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# Maths Year 2 Spring More 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 Multiply by 2, 5 and 10 (suggested as 2 days)

### Objectives

Multiply by 2, 5 and 10
Unit 3: ID# 2767

National Curriculum
Mult/Div (i) (ii) (iv)

Hamilton Objectives
16. Know 2×, 5× and 10× tables, and related division facts, e.g. saying how many 10s in 40; use × and ÷ signs correctly.
19. Write multiplications and divisions, using ×, ÷ and = signs. Calculate answers.
21. Solve multiplication/division problems in context, using recall of ×/÷ facts, doubling, halving, arrays, ‘clever counting’.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a 0–50 beaded line (see resources) on the Interactive Whiteboard. Write 4 × 5 =  on the board. This is 4 lots of 5, or 4 times 5. Children ring groups of 5 beads until they have 4 groups. Say that this is 4 lots of 5 beads. Count in 5s to show that 4 × 5 = 20. Repeat with 3 × 5, 6 × 5, 10 × 5.
Group Activities
-- Generate and solve times 5 multiplication sentences with dice, using hops on beaded lines or fingers.
-- Solve and create word problems for multiplication by 5.

Day 2 Teaching
Display a 0–30 beaded line on the Interactive Whiteboard (see resources). Write 4 × 2 =  on the board. We can read this as 4 lots of 2, or 4 times 2. Ask children to ring groups of 2 beads, until they have ringed 4 groups (4 lots of 2 beads). Count in 2s to show that 4 × 2 = 8. Repeat with 8 × 2, 3 × 10, 5 × 5.
Group Activities
Use the in-depth problem-solving investigation ‘Odd Times Even’ from NRICH as today’s group activity.
Or, use these activities:
-- Generate and solve times 2, times 5 and times 10 multiplication sentences, using hops on beaded lines or fingers.
-- Solve and create word problems for multiplication by 2, 5 and 10.

### You Will Need

• 0–50 beaded line (see resources)
• 1–10 dice
• ‘Multiplying by 5 using beaded lines’ sheet (see resources)
• 0–30 beaded line (see resources)
• Spinners (see resources)
• ‘Multiplying by 2, 5 and 10 using beaded lines’ sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Count in 10s and 5s (pre-requisite skills)

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

### Procedural Fluency

Day 1
Complete multiplication sentences (times 5) using beaded lines, counting on fingers, or counting in heads.

Day 2
Complete multiplication sentences (times 2, times 5 and times 10) using beaded lines, counting on fingers, or counting in heads.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers.
6, 8, ☐ , ☐ , 14, 16, ☐
25, 30, ☐ , ☐ , ☐ , 50
80, 70, 60, ☐ , ☐ , ☐
• What are:
4 lots of 5?
9 lots of 2?
8 lots of 10?
• Sam counts in 2s from 0. What are the 5th, 6th and 7th numbers he says?
• Gill counts in 5s from 0. What are the 6th, 7th and 8th numbers she says?
• Complete these multiplications.
8 × 5 =
7 × 2 =
4 × 10 =
11 × 2 =

In-depth Investigation: Odd Times Even
Try multiplying any odd and even number together. Use different models to show this. Can children make any observations or generalisation about what happens when you multiply an odd and an even number? Odd Times Even from nrich.maths.org.

### Extra Support

Clever Twos
Carrying out early multiplication (in 2s)

## Unit 2 Division as inverse of multiplication (suggested as 3 days)

### Objectives

Understand division as inverse of multiplication
Unit 4: ID# 2777

National Curriculum
Mult/Div (ii) (iii) (iv)

Hamilton Objectives
16. Know 2×, 5× and 10× tables, and related division facts, e.g. saying how many 10s in 40; use × and ÷ signs correctly.
19. Write multiplications and divisions, using ×, ÷ and = signs; calculate answers.
20. Understand that multiplication can be done in any order (commutative) and division cannot.
21. Solve multiplication/ division problems in context, using recall of ×/÷ facts, doubling, halving, arrays, ‘clever counting’.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a beaded line with 3 hops of 5 (see resources). Children think, pair, share what multiplication is shown. Discuss how division is also shown. How many 5s are in 15? Repeat with 4 hops of 2. How many 2s in 8? Write 4 × 2 = 8 and 8 ÷ 2 = 4. Repeat with multiplications (times 2 and times 5, products up to 30). Write each multiplication with a corresponding division, e.g. 5 × 2 = 10, 10 ÷ 2 = 5.
Group Activities
-- Find the answer to multiplications using number lines and hops; write the matching division.
-- Use a beaded line to help solve division problems.

