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# Maths Year 4 Summer Addition and 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 Column addition, including money (suggested as 2 days)

### Objectives

Use column addition, including to add amounts of money
Unit 1: ID# 4721

National Curriculum
Dec/Fr (x)
Meas (iv)

Hamilton Objectives
32. Solve simple money problems involving decimals to 2 decimal places.
36. Estimate, compare and calculate money in pounds and pence.
11. Use column addition to add 3-digit numbers: first expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 426 + 257 + 582 and 275 + 446 + 385. Estimate the answer to each addition. Point out that lots of the numbers round up so looking at the first digit only does not give a good estimate. Model using compact addition for the first addition. Compare with children’s estimates. Children use compact addition for 2nd addition, then for 726 + 457 + 582.
Group Activities
-- Whole class investigation: Apply compact addition skills to add trios (or pairs) of 3-digit numbers, aiming for given target totals.

Day 2 Teaching
Show a complete compact addition for £3.55 + £2.76. Ask children to explain to their partners how this was done, talking through each stage. Discuss each stage. Show books with price labels: £4.79, £5.49, £5.25, £4.65, £4.29. Children collaborate to find totals of pairs for under £10.
Group Activities
-- Add pairs of amounts of money using expanded and then compact addition.
-- Choose the most efficient method to add pairs of 3-digit amounts (some money).
-- Apply compact addition skills to add trios of 3-digit amounts of money.

### You Will Need

• Mini-whiteboards and pens
• Books with price labels: £4.79, £5.49, £5.25, £4.65, £4.29
• ‘Adding amounts of money’ (see resources)
• Flipchart and pens
• ITP: Number Grid

### Mental/Oral Maths Starters

Day 1
Add 3 multiples of 10 (pre-requisite skills)

Suggested for day 2
8 times table (simmering skills)

### Procedural Fluency

Day 1
Use a written method to add pairs, or trios, of 3-digit numbers. Estimate answers by rounding numbers to the nearest 10.

Day 2
Use expanded and compact column addition to find totals of pairs of amounts of money. Estimate whether totals are <£10 or >£10.
Estimate totals and use compact column addition to find totals of pairs of amounts of money.

### Mastery: Reasoning and Problem-Solving

• Write these 2 numbers in expanded form, i.e. as hundreds + tens + ones:
475
205
Add them mentally; write the total.
• Complete these using column addition:
(i) 367 + 272
(ii) 548 + 237
(iii) 479 + 258 + 382
(iv) £6.29 + £5.75
• Write the missing numbers in this calculation:
£10.64 = £4.8 + £.7

In-depth Investigation
Use Whole Class Activity from Day 1.

### Extra Support

Expanded Sums
Using expanded column addition to add pairs of 3-digit numbers (one ‘carry’)

## Unit 2 Expanded & compact column subtraction (suggested as 3 days)

### Objectives

Use expanded and compact column subtraction with numbers <1000
Unit 2: ID# 4729

National Curriculum

Hamilton Objectives
14. Use column subtraction to subtract 3-digit numbers: first expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Record expanded layout for 782 – 467. What’s the first step? We can’t work out 2 – 7 without using negative numbers, so what do we do? Agree we move a 10 from the 10s to add to the 1s. Work through the stages. Repeat with other subtractions requiring just 1 move, e.g. 425 – 283, 945 – 328, 815 – 382.
Group Activities
-- Use base 10 equipment and place value cards to support expanded column subtraction.
-- Subtract pairs of 3-digit numbers using the most efficient method, including expanded column subtraction.

Day 2 Teaching
Use expanded column subtraction to work out 652 – 327. Model compact subtraction alongside. This second method is called the ‘compact’ method. What is the same and what is different about these two subtraction methods? Repeat with 725 – 484. Ask children to work out 452 – 138 and 627 – 243 using both expanded and compact methods. Plenary: Discuss how to check subtraction with addition.
Group Activities
-- Use expanded column subtraction to subtract pairs of 3-digit numbers: Use base 10 equipment to aid.
-- Begin to use compact column subtraction.
-- Use compact column subtraction.

