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# Maths Year 4 Spring Addition & Subtraction

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 Adding money using column addition (suggested as 2 days)

### Objectives

Unit 1: ID# 4637

National Curriculum
Fr (including decimals) (x)
Meas (iv)

Hamilton Objectives
11. Use column addition to add 3-digit numbers: first expanded, then compact method.
32. Solve simple money problems involving decimals to two decimal places.
36. Estimate, compare and calculate money in pounds and pence.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Remind children how to use expanded addition to add £3.24 and £2.58. Ask children to work out 324 + 258 using compact addition. Point out that this is also how we can add two amounts of money. Share other examples, e.g. £5.45 + £3.25; £4.17 + £2.76.
Group Activities
-- Use expanded addition and compact addition to add amounts of money.

Day 2 Teaching
Ask children to use both expanded and compact addition to work out £4.62 + £2.75, and £5.58 and £5.75 and to check that they get the same answer. Discuss how we leave a space above the answer to write the extra 10ps and £s.
Group Activities
Use the ‘Present Prices’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use expanded addition and compact addition to add 3-digit numbers.
-- Choose which method to use to add amounts of money.

### You Will Need

• On board practice 1 (see resources)
• On board practice 2 (see resources)
• 1p, 10p and £1 coins
• Flipchart

### Mental/Oral Maths Starters

Day 1
Add any pair of 2-digit numbers (pre-requisite skills)

Day 2
Use place value to add and subtract (pre-requisite skills)

### Procedural Fluency

Day 1
Find missing numbers in column additions of money.

Day 2
Use expanded addition and compact addition to add amounts of money.

### Mastery: Reasoning and Problem-Solving

• Complete these additions, using expanded column addition.
(i) £5.78 + £4.22
(ii) £2.56 + £7.44
(iii) £3.17 + £6.83
• Is a column addition calculation the most efficient way to find: £4.99 + £7.46, £8.06 + £8.06, £4.31 + £5.69?
• Write the missing numbers in this calculation:
 £ 10p 1p 4 ☐ 7 + 5 6 ☐ ☐ 4 5
• If £3.47 is subtracted from a number to leave £3.85, what was the number?

In-depth Investigation: Present Prices
Children use logic and addition, along with some trial and improvement to solve a problem involving money.

### Extra Support

Pocket Money
Adding two prices with a total of more than £1 using partitioning

## Unit 2 Count up to find change & differences (suggested as 2 days)

### Objectives

Counting up to find change and price differences
Unit 2: ID# 4643

National Curriculum
Fr (including decimals) (x)
Meas (iv)

Hamilton Objectives
12. Subtract numbers from 3-digit numbers using counting up (Frog).
32. Solve simple money problems involving decimals to two decimal places.
36. Estimate, compare and calculate money in pounds and pence.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show children items with prices tags less than £5 and a £5 note. Together work out the change. Use Frog. Draw a line from £2.85 to £5, so Frog jumps first to £3 and then to £5. Write each ‘jump’ then add these to find the difference between £2.85 and £5. Repeat, finding the change from £10.
Group Activities
-- Count up to find change from £5 and £10.

Day 2 Teaching
Show a set of prices and also a set of prices reduced in a sale. Demonstrate how we can use Frog to help us count up to find the difference between each pair of prices. What is it about this type of calculation that allows us to almost do them in our heads?
Group Activities
Use the in-depth problem-solving investigation ‘Dicey operations in line’ from NRICH as today’s group activity.
Or, use these activities:
-- Use an empty number line to count up to find the difference between two amounts of money.
-- Use addition to check answers to subtractions.

### You Will Need

• Items with price tags less than £5
• £5 note
• Flipchart

### Mental/Oral Maths Starters

Day 1
Change from £1 (pre-requisite skills)

Suggested for Day 2
6 times table (simmering skills)

### Procedural Fluency

Day 1
Find change from £5 and £10 by counting up.

Day 2
Draw empty number lines and find the difference between two amounts of money by counting up.

### Mastery: Reasoning and Problem-Solving

• Tim buys a DVD and Frog finds the change from £10. He says it is £3.46. How much was the DVD?
Complete each diagram.
Diagram 1

 £10 £6.83

Diagram 2

 £5 £2.27

Diagram 3

 £10 £3.58
• Write a list of ‘Top Tips’ for how you would find the difference between these two prices: £4.52 and £6.18.

In-depth investigation: Dicey Operations in Line
Adapt Game 2 to subtract pairs of 3-digit numbers, aiming for a difference as close as possible to 400. Dicey Operations in Line from nrich.maths.org.

### Extra Support

Winter Warmers
Finding the change from £5 (answers less than £1)

## Unit 3 Column addition: 3 or more 2-digit nos (suggested as 2 days)

### Objectives

Written column addition with 3 or more 2-digit numbers
Unit 3: ID# 4651

National Curriculum
Num/PV (viii); Add/Sub (i)

Hamilton Objectives
6. Add multiples of 1, 10, 100, 1000 without difficulty.
Working towards 11. Use column addition to add 3-digit and 4-digit numbers: first expanded, then compact method by adding columns of 2-digit numbers.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Ask a child to choose three numbers from a 100-square, such that the total will be more than 100. Model adding the numbers using expanded addition. Alongside, model compact addition. Repeat with other trios of numbers, including 56, 37 and 28 and 87 + 94 + 78.
Group Activities
-- Use compact addition to add three 2-digit numbers.