Day 2 Teaching
Write 20 ÷ 5 = . How many lots of 5 are there in 20? Display a 0–30 beaded line and ring 20. Model drawing hops of 5 to 20. Count hops to find that 20 ÷ 5 = 4, i.e. there are four 5s in 20. Say matching multiplications and divisions. Repeat with 12 ÷ 2 and 25 ÷ 5.
Group Activities
Use the in-depth problem-solving investigation ‘Leftovers’ as today’s group activity.
Or, use these activities:
-- Find the answer to divisions using number lines and hops, and then write the matching multiplication.
-- Create and solve word problems for division by 2, 5 or 10.

Day 3 Teaching
Show ‘Mystery Multiplications and Divisions’. Explain that children need to be detectives to find the missing numbers. Work as a class to find the missing numbers in the first two Qs, using the knowledge that division is the inverse of multiplication. Children solve the next question in pairs.
Group Activities
-- Work out mystery numbers in given multiplications and divisions.

### You Will Need

• 'Beaded line with hops' (see resources)
• '0-30 beaded line' (see resources)
• 'Multiplication to solve' cards (see resources)
• Bag
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count in 2s, 5s, 10s (pre-requisite skills)

Suggested Day 2
Count in steps of 1/4 hour (simmering skills)

Suggested Day 3
Tell the time to the nearest 1/4 hour (simmering skills)

### Procedural Fluency

Day 1
Draw hops on beaded lines to match multiplications with answers, then complete corresponding divisions.

Day 2
Draw hops on beaded lines to solve divisions, then complete corresponding multiplications.

Day 3
Use number lines or multiplication facts to find the missing numbers in a series of multiplications and divisions.

### Mastery: Reasoning and Problem-Solving

• How many hops of 5 in:
20?
35?
50?
• How many 2s in:
16?
20?
24?
• Explain why 20 ÷ 5 = ☐ can also be written as ☐ × 5 = 20.
• Write the missing numbers:
☐ × 2 = 12.
☐ × 2 = 20
☐ × 5 = 30
☐ × 10 = 60
• Divide each number by 5. Divide the answer by 2.
30, 20, 50, 40
What could you have divided by to do this in one step?

In-depth Investigation: Leftovers
Children investigate which numbers leave 1 left over when divided by 5.

### Extra Support

Ring the Twos
Carrying out early division (in 2s)

## Unit 3 Multiplying and doubling and inverses (suggested as 3 days)

### Objectives

Multiplying and doubling and inverses
Unit 5: ID# 2789

National Curriculum
Num/PV (vi)
Mult/Div (i) (ii) (iv)

Hamilton Objectives
16. Know 2×, 5× and 10× tables, and related division facts, e.g. saying how many 10s in 40; use × and ÷ signs correctly.
17. Understand equivalence in simple calculations: 3 × 4 = 6 × ☐
18. Double and halve numbers up to 20 and multiples of 5 to 50; recognise odd and even numbers.
19. Write multiplications and divisions, using ×, ÷ and = signs; calculate answers.
20. Understand that multiplication can be done in any order (commutative) and division cannot.
21. Solve multiplication/division problems in context, using recall of ×/÷ facts, doubling, halving, arrays, ‘clever counting’.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use two 1–20 bead strings to show double 20. Remind children that double 20 is 40, and half of 40 is 20. Doubling and halving are inverses. Stress that doubling is multiplying by 2 and halving is dividing by 2. Use ‘Mystery Machines’ (resources) to generate and discuss halves/doubles.
Group Activities
-- Work out the missing number or operation in Mystery Machines.
-- Play double and half pairs.

Day 2 Teaching
Show an array of 3 rows of 5 counters. Match this to a multiplication: 3 lots of 5. Rotate the array and show that 5 rows of 3 is the same total. Use a bead string to show that 3 × 5 = 5 × 3. Then demonstrate 2 × 8 = 4 × 4. Discuss the way this number sentence shows an equality.
Group Activities
Use the in-depth problem-solving investigation ‘Golden numbers’ as today’s group activity.
Or, use these activities:
-- Work out multiplications using a chosen strategy.
-- Record the corresponding number sentences to arrays.

Day 3 Teaching
Tell children that you have bought 7 packets of football stickers, and that each packet has 5 stickers. How many stickers altogether? Children discuss how they work it out. Agree that you have 7 lots of 5 stickers. Model drawing this as an array (7 × 5) and on a 0–50 beaded line, with 7 hops of 5. Repeat with another word problem involving 7 lots of 3.
Group Activities
-- Solve multiplication word problems.
-- Write multiplication word problems.

