Maths Year 5 Summer Addition and Subtraction

Day 1 Teaching
Write on the board 4658 + 198 and 4658 + 205. Children work in pairs, one to work out each calculation. What do you notice about 198 and 205? What calculation could you work out that will help both of you? Agree that 4658 + 200 will be a useful step towards calculating both additions. Repeat with additions/subtractions of other near multiples.
Group Activities
-- Add, then subtract near multiples of 10, 100, 1000 to/from 5468.
-- Add/subtract near multiples of 10, 100, 1000 to/from 23,456.

Day 2 Teaching
Show the children some ‘Mental addition and subtraction’ calculations, all to be worked out mentally. No written column methods are allowed today! Point to £2.68 + □ = £3. Discuss, in pairs, what number fact can be used to help find the answer. Repeat with others that entail different mental strategies, including place value addition and subtraction.
Group Activities
-- Play fluency challenges – pairs to 100, £1 and 1 (numbers with two decimal places), then play an online game using pairs to 1.
-- Play against the clock, matching mental calculations to answers.

Day 3 Teaching
Write these equations on the board: 134 + 8 = 200 − □; 32 × 4 = □ × 2; 48 ÷ 4 = 12 × □; 3.6 × □ = 10 – 2.8
Tell me what you see. What do these equations mean? Emphasise that each equation must balance. Go through the equations, in turn: What numbers are missing? Work in groups of four to play a number sentences ‘Consequences’ game, to generate equations that balance, e.g. four different operations, each with the answer 72.
Group Activities
-- Write sets of balancing equations, using a mix of operations in each equation and across each set.

• Mini-whiteboards and pens
• Flipchart and pens
• ‘Add and subtract near multiples’ sheets 1 and 2 (see resources, cut up into cards)
• ‘Mental addition and subtraction’ sheet (see resources)
• ‘Mental addition and subtraction cards’ (2 sheets - see resources)
• Scissors
• Stopwatch or classroom clock
• Sheets of A4 paper

Day 1
Add/subtract 1-digit numbers to/from 4-digit numbers (pre-requisite skills)

Day 2
Complements to 100 (pre-requisite skills)

Suggested for Day 3
Double numbers with one decimal place (simmering skills)

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

Day 2
Mental calculations using number facts and place value.

Day 3
Solve equalities using a range of operations.

• How many times must I add 7 to 7728 get to 7777?
• Subtract 205 from each of…
  12,321
  45,254
  20,062
• What will the ones digit of your answer be if you carry out the following sequence?
  1. Start with 30,460.
  2. Add 9999
  3. Subtract 999
  4. Add 99
  5. Subtract 9
  6. What’s your final number?
• What numbers must be subtracted from 21,234 to leave:
  9999
  19,235
  21,035
• Complete each sentence:
  £4.36 + ☐ = £5
  £6.72 + ☐ = £10
  4.83 + ☐ = 10
• Write the value of each shape.
  701 – ★ = 3 × 152
  (6.25 × 6) + ☐ = 120 ÷ 3
  100 – 55.68 = 1/2 of Δ
• Here is an equation with two empty spaces. What ONE number will make the equation balance?
  (34 × 5) – ☐ = 4 × ☐ × 4

In-depth Investigation
Use the whole-class group activity on Day 3.

Reach 100
Place digits in a 2 × 2 grid so that the four 2-digit numbers made total 100. Can this be done on a 3 × 3 grid? Reach 100 from nrich.maths.org.

Day 1 Teaching
Write on the board 45,782 + 52,476; 4789 + 2997; 52,378 + 2641. Children work in groups of three, one to work out the answer to each. They share their workings with each other. Did children spot that the second could be worked out quite efficiently using a mental method? Did children align the numbers correctly in the third addition
Group Activities
-- Discuss several additions to focus on efficient methods for calculation. Find the answers.
-- Calculate several 4-digit and 5-digit additions, before discussing what makes numbers straightforward to add mentally.