Day 2 Teaching
Ask children to choose four numbers from a 100-square, such that the total is more than 200. Model adding the numbers using compact addition. Repeat with another four numbers.
Play a game involving adding two, three or four 2-digit numbers with the aim of getting as close as possible to a total of 200, without going over.
Group Activities
Use the in-depth problem-solving investigation ‘Dicey operations in line’ from NRICH as today’s group activity.
Or, use these activities:
-- Solve word problems that involve adding two, three or four 2-digit numbers.
-- Use compact addition to add four 2-digit numbers.

### You Will Need

• ITP: Number Spinners
• 1-100 grid (see resources)
• Counters
• A set of 10–100 cards
• Word problems sheet (see resources)
• 10s and 1s cards
• Flipchart

### Mental/Oral Maths Starters

Day 1
Add four single-digit numbers (pre-requisite skills)

Day 2
Add four multiples of 10 (pre-requisite skills)

### Procedural Fluency

Day 1
Add three 2-digit numbers using expanded then compact addition.

Day 2
Add four 2-digit numbers using expanded then compact addition.

### Mastery: Reasoning and Problem-Solving

• True or false?
Adding three 2-digit numbers always produces a number over 50.
Adding three 2-digit numbers cannot produce 299.
There are three identical numbers which add to 252.
• Choose three consecutive numbers, e.g. 39, 40 and 41.
Repeat twice with different sets of consecutive numbers.
Can you see any relationship between the total in each case and the numbers added?
Simplify the numbers if it’s hard to spot a pattern.
Use a calculator to play with the numbers if necessary.
Does this work with all sets of three consecutive numbers, regardless of their size?
Can you explain why?

In-depth investigation: Dicey Operations
Adapt Game 1 to add three or four 2-digit numbers, aiming for a target total as close as possible to 200. Dicey Operations from nrich.maths.org.

### Extra Support

Do the Splits
Adding two 3-digit numbers using partitioning

## Unit 4 Subtraction strategies; written methods (suggested as 4 days)

### Objectives

Subtraction: written methods and choosing strategies
Unit 4: ID# 4663

National Curriculum
Add/Sub (i) (ii) (iii)

Hamilton Objectives
12. Subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426 – 278, 321 – 87.
14. Use column subtraction to subtract 3-digit and 4-digit numbers: first expanded, then compact method.
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Although column subtraction is specified for Year 3 in the National Curriculum, Hamilton believe that teaching column subtraction in Year 4 will be more successful. The National Curriculum Guidance specifies that teachers can teach areas of study in different year groups than those mentioned in the Curriculum, so long as they are taught within the same Key Stage. You can choose to teach this column subtraction content in Year 3 or in Year 4.

Day 1 Teaching
Display a word problem where we have to find how much further to cycle from 625 to 874 miles. Sketch a bar model to represent this then discuss how we can count up using Frog to find a difference. Model using Frog and adding the hops. Repeat this for 524 – 378 and 705 – 567.
Group Activities
Use the ‘Wonderful 1089’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Use counting up to find the difference between two 3-digit numbers.

Day 2 Teaching
Write on the board 725 – 462. We can easily subtract the ones, but we have 20 subtract 60. What do we do? Discuss taking a hundred and adding it to the tens. This process is called ‘decomposition’. Why do you think this might be? Model expanded column subtraction. Repeat for 417 – 254 and 624 – 381.
Group Activities
--Use expanded column subtraction to subtract 3-digit numbers using decomposition.

Day 3 Teaching
Write 403 – 267. Work this out using expanded decomposition. Make sure every child follows the process. Point out that this was quite a performance! Say that we could, in this case, use Frog. Model counting up. Point out that counting up is often easier if there is a zero in the larger number.
Group Activities
-- Choose an efficient method to subtract pairs of 3-digit numbers.
-- Solve word problems, which involve subtracting 3-digit numbers, choosing an appropriate method.

Day 4 Teaching
Display four subtractions (see resources) and ask which are correct. Identify errors and discuss methods. Write 654 – 456 and discuss methods. Repeat for 753 – 357. Point out we are subtracting numbers with reversed digits.
Group Activities
-- Investigate patterns that occur when subtracting reversed 3-digit numbers.

### You Will Need

• Whiteboards and pens
• Flipchart
• Base-10 equipment
• 0–9 dice
• Sticky notes
• Subtractions sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Subtract multiples of 10 (pre-requisite skills)

Day 2
Say what calculation is necessary to solve word problems (pre-requisite skills)

Day 3
Complements to next 100 (pre-requisite skills)

Suggested for Day 4
Round 3-digit numbers to the nearest 10 or 100 (simmering skills)

### Procedural Fluency

Day 1
Use empty number lines to subtract pairs of 3-digit numbers by counting up.

Day 2
Use expanded column subtraction to subtract 3-digit numbers.

Day 3
Choose counting up or column subtraction to subtract 3-digit numbers.

Day 4
Find and correct mistakes in subtractions using counting up and column subtractions.

### Mastery: Reasoning and Problem-Solving

• Complete each diagram.
Diagram 1
 604 387

Diagram 2

 912 868

Diagram 3

 1003 578
• Here is Ali’s homework.
1. 403 – 265
2. 648 – 356
3. 752 – 199
4. 812 – 754
Advise him on the most efficient or error-proof subtraction strategy to calculate each one, explaining why you are suggesting that method.
Work out the answers.
• Complete this subtraction calculation that uses decomposition:
 700 30 4 – 300 60 5
• Fill the gaps in this subtraction:
81☐ – 4☐7 = ☐46

In-depth Investigation: Wonderful 1089!
Children add two 3-digit numbers and subtract a pair of 3-digit numbers to find patterns. They use mathematical reasoning to begin to explain what they find.

### Extra Support

Are We Nearly There Yet?
Using counting up (Frog) to subtract numbers either side of 100, e.g. 102 - 97 and 102 - 78