Maths Year 3/4 Summer Addition and Subtraction

Day 1
Model expanded and compact column addition. Y3 practise adding two 3-digit numbers; Y4 add two 4-digit numbers.
Group Activities: T with Y3
Y3 -- Add two 3-digit numbers, using expanded and/or compact addition.
-- Make two 3-digit numbers using dice; add the numbers using compact addition.
Y4 -- 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.

Day 2
Estimate totals by rounding to the nearest 100 or the nearest 10 before solving 3-digit additions.
Further Teaching with Y4
Revise compact decomposition for subtracting 3-digit numbers.
Group Activities: T with Y4
Y3 -- Think mathematically to use chosen digits to make two (or three) 3-digit numbers with a total as close as possible to 600 (or 1000). Use compact addition.
-- Estimate the total of two 3-digit numbers; find the exact total using compact addition.
Y4 – Work towards securing a written method for 3-digit subtractions.
– Consolidate use of compact column subtraction. Consider the most appropriate/efficient method for subtraction.

Day 3
Discuss why and where there will be ‘carries’ in 3-digit additions.
Further Teaching with Y4
Model compact decomposition of 4-digit numbers. Discuss why and where there will be ‘moves’ across columns in 4-digit subtractions.
Group Activities: T with Y4
Y3 -- Investigate addition of pairs of palindromic numbers.
Y4 – 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 4
Model addition of several 2-digit numbers using column addition.
Further Teaching with Y4
Further use of decomposition to subtract 4-digit numbers: 2 moves across columns.
Group Activities: T with Y3
Y3 -- Add three or four 2-digit numbers, using expanded and compact addition.
-- Estimate the total when adding three or four 2-digit numbers, then find the answer using compact addition.
Y4 -- Begin to secure use of expanded column subtraction to subtract pairs of 4-digit numbers.
-- Secure use of expanded column subtraction to subtract pairs of 4-digit numbers; begin to use compact subtraction. Subtract amounts of money.

Day 5
Consider mental strategies to solve 300 – 256, 678 – 523 and 678 – 199.
Further Teaching with Y3
Estimate and add three or four 2-digit numbers using expanded or compact addition.
Group Activities: T with Y3
Y3 -- Add several 2-digit numbers with a given target total.
Y4 Use the in-depth problem-solving investigation ‘Subtraction Surprise’ from NRICH as today’s group activity.
Or, use this activity:
-- Create subtraction questions that can be solved mentally.

• Mini-whiteboards and pens
• ‘3-digit number cards’ (cut into cards, see resources)
• Calculators
• 0–9 Dice (3 per child)
• 0–9 Digit cards
• Counters
• 100s, 10s and 1s place value cards/dice
• Flipchart and pens
• A3 paper
• Base-10 equipment (1000s, 100s, 10s, 1s)
• ‘Column subtraction of 4-digit numbers’ (see resources)
• ‘2-digit number cards’ (cut into cards, see resources)
• ‘Addition’ Sheets 1 and 2 (cut into cards, see resources)
• ‘Whole class practice’ (see resources)
• ‘Estimating totals’ Sheets 1 to 3 (see resources)

Day 1
Add multiples of 10

Day 2
Add four 1-digit numbers (uses the Number Spinners ITP)

Day 3
Subtract 1-digit numbers from numbers less than 100

Day 4
Subtraction facts to 20

Day 5
Subtraction facts: Multiples of 10

Day 1
Y3 Add two 3-digit numbers.
Y4 Column addition.

Day 2
Y3 Add numbers to reach a target.
Y4 Subtract 3-digit numbers.

Day 3
Y3 3-digit addition.
Y4 Column subtraction of 3-digit numbers.

Day 4
Y3 Add three and four 2-digit numbers.
Y4 Subtraction practise.

Day 5
Y3 Estimate and add several 2-digit numbers.
Y4 Subtraction strategies.