### You Will Need

• 'Mystery machine A, B and C' sheets (see resources)
• 'Mystery machine doubling and halving' sheets 1 and 2 (see resources)
• Calculators and sticky notes
• Number cards 10-40
• Blank cards
• Additional activity sheets (see resources)
• Cubes and counters

### Mental/Oral Maths Starters

Day 1
Double multiples of 5 to 50 (pre-requisite skills)

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

Day 3
Count in 5s (pre-requisite skills)

### Procedural Fluency

Day 1
Find the missing number or function for halving and doubling calculations.

Day 2
Choose a strategy to solve multiplications.

Day 3
Solve and create multiplication word problems.

### Mastery: Reasoning and Problem-Solving

Write the missing halves/ doubles.
Diagram 1:

 40 ? ?

Diagram 2:

 18 ? ?

Diagram 3:

 ? 25 25
• Which equivalences are correct?
3 × 5 = 5 × 3
4 × 10 = 6 × 5
8 × 2 = 4 × 4
5 × 5 = 10 × 2
• Rewrite this incorrect equivalence 10 × 6 = 3 × 5 to be correct, using the same 4 numbers.
• Tammy has 5 pages of stickers. There are 8 stickers on each page. How many stickers does Tammy have?
• Maisie has four 5p coins and four 2ps coins in her purse. How much does she have in total?

In-depth Investigation: Golden Numbers
Children explore which numbers are ‘golden numbers’ when we are counting in steps of different sizes.

### Extra Support

Doubling 11 to 20

and/or

Fair or not fair
Halving even numbers from 20 to 30

## Unit 4 Solve divisions as inverse of multiplication (suggested as 2 days)

### Objectives

Solve divisions as inverse of multiplication
Unit 5: ID# 2791

National Curriculum
Mult/Div (i) (ii) (iv)

Hamilton Objectives
21. Solve multiplication/division problems in context, using recall of ×/÷ facts, doubling, halving, arrays, ‘clever counting’.
19. Write multiplications and divisions, using ×, ÷ and = signs; calculate answers.
16. Know 2×, 5× and 10× tables, and related division facts, e.g. saying how many 10s in 40; use × and ÷ signs correctly.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show an array of 3 rows of 5 counters. Describe the division shown. Record 15 ÷ 5 = 3. 15 has 3 lots of 5 in it. Rotate the array so it has 5 rows of 3 counters. What number sentence can we write? 15 ÷ 3 = 5. 15 has 5 lots of 3 in it. Show on a beaded line. Then use a beaded line to find 18 ÷ 3.
Group Activities
-- Solve divisions using beaded lines and write related multiplications.
-- Write division and multiplication facts from arrays then play pairs with them.

Day 2 Teaching
Remind children of previous word problems. Those were all multiplication problems. Today we will decide whether to multiply or divide to solve a word problem. Display the first two questions on the sheet and assist children in deciding whether to multiply or divide.
Group Activities
Use the in-depth problem-solving investigation ‘Lots of Lollies’ from NRICH as today’s group activity.
Or, use these activities:
-- Solve multiplication and division problems.
-- Find division and multiplication number families for three given numbers, then write a word problem to match.

### You Will Need

• 'Array' sheet (see resources)
• '0-20 beaded line' (see resources)
• 'Divisions' sheet (see resources)
• Calculators, card and cubes
• Additional activity sheets (see resources)
• Interactive whiteboard or individual devices with internet access

### Mental/Oral Maths Starters

Day 1
Count in 2s, 5s, 10s (pre-requisite skills)

Suggested Day 2
Doubling and halving (simmering skills)

### Procedural Fluency

Day 1
Solve multiplications and divisions then write a related calculation.

Day 2
Solve word problems using either division or multiplication.

### Mastery: Reasoning and Problem-Solving

• Rewrite each multiplication as a division:
 × 2 = 18
 × 5 = 35
 × 10 = 70
• Solve
25 ÷ 5 =
24 ÷ 2 =
40 ÷ 5 =
16 ÷ 2 =
• How many 5s in 35? So, can you say how many 5s in 70?
• Bella has 30 stickers. She puts 6 on each page. How many pages of her sticker album will she fill?
• Bill has six 5p coins. How many 10ps can he exchange these for and still have the same amount of money?

In-depth Investigation: Lots of Lollies
Children use their knowledge of factors and multiples to work out how many lollies were in the bag. Lots of Lollies from nrich.maths.org.

### Extra Support

Row - Row - Row Your Bakes
Understanding and using arrays