Day 3 Teaching
Use expanded column subtraction to work out 722 – 347. By the side, record compact layout, talking through each stage. Repeat with 934 – 476. Now 6 children at front of class hold 3 digit cards each to create a subtraction. Children work out the answer. Were they right? Repeat several times.
Group Activities
Use the ‘Mobile subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use expanded column subtraction to subtract pairs of 3-digit numbers: Use base 10 equipment to aid.
-- Consolidate use of compact column subtraction. Begin to recognise the most appropriate method for subtraction.

### You Will Need

• Base 10 blocks
• Place value cards: 100s, 10s and 1s
• ‘Subtractions for whole class practice’ (see resources)
• Flipchart and pens
• Base 10 equipment
• Mini-whiteboards and pens
• 1 to 6 dice
• 0 to 9 dice or 100s, 10s & 1s place value dice
• Large 1 to 9 digit cards

### Mental/Oral Maths Starters

Day 1
Subtract 2-digit numbers (pre-requisite skills)

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

Suggested for Day 3
Order positive and negative numbers (simmering skills)

### Procedural Fluency

Day 1
Use expanded column subtraction to subtract pairs of 3-digit numbers.

Day 2
Use expanded column subtraction to subtract pairs of 3-digit numbers.
Use expanded, then compact column subtraction to subtract pairs of 3-digit numbers.

Day 3
Choose an appropriate method to subtract pairs of 3-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Write these 2 numbers in expanded form, i.e. as hundreds + tens + ones:
749
321
Mentally find the difference between them; write the answer.
• Complete these using column subtraction:
(i) 538 – 264
(ii) 783 – 427
(iii) 446 – 382
(iv) 621 – 355
• Write the missing numbers in this calculation:
88☐ - 3☐7 = 535

In-depth Investigation: Mobile Subtractions
Children select 3 contiguous numbers from a mobile phone display
and create a subtraction.

### Extra Support

Hops to 100 and Beyond
Using counting up (Frog) to subtract numbers either side of a multiple of 100, e.g. 304 – 297, then 304 – 267

## Unit 3 Column subtraction, 3- & 4-digit numbers (suggested as 3 days)

### Objectives

Use column subtraction with 3- and 4-digit numbers
Unit 3: ID# 4751

National Curriculum

Hamilton Objectives
14. Use column subtraction to subtract 3-digit and 4-digit numbers: First expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 543 – 357, 347 – 178 and 481 – 235 on the board. Discuss in pairs which will have the largest/smallest answer. Take feedback on estimates. Children help you use compact column subtraction to find 543 – 357; model expanded method for any children who prefer. Children complete the other 2 subtractions, comparing answers with estimates.
Group Activities
-- Work towards securing a written method for 3-digit subtractions.
-- Consolidate use of compact column subtraction. Continue to consider the most appropriate method for subtraction.

Day 2 Teaching
Ask children to talk you through the steps in expanded column subtraction to find 5927 – 3456 (don’t forget to recombine the answer). Point out that this is really no harder than subtracting 3-digit numbers; there are just more subtractions to do along the way. Children to come up with - and solve - a subtraction where we only need to move a 10 to the 1s; then a subtraction where we only need to move a 1000 to the 100s.
Group Activities
Use the in-depth problem-solving investigation ‘Subtraction Surprise’ from NRICH as today’s group activity.
Or, use these activities:
-- Use base 10 equipment in a place value grid to help with expanded column subtraction of 4-digit numbers (1 move).
-- Begin to use compact column subtraction of 4-digit numbers (1 move).

Day 3 Teaching
A plane is flying at 9240 metres above sea-level. It descends 1425 metres. Show children how to use expanded column subtraction to work out the new height, taking time to discuss the 2 moves across PV columns. Repeat for a new descent, introducing the compact method for the same calculation alongside.
Group Activities
-- Begin to secure use of expanded column subtraction to subtract pairs of 4-digit numbers needing 1 move.
-- Secure use of expanded column subtraction to subtract pairs of 4-digit numbers; begin to use compact subtraction. Subtract amounts of money.