Y3

• Choose a different method to solve each addition:
  375 + 567 =
  638 + 51 =
  24 + 36 + 25 =
• Use column addition to help you to find each missing number:
  548 + 175 = ☐
  ☐ – 356 = 387
  635 + 296 = ☐
  ☐ – 466 = 247
• Sally has 45 Pokémon cards, Bill has 67, Jon has 28 and Parvati has 86. How many do they have altogether?
• Choose four of these numbers likely to give a total close to 200:
  73, 68, 56, 75, 66, 37.
  Add them using column addition. Is this the closest possible total to 200?

Y4

• 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. Calculate the correct answers, then advise Ali what mistake he has made in each.
• Write these two 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

Y3 In-depth investigation:
Look for patterns when adding numbers with a difference of 11 (Day 5 Working at Greater Depth, Group Activity 2).

Y4 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.

Y3: Totally investigative
Adding any pairs of 2-digit numbers using partitioning (including 1s greater than 10 and 10s greater than 100).

Y4: Expanded Sums
Using expanded column addition to add pairs of 3-digit numbers (one ‘carry’).

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

Day 1
Model subtraction using Frog, crossing 100, e.g. 137 – 72.
Further Teaching with Y4
Subtract from 4-digit numbers. Discuss what to look for when choosing between use of Frog and decomposition.
Group Activities: T with Y3
Y3 -- Use Frog to calculate the amount left in a purse after buying an item.
-- Use Frog to calculate differences.
Y4 Use the ‘Subtraction Trios’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- 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
Model finding differences using Frog (3-digit numbers).
Further Teaching with Y4
4-digit subtractions using decomposition and ‘Frog’. Reason about choices of strategy for subtraction.
Group Activities: T with Y4
Y3 -- Subtraction investigation using Frog.
Y4 -- Make and justify choice between ‘Frog’ and column subtraction to find differences. Some children will also include counting back in their strategy choice.

• Mini-whiteboards and pens
• ‘Heights to descend from Everest summit to base camp’ (see resources)
• ‘At the charity shop’ (see resources)
• ‘Purses’ (see resources)
• Bead string
• Real coins
• Flipchart and pens
• ‘Table of heights of camps on Everest’ (see resources)
• 0–9 cards
• Place value cards.
• ‘Mixed subtractions’ (see resources, copy onto A3 and cut up)

Day 1
Pairs with a total of 10 and multiples of 10 that total 100

Day 2
Pairs with a total of 100

Day 1
Y3 Use Frog to subtract.
Y4 Frog or column subtraction.

Day 2
Y3 Subtract 2- and 3-digit numbers using Frog.
Y4 Choose Frog or column subtraction.

Y3

• Use Maths Frog to help you write the missing numbers:
  78 + ☐ = 125
  68 + ☐ = 134
  375 – ☐ = 328
  571 = 518 + ☐
  127 + ☐ = 163
  836 = 862 – ☐
• Write two numbers either side of 100 which have a difference of 37.

Y4

• Estimate the answer to each of these subtractions:
  628 – 363
  772 – 538
  236 – 187
  Now calculate each.
  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.

Y3 In-depth investigation
Use the Group Activity on Day 2.

Y4 In-depth investigation: Subtraction Trios
Children look for patterns in answers when subtracting 3-digit numbers from 4-digit numbers with consecutive digits.

Y3: Frog goes freestyle
Subtracting pairs of 2-digit numbers with a bigger gap, e.g. 84 – 37, using counting up.

Y4: Frogs Epic Jumps
Subtracting numbers either side of a gap of 100, e.g. 502 – 396, 524 – 397 and 503 – 375.

Day 1
Model using Frog to find change from £5, £10 and £20 when buying one or several items.
Group Activities: T with Y3
Y3 -- Practise finding change from £5, £10 and £20.
-- Choose two items that add up to under £5, £10 or £20, then calculate change.
Y4 -- Buy multiple items that add up to under £20, then calculate change.
-- Choose two items that add up to under £5, £10 or £20, then calculate change.

Day 2
Model using Frog to find change from £100 when buying several items. Represent problems with a bar model.
Group Activities: T with Y4
Y3 Use the in-depth problem-solving investigation ‘Step Change’ as today’s group activity.
Or, use these activities:
-- Practise finding change from £100 for a range of items.
-- Play ‘Change from £100 pairs’.
Y4 -- Practise finding change from £100 when buying 2 or 3 items.

