just beyond the times tables
Unit 5: ID #3917

National Curriculum
Mult/Div (ii) (iii)

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.
21. Solve problems, including missing number and scaling problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 65 ÷ 5, then sketch a line from 0 to 65. We could draw every hop of 5, but we don’t need to! Are there more than 10 lots of 5 in 65? Draw a jotting to show 10 lots of 5 to 50 and 3 lots of 5 to 65. Add: 10 lots + 3 lots = 13 lots of 5. Repeat for 70 ÷ 5, 52 ÷ 4 and 42 ÷ 3.
Group Activities
-- Practise divisions just beyond the times tables by drawing ENL jottings.
-- Play ‘more or less than 10’ card game, predicting, then checking selected divisions by drawing empty number line (ENL) jottings.

Day 2 Teaching
Write 54 ÷ 3. How many 3s in 54? More than 10? Where do 10 lots of 3 get to on the line? How much is left? How many 3s? Draw an empty number line jotting to show this, writing 10 × 3 then 8 × 3. Repeat with other divisions, e.g. 112 ÷ 8 and 51 ÷ 3. Use an ENL to find 43 ÷ 3. Once you get to 42, point out that there is 1 left over. If we had 43 children and we wanted to put them into groups of 3, we’d have 14 groups and 1 child left over. We call this ‘left over’ number a remainder. This is an important word to remember…
Group Activities
-- Play division mini-bingo with divisions that are just beyond the times tables (no remainders).
-- Investigate numbers that will divide by 3 or 4 or both without leaving a remainder.

Day 3 Teaching
Write 46 ÷ 3. Children help you to sketch an ENL a jotting: a jump of 10 × 3 to 30, then a jump of 5 × 3 to 45. Point to the gap between 45 and 46. Label it ‘r1’ to stand for remainder 1. There is 1 left over. Repeat for 78 ÷ 5, 115 ÷ 5 and 51 ÷ 4.
Group Activities
Use the in-depth problem-solving investigation ‘Threes and Fours’ as today’s group activity.
Or, use these activities:
-- Play a game choosing and calculating divisions then collecting counters for the remainders.
-- Division with remainders card game.

### You Will Need

• ITP: Number Dial
• ‘Division jottings’ sheet (see resources)
• ‘Number cards’ sheet (see resources)
• 1–9 and 1–6 dice
• ‘Recording table’ sheet (see resources)
• Additional activity sheets (see resources)
• Mini-whiteboards and pens
• Counters
• ITP: Tell the Time

### Mental/Oral Maths Starters

Day 1
Division facts for the 3 and 4 times tables (pre-requisite skills)

Day 2
8 times table (pre-requisite skills)

Suggested for Day 3
Find a time later (simmering skills)

### Procedural Fluency

Day 1
Complete division calculations that sit slightly beyond the times tables.

Day 2
Complete division calculations that sit slightly beyond the times tables: some with remainders.

Day 3
Division calculations with remainders for just beyond the 3-, 4-, 5- and 8-times tables.

### Mastery: Reasoning and Problem-Solving

• How many 3s in each number?
45
52
39
• Will the remainder be the same in these divisions?
(i) 53 ÷ 4
(ii) 66 ÷ 5
(iii) 40 ÷ 3
Guess first and then work each one out to check.

In-depth Investigation: Threes and Fours
Children explore multiples of 3 and 4 to find divisibility patterns.

### Extra Support

Flip-flops
Dividing within tables by 3, 4 and 5 (no remainders)

## Unit 6 Gain fluency using multiplication & division (suggested as 3 days)

### Objectives

Gain fluency using multiplication and division
Unit 6: ID #3923

National Curriculum
Mult/Div (iii)

Hamilton Objectives
19. Multiply a 1-digit number by a 2-digit number using partitioning.
16. Understand that division is the inverse of multiplication, e.g. ? × 3 = 21 ≡ 21 ÷ 3 = ?
21. Solve problems, including missing number and scaling problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a grid on the board and ask children to explain each stage to a partner. Take feedback. Ensure children remember how this method works. Children work out 7 × 35. Ask a pair up to the board to model solving the calculation: one to write, the other to ‘commentate’.
Group Activities
-- Practise multiplying numbers between 20 and 40 by 1-digit numbers.

Day 2 Teaching
Say that 4 shells decorate each sandcastle. We have 18 shells, how many sandcastles can they decorate? Sketch a 0–18 line and draw 4 hops to 16. Point out the remainder (2). Agree that 4 castles can be decorated and 2 shells are left over. Repeat to solve other problems.
Group Activities
-- Complete divisions and score for each reminder. Reason about possible remainders for a given divisor.

Day 3 Teaching
Write names of 4 roller coaster rides on cards. 4 children each hold one. Imagine we are at a theme park and we are deciding which two rides to go on, and in which order. Together, we will find all the possible options. Work systematically to find all 12 possible combinations.
Group Activities
Use the in-depth problem-solving investigation ‘Yuck or Yum!’ as today’s group activity.
Or, use these activities:
-- Investigate all possible combinations for 3 beach holiday activities.
-- Investigate the possible combinations of children and cats there could be for a given number of legs.

### You Will Need

• 1–6 dice
• 1–9 dice
• Mini-whiteboards and pens
• ‘Blank multiplication grids’ sheet (see resources)
• ‘Finding remainders’ sheet (see resources)
• 4 large cards
• ‘Holiday activities’ sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Division facts for the 4 times table (pre-requisite skills)

Day 2
8 times table (pre-requisite skills)

Suggested for Day 3
40 times table (simmering skills)

### Procedural Fluency

Day 1
Complete calculations using the grid method: 2-digit numbers to 25.
Complete calculations using the grid method: 2-digit numbers to 40.

Day 2
Divide a big box of cakes into smaller bags. How many bags can be made; how many cakes left over?
Divide a big box of chocolates into smaller gift boxes. How many gift boxes can be made; how many chocs left over?

Day 3
Work out all possible clothing outfit combinations.

### Mastery: Reasoning and Problem-Solving

• Start with 11.
Multiply by 4 and then multiply the answer by 5.
Halve your answer.
Divide that answer by 10.
What do you notice?
Start with 12. Repeat the steps. Does the same thing happen? Can you explain why?
Challenge! Repeat, starting with 13.
• Tim uses four wheels on each Lego car. He counts up and sees that he has 54 wheels. How many cars can he make?
• There are three ice-cream flavours: strawberry, chocolate and vanilla. You choose any two and have one on top and one underneath. How many possible ways can we choose the pair?

In-depth Investigation: Yuck or Yum!
Children find all possible food combinations from given lists and then decide which are ‘yuk’ and which are ‘yum’!

### Extra Support

Multiplication Tables - Matching Cards
Use this game from NRICH to gain fluency with recall of tables facts. Matching Cards from nrich.maths.org.