### You Will Need

• Mini-whiteboards and pens
• 0 to 9 digit cards
• Flipchart and pens
• A3 paper
• Base 10 equipment (1000s, 100s, 10s, 1s)
• ‘Column subtraction of 4-digit numbers’ activity sheet (see resources)
• ‘Vertical place value chart’ (see resources)
• ‘Whole class practice’ activity sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Subtraction facts to 20 (pre-requisite skills)

Day 2
Subtraction facts: Multiples of 10 (pre-requisite skills)

Suggested for Day 3
6 times table (simmering skills)

### Procedural Fluency

Day 1
Use column subtraction to subtract pairs of 3-digit numbers, watching out for one or two that would be more efficiently solved using counting up.

Day 2
Column subtraction of 3-digit numbers.
Column subtraction of 4-digit numbers.

Day 3
Column subtraction of 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Estimate the answer to each of these subtractions:
628 – 363
772 – 538
236 – 187
Now calculate each 1.
Find the difference between your estimate and the exact answer in each case.
• How many times can you subtract 2816 from 9999?
Find out by doing the subtractions.
You should have a palindromic number left!
• Use these digits to create 2 different 4-digit numbers:
4 1 6 8
Subtract the smaller from the larger. Repeat this. Will your answer always be an even number? Justify your opinion.

In-depth Investigation: Subtraction Surprise
Watch a short video of some calculations which lead to a surprising result! What do you notice? Can you describe the steps carried out in each calculation? Subtraction Surprise from nrich.maths.org.

### Extra Support

Hops and Jumps
Subtracting numbers either side of a multiple of 100 using Frog, e.g. 624 – 596, 403 – 376 and 512 – 487

## Unit 4 Appropriate strategies to add/subtract (suggested as 2 days)

### Objectives

Subtract 3-digit and 4-digit numbers using an appropriate strategy
Unit 4: ID# 4759

National Curriculum

Hamilton Objectives
12. Subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426–278, 321-87.
13. Use 'Frog' to subtract from multiples of 1000 where the difference is less than 500.
14. Use column subtraction to subtract 3-digit & 4-digit numbers: First expanded, then compact method.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Everest is the highest mountain in the world at 8848m above sea level. Display table of heights to descend from the summit to base camp (see resources). Use column subtraction to subtract 453m from 8848m to find the height of ‘The balcony’ (1 move). Stress aligning the digits to the right. Repeat for 8848 – 952 (two moves: 100s & 10s), then 8848 – 985 (two moves: 100s & 1s).
Group Activities
-- Use counting up (Frog) to find height differences between camps on Everest.
-- Use compact subtraction to calculate the heights of each camp on Everest; check each subtraction using addition.

Day 2 Teaching
Write 3000 – 2674 on the board. Model compact column subtraction to find the answer (make quite an ordeal of it!). What might be a more efficient way to do this subtraction? Draw out using Frog. Draft a line from 2674 to 3000 and use Frog to solve. MUCH quicker! Write 4002 – 3978. Discuss an appropriate strategy. Choose strategies for other subtractions, e.g. 5324 – 5297, 6542 – 4362, 9874 – 2344, 6000 – 5873, 4012 – 3679, 6124 – 5968.
Group Activities
Use the ‘Subtraction trios’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Make and justify choice of Frog or column subtraction to find differences.
-- Make and justify choice of Frog, counting back or column subtraction to find differences.

### You Will Need

• Table of ‘Heights to descend from Everest summit to base camp’ (see resources)
• Mini-whiteboards and pens
• ‘Table of heights of camps on Everest’ (see resources)
• Flipchart and pens
• ‘Mixed subtractions’ (see resources)
• Three sheets of paper
• ITP: Number Grid

### Mental/Oral Maths Starters

Suggested for Day 1
7 times table (simmering skills)

Day 2
Complements to 100 (pre-requisite skills)

### Procedural Fluency

Day 1
Use Frog to subtract 4-digit numbers mainly either side of a multiple of 100.
Use column subtraction to subtract 3-digit from 4-digit numbers.