Day 3
Model finding differences using Frog, e.g. a game costs £18, if I have £7.55 how much more will I need to save?
Further Teaching with Y4
Use Frog to calculate differences between two amounts: £28.84 and £32.37; £23.24 and £18.78.
Group Activities: T with Y3
Y3 -- Calculate how much more money is needed to pay for a range of items.
-- Calculate how much more money is needed to pay for a more expensive version of an item.
Y4 -- Find the difference between two amounts of money.

Day 4
Explore a range of 3-digit subtractions to discuss the choice of most appropriate/efficient strategies.
Further Teaching with Y4
Reasoning about when to use mental or written subtraction in a range of examples.
Group Activities: T with Y4
Y3 -- Subtract two 3-digit numbers, beginning to recognise when to use each of two different mental strategies.
-- Find the mystery missing numbers that have been subtracted from 3-digit numbers.
Y4 -- Justify choices for, then use, mental or written strategies for subtraction.
-- Sort calculations according to whether they are more efficiently solved mentally or using a written method.

Day 5
Discuss several word problems. Would you use addition or subtraction calculations? Discuss how a sketch, number line or bar model can support visualisation before answering.
Group Activities: T with Y3
Y4 Use the in-depth problem-solving investigation ‘Prime Addition Squares’ as today’s group activity.
Or, use these activities:
Y3/Y4 -- Solve single-step word problems in a group, then in pairs.
-- Fill the gaps with missing numbers in multi-step number stories.

• Mini-whiteboards and pens
• Items that might be for sale in a seaside shop, e.g. sun cream, beach towel, bucket, spade with prices £2.74, £1.43, £8.53 and £5.72
• Toy labelled £4.67; a real £5 and £10 note
• ‘Finding change’ (see resources)
• ‘Penny lines’ (see resources)
• ‘The beach shop’ (see resources)
• Coins
• 1–6 dice
• Calculators
• ‘Finding change from £100’ (see resources)
• ‘Finding change from £20’ sheets (see resources)
• ‘Set A’ and ‘Set B’ game cards (cut up and separated into two piles for each game, see resources)
• Picture of a console/computer game
• ‘How much more?’ Sheets 1 and 2 (see resources)
• ‘0–£1 penny line’ (see resources)
• ‘Items for sale’ sheet (see resources)
• ‘Money cards’ Sets A and B’ (see resources)
• Flipchart and pens
• ‘Mental or written?’ Sheet 1 and 2 (see resources)
• Red and blue interactive whiteboard pens
• ‘Subtracting mentally’ (see resources)
• ‘Word problems’ Sheet 1 and 2 (see resources)
• Sticky notes

Day 1
Add to the next 10

Day 2
Subtraction facts to 20

Day 3
Count on in steps of 10p from any amount

Day 4
Add/subtract multiples of 10 and 100 to/from 3-digit numbers

Day 5
Match digital and analogue times

Day 1
Y3 Find change from £5, £10 or £20.
Y4 Find change from £5, £10 or £20.

Day 2
Y3 Find change from £20 or £100.
Y4 Find change from £50 or £100.

Day 3
Y3 How much more (comparing costs)?
Y4 Find differences (money).

Day 4
Y3 Subtract mentally.
Y4 Mental or written subtraction?

Day 5
Y3 Addition and subtraction word problems.
Y4 Addition and subtraction word problems.

Y3

• Calculate the change from £10 when buying:
  Key ring £5.68
  Cards £7.75
  Pen £6.43
• Calculate the change from £50 when buying:
  Game £34.75
  Controller £42.56
  Case £28.67
• Calculate the change from £100 when buying:
  Game £67.43
  Console £85.85
  Tablet £73.68

Y4

• Write the missing numbers:
  £26.67 = £100 – ☐
  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.

Y3 In-depth investigation: Step Change
Children find change from 2 or 3 notes. They explore patterns in the pence.

