Maths Year 4 Summer Addition & Subtraction (A)

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.

• 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

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

Suggested for day 2
8 times table (simmering skills)

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.

• 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.

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

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.

• 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

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)

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.

• 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.

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

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.

• 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)

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)

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.

• 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.

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