Day 2
Choose Frog or column subtraction to subtract pairs of 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

• Write the missing numbers:
☐ + 886 = 1532
5875 + ☐ = 6293
9381 – 5864 = ☐
1001 – ☐ = 784
• True or false? Explain your ideas…
-- Subtracting from a multiple of 1000, it is best to use Frog.
-- Subtracting a 3-digit number from a 4-digit number always gives an answer greater than 1000.
-- Subtracting 4827 from 7284 will only involve moving amounts from 1 column.
-- Subtracting 895 from 2222, column subtraction is not the best method.

In-depth Investigation: Subtraction Trios
Children look for patterns in answers when subtracting 3-digit numbers from 4-digit numbers with consecutive digits.

### Extra Support

Frog's Epic Jumps
Subtracting numbers either side of a gap of 100, e.g. 502 – 396, 524 – 397 and 503 – 375

## Unit 5 Column add/subt with 3- & 4-digit numbers (suggested as 2 days)

### Objectives

Column addition and subtraction with 3- & 4-digit numbers
Unit 5: ID# 4783

National Curriculum

Hamilton Objectives
11. Use column addition to add 3-digit numbers: first expanded, then compact method.
14. Use column subtraction to subtract 3-digit & 4-digit numbers: first expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 5721 – 3456. Remind children of both expanded and compact column subtraction, talking through the two necessary ‘moves’ between place value columns. Write 4123 – 2785. What moves are necessary? We need 3 moves! Write 6234 – 2174, 6234 – 2678, 6234 – 2003, 6234 – 2418. Discuss what moves are necessary for each. Recognise that 6234 – 2003 is most efficiently solved using a mental method.
Group Activities
-- Secure use of expanded column subtraction to subtract pairs of 4-digit numbers (1 or 2 moves).
-- Consolidate use of expanded and compact column subtraction to subtract pairs of 4-digit numbers (2 or 3 moves).
-- Use digits 2 to 9 to create 4-digit compact subtractions needing 3 moves.

Day 2 Teaching
Write 2454 + 1327. Children discuss an addition strategy in pairs. Confirm and model the expanded layout. Also show how the compact layout can be used. Repeat for 2458 + 1377, then ask children to choose the expanded or compact layout to find 2451 + 1827 and 8451 + 4327.
Group Activities
Use the in-depth problem-solving investigation ‘Images of addition and subtraction’ from NCETM as today’s group activity.
Or, use this activity:
-- Whole-class activity: Use the digits 6, 7, 8 and 9 (or 3, 4, 5 and 6) to make a 4-digit number. Reverse the digits and find the total, e.g. 7689 + 9867. Find the digit sum of the answer. Describe patterns.

### You Will Need

• Mini-whiteboards and pens.
• ‘Column subtraction’ activity sheet (see resources).
• 2 to 9 digit cards.

### Mental/Oral Maths Starters

Suggested for Day 1
Subtract pairs of 2-digit numbers (simmering skills)

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

### Procedural Fluency

Day 1
Use a column subtraction method to subtract pairs of 4-digit numbers, watching out for the occasional calculation best solved mentally.

Day 2
Use column addition to add pairs of 4-digit numbers, watching out for the occasional calculation best solved mentally.

### Mastery: Reasoning and Problem-Solving

Complete each diagram.
Diagram 1:

 6614 4875 ?

Diagram 2:

 9712 ? 7685

Diagram 3:

 ? 3578 846

Here is Ali’s homework.

 1. 4278 + 2675 = 6842 2. 5678 + 2656 = 7224 3. 7552 + 1995 = 8447 4. 1862 - 7543 = 8305

He is upset as he has them all wrong! Work out the correct answers then advise him what mistake he has made in each.