Y4 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.

Y3: Read it
Finding change from £1.

Y4: Pick ‘n’ Mix
Using place value to add and subtract to/from 3-digit numbers.

Day 1
Model adding three 3-digit numbers using expanded and compact addition. Estimate by rounding to the nearest 100.
Further Teaching with Y4
Model solving 4-digit subtractions using decomposition, discuss how to recognise the number of column ‘moves’.
Group Activities: T with Y3
Y3 -- Practise adding trios of 3-digit numbers, using either expanded or compact addition (totals less than 1000 and greater than 1000).
Y4 -- Secure use of expanded column subtraction to subtract pairs of 4-digit numbers.
-- Consolidate use of expanded column subtraction to subtract pairs of 4-digit numbers.

Day 2
A confident Y4 shows Y3s how they solve 5721 – 3456 using column subtraction.
Further Teaching with Y3
Model using column addition to solve money problems.
Group Activities: T with Y3
Y3 -- Practise using expanded or compact addition to add amounts of money.
-- Estimate then calculate multiple costs that add to less than £10.
Y4 -- Use digits 2–9 to create 4-digit compact subtractions needing 3 moves.
-- Use digits 3–8 to create 3-digit compact subtractions needing 2 moves.

Day 3
Discuss a range of additions that illustrate use of different strategies, including mental methods (place value and ‘add and adjust’).
Further Teaching with Y4
Share the thinking behind what to look for when choosing calculation methods (all four operations).
Group Activities: T with Y4
Y3 Use the in-depth problem-solving investigation ‘Mobile Towers’ as today’s group activity.
Or, use these activities:
-- Add two 3-digit numbers, beginning to recognise when to use each of two different mental strategies.
-- Pick two cards and decide if using a written method for addition or a mental calculation is more efficient.
Y4 Use the ‘Prime Addition Squares’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Choose methods for a range of calculations (all operations); justify choices.

• ‘Adding three 3-digit numbers’ Sheets 1 and 2 (see resources)
• ‘Adding pairs of 3-digit numbers’ Sheet 3 (see resources)
• ‘Bicycles for sale’ (see resources)
• ‘Column subtraction’ (see resources)
• ‘Adding amounts of money’ Sheets 1 and 2 (see resources)
• Flipchart and pens
• Books with price tags: £4.79, £3.14, £6.01, £5.49, £5.88, £5.25, £3.23, £4.65, £4.29, £2.35, £5.17, £2.52
• 2–9 digit cards
• Calculators
• ‘Choosing how to do calculations’ Sheets 1 and 2 (see resources)
• ‘Adding mentally’ (see resources)
• 100s, 10s and 1s place value cards
• ‘3-digit number cards’ Sheets 1 and 2 (see resources - cut into cards)
• A3 paper
• Mini-whiteboards and pens

Day 1
Add three multiples of 10

Day 2
Complements to £1

Day 3
Subtract pairs of 2-digit numbers

Day 1
Y3 Target numbers: add 3-digit numbers.
Y4 Column subtraction.

Day 2
Y3 Add money.
Y4 More column subtraction.

Day 3
Y3 Methods for adding 3-digit numbers.
Y4 Choose how to do calculations.

Y3

• Use a different method to add each pair of numbers:
  682 + 199
  365 + 532
  26 + 35 + 74
• Choose three of these numbers and write an estimate of their total:
  475, 386, 287, 349, 248.
  Add the three numbers and compare the actual answer with your estimate. Repeat, choosing three different numbers. Was your second estimate closer?
• Work out the missing numbers in this addition puzzle:
  £4 ☐p 8p
  £7 80p ☐p
  £☐ 60p 1p

Y4

• 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?

Y3 In-depth investigation: Mobile Towers
Children create four or five 2-digit numbers and add these to get different totals.

Y4 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.

Y3: Addition of 3-digit Numbers
Using the interactive tool from Harcourt School at http://www.harcourtschool.com, children use base-10 blocks to explore regrouping in addition.

Y4: Pick ‘n’ Mix – Using place value to add and subtract to/from 3-digit numbers.