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Maths Year 4 Summer Addition & Subtraction (A)

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 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