Day 2 Teaching
Write on the board 4567 + 24 + 236 as a column addition but aligning the first digits of each number rather than the 100s, 10s and 1s. Discuss what is wrong, and estimate the total. Model the correct layout. Repeat for 724 + 7.8 + 2365.
Group Activities
-- Add three, four or five numbers – with different numbers of digits – to give answers within stated ranges.

Day 3 Teaching
Write on the board 345.7 + 278.6 and £24.78 + £52.69. Children work in pairs, one to work out the answer to each. Show both expanded and compact layouts. Talk through the similarities in adding 0.7 + 0.6 = 1.3 in the first and of 70p + 60p = £1 and 30p in the second.
Group Activities
-- Explore the use of expanded and compact addition for adding decimals, noting similarities when adding measures and money.
-- Collaborate to find pairs of amounts of money with a total of £44.44. and pairs of lengths with a total of 33.3cm. Note the digit restrictions!
-- Consolidate addition of two or more numbers with different numbers of decimal places.

• Mini-whiteboards and pens
• Flipchart and pens
• ‘Adding 3-digit and 4-digit numbers’ (see resources)
• ‘Adding 4-digit and 5-digit numbers’ (see resources)
• ‘Adding towers’ (see resources)

Day 1
Add and subtract 1999 (pre-requisite skills)

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

Suggested for Day 3
Place value in numbers with three decimal places (simmering skills)

Day 1
Add pairs of 3- and 4-digit numbers.

Add pairs of 4- and 5-digit numbers.

Day 2
Add ‘towers’ of 2-digit, 3-digit and 4-digit numbers.

Day 3
Add decimals, money and lengths in metres.

• Arrange the digits 4, 5 and 6 to create an addition of two 3-digit numbers which add to 1000. You may use each digit as often as you like.
• Explain why it would probably be sensible to choose different methods to solve (a) and (b) below. Then solve both.
  (a) 67,493 + 21,561
  (b) 50,005 + 9,998
• Complete the addition by finding ☐, ✜ and △:
  1 2 ☐ 6 2
  + 9 3 8 ✜
  2 △ 2 5 1
• Use all digits 2 to 8 once to create two amounts of money. Both amounts must have two decimal places, e.g. £23.45 and £6.78. Add these. Now re-arrange the digits to give the largest total possible. Now re-arrange the digits to give the smallest total possible.

In-depth investigation
Use the whole-class group activity on Day 2.

Super 7000
Using compact column addition to add pairs of 4-digit numbers

Day 1 Teaching
Write on the board 45,706 – 28,342 as an expanded vertical subtraction and a compact vertical subtraction. Solve together to revise these strategies. Next, write on the board 42,567 – 21,348; 51,230 – 24,769; and 34,213 – 22,048. Ask children which will be the fastest to work out and why. Discuss what makes column subtractions more or less efficient (more digit moves could make it more error-prone).
Group Activities
-- Explore moves between columns in 4-digit subtractions.
-- Explore moves between columns in 5-digit subtractions.
-- Consolidate subtractions of 5-digit, then 6-digit numbers which require 1, 2, 3, then 4 moves.

Day 2 Teaching
Write on the board 58,274 – 32,689; 50,000 – 47,892; 45,678 – 29,999; 63,428 – 20,002; 4002 – 3789; 3567 – 1999; 6428 – 2731; and 5438 – 3002. Children discuss, choosing four calculations they would solve mentally, and one for which they would use column subtraction. Which of the calculations lends itself to being solved by counting up (Frog)? (50,000 – 47,892, as it would need moves across four columns). Remind children that there are no ‘right’ or ‘wrong’ choices of preferred methods to solve calculations.
Group Activities
-- Explore the choice of methods available for subtraction; solve and create calculations.
-- Justify your choice of methods available for subtraction; create and solve calculations.

Day 3 Teaching
Write on the board: 4005 – 3789; £10.00 – £7.46; 61,003 – 45,869. Children use counting up (Frog) to work out one of these, sharing workings. Demonstrate on the