In-depth Investigation: Images of Addition and Subtraction
Children look at some models and images used for addition and subtraction then sort cards, thinking about the skills used. Images of Addition and Subtraction from www.ncetm.org.uk

### Extra Support

Digit Twist
Using expanded column addition to add pairs of 3-digit numbers (1 ‘carry’)

## Unit 6 Choose methods for add/subt problems (suggested as 3 days)

### Objectives

Choose appropriate methods to solve addition and subtraction problems
Unit 6: ID# 4789

National Curriculum

Hamilton Objectives
11. Use column addition to add 3-digit numbers: First expanded, then compact method.
14. Use column subtraction to subtract 3-digit & 4-digit numbers: First expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write +29, –19, +195, –203, +1998, –999. Point to each. Children discuss how to add/subtract these numbers. After each discussion, model drawing an empty number line (ENL) jotting to show the addition/subtraction to/from 6745, e.g. a jump back of 200, then hop forward of 5 to subtract 195.
Group Activities
-- Add/subtract multiples of 10 and 100, then related near multiples.
-- Guided calculation of questions from activity sheet: Add and subtract near multiples of 10, 100 and 1000.
-- Discuss what calculation might be shown on largely unlabelled number line jottings.

Day 2 Teaching
Explain that children now have the skills to choose appropriate method for any addition/subtraction! Some are written and some are mental methods. Display ‘Mental or written?’ calculations (see resources). Ask children to spot an addition or subtraction which they would do mentally. Ring it in blue. Ring in red for a written method. Discuss any disputes!
Group Activities
-- Justify choices for, then use mental or written strategies.
-- Sort calculations according to whether they are best worked out mentally or using a written method.

Day 3 Teaching
Give each pair of children 3 word problems (see resources). Ask them to read the first and discuss what they need to do to the numbers in the problem to solve it. They then write + or – beside it. Ask pairs to say how they decided which operation to use. Solve this problem, and then repeat for the other 2.
Group Activities
Use the ‘Prime addition squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Solve single-step word problems in a group, then in pairs.
-- Fill the gaps with missing numbers in multi-step number stories.

### You Will Need

• Flipchart and pens
• ‘Adding and subtracting near multiples’ activity sheet (see resources)
• ‘Mystery additions and subtractions’ activity sheet (see resources)
• ‘Mental or written?’ sheet 1 (see resources)
• Addition activity sheets (see resources)
• Red and blue IWB pens
• Sticky notes

### Mental/Oral Maths Starters

Day 1
Add/subtract multiples of 10, 100 1000 to/from 4-digit numbers (pre-requisite skills)

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

Suggested for Day 3
Convert from cm to m and cm (simmering skills)

### Procedural Fluency

Day 1
Add and subtract multiples, then near multiples of 10, 100 and 1000.
Add and subtract near multiples of 10, 100 and 1000.

Day 2
Choose at least 2 mental additions, 2 mental subtractions, 2 written additions and 2 written subtractions to work out. (4-digit numbers +/- 3 or 4-digit numbers.)

Day 3
Read and addition and subtraction word problems.
Solve multi-step word problems.

### Mastery: Reasoning and Problem-Solving

• Use a different method to add each pair of numbers:
3682 + 199
4385 + 3784
26 + 35 + 74
• Use a different method to find the difference between each pair of numbers:
3483 – 201
5005 – 3896
7624 – 4378
• Use these digits: 5, 8, 3
Create two 3-digit numbers by placing the digits in a different order.
Add these two numbers – this is answer A.
Find the difference between these numbers – this is answer B.
Find the difference between A and B.
Double the smaller of your first 2 numbers.
What do you notice?

In-depth Investigation: Prime Addition Squares
Children add sets of three 3-digit numbers to find patterns in a magic square based on prime numbers.

### Extra Support

Pick 'n' Mix
Using place value to add and subtract to/from 3-digit numbers