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# Maths Year 2 Summer Calculation

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 Add by partitioning or counting on (suggested as 2 days)

### Objectives

Add by partitioning or counting on
Unit 1: ID# 2741

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 - 40 = 20
10. Add a 2-digit number and tens; add two 2-digit numbers that total less than 100 by counting on in 10s and 1s.
15. Solve problems involving addition and subtraction of numbers, quantities and measures, using recall of number facts and appropriate models and images.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children make 24 and 32 using place value cards. Model this process using Place value ITP. Demonstrate how to add the two 10s and the two 1s and then recombine: 30 + 20 = 50 and 2 + 4 = 6. Total = 56. Also show how to count on in 10s and 1s (start at 32; add 20 then 4): 32..42..52..53..54..55..56. Which strategy do you prefer? Ask children to work out 73 + 21, 52 + 37, 54 + 26. Model 47 + 35 using partitioning, to show what happens when the ones add to more than ten.
Group Activities
-- Add two 2-digit numbers from number cards, noting methods used.
-- Add two 2-digit numbers from dice, explaining reasons for methods used.

Day 2 Teaching
Remind children of the two methods they used in Day 1 for adding: partitioning and counting on. Practise adding two 2-digit numbers, allowing children to choose their preferred method. Ask two children using different methods to explain why they used the method they chose.
Group Activities
Use the in-depth problem-solving investigation ‘Diagonal hundreds’ as today’s group activity.
Or, use these activities:
-- Add two 2-digit numbers from spinners, choosing appropriate methods.
-- Add two 2-digit numbers, suggesting the method to be used and devising ‘top tips’ for method selection.

### You Will Need

• Place value cards
• Place value ITP
• Whiteboards and pens
• 2-digit number cards
• 10 second timer
• Calculators
• Customised dice (see activity for details)
• Top Marks spinners from www.topmarks.co.uk
• Mobile internet access devices

### Mental/Oral Starters

Day 1
Add a 1-digit number to a 2-digit number (pre-requisite skills)

Day 2
Subtract a 1-digit number from a 2-digit number (pre-requisite skills)

### Procedural Fluency

Day 1
Select appropriate methods to add two 2-digit numbers.

Day 2
Select appropriate methods to add two 2-digit numbers for more challenging calculations.

### Mastery: Reasoning and Problem-Solving

Look at this bar diagram. Work out the value of the missing number:

 ? 32 64
• Explain why it might help to change the order of this addition before we try to find the answer.
15 + 62 = ☐
• Would you use counting on or partitioning to work out these additions? Why? Find the answers.
35 + 57
77 + 22
84 + 6
• Sam had some stickers. His sister takes 22 and he gives his friend 45. He has none left. How many did he start with?

In-depth Investigation: Diagonal hundreds
Children use trial and improvement to place numbers in a grid to give a pair of diagonals whose sum is equal to 100.

### Extra Support

Square Sums
Adding ‘friendly’ 2-digit numbers using partitioning (1s<100)

## Unit 2 Choose strategies to subtract (suggested as 3 days)

### Objectives

Choose strategies to subtract
Unit 2: ID# 2753

National Curriculum
Add/Sub (ib) (iiia) (iiib) (iiic) (v)

Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 or 17.Count back in 1s or 10s or use number facts to take away, e.g. 27 – 3 = or 54 – 20 =.
12. Begin to count up to find a difference between two numbers with a small gap, e.g. 42 – 38.
15. Solve problems involving addition and subtraction of numbers, quantities and measures, using recall of number facts and appropriate models and images.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Start with 87p and say you will spend 33p. Model marking these numbers on a 0p to £1 number line, and showing how we can count back three 10ps and then hop back another three 1ps to land on 54p.
Now spend another 38p, this time showing how we can count up using Frog to hop up the number line from the smaller to the bigger number.
Group Activities
-- Find the difference between two numbers involving money, using different methods.
-- Find the difference between two 2-digit number cards, explaining reasons for choosing methods used.

Day 2 Teaching
Remind children of the two methods they have explored for subtracting. Generate a 2-digit – 2-digit subtraction and model using both methods. Repeat. Discuss which methods the children used for their calculations and why. Which do you think was more efficient in this example…?
Group Activities
-- Find the difference between a pair of 2-digit numbers, choosing an appropriate method.
-- Find the difference between a pair of 2-digit numbers, suggesting the method to be used and devising ‘top tips’ for method selection.

Day 3 Teaching
Display three word problems (see resources). Read each. Agree whether we need to add or subtract. Give children time to work out answers before working through as a class. Refer to the Top Tips notes (made previously) to help decide which addition or subtraction strategy to use.
Group Activities
Use the ‘problem-writing’ group activity from today to apply skills from across this unit.
Or, use these activities:
-- Solve addition and subtraction word problems.
-- Write addition and subtraction word problems.

### You Will Need

• 0 to £1 penny number line (see resources)
• Resource sheets for tables A, B and C (see resources)
• 1-100 grids
• 2-digit number cards, timers and calculators
• Top marks spinners from www.topmarks.co.uk
• Internet access and digital devices
• Additional activity sheets (see resources)
• Whiteboards and pens
• Priced items

### Mental/Oral Starters

Day 1
Add to the next 10 (pre-requisite skills)

Day 2
Bonds to 10 (pre-requisite skills)

Day 3
Add 1-digit numbers to 2-digit numbers (pre-requisite skills)

### Procedural Fluency

Day 1
Solve subtraction with money using various methods.

Day 2
Solve subtractions then sort them according to the methods used.

Day 3
Complete and create addition and subtraction word problems.

### Mastery: Reasoning and Problem-Solving

• Four purses contain the following amounts: 37p, 48p, 25p, 53p.
Take 23p out of each purse. How much is left in each?
• Choose whether to use Frog to count up or whether to count back. Explain why you chose that method:
62 – 38
66 – 33
75 – 6
83 – 79
84 – 12
24 – 18
• Calculate the missing number in each bar model diagram. Diagram 1:
 64 ? 57

Diagram 2:

 79 31 ?

In-depth Investigation
Use and apply skills from this unit by completing the ‘Problem-writing’ group activity from Day 3.

### Extra Support

Pocket Money
Subtracting 11, 12, 13 from 2-digit numbers by counting back

## Unit 3 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 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 4 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 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 5 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 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 6 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 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

Mrs Multiple’s Cakes
Arranging 'cakes' in arrays and find which numbers between 10 and 20 can be arranged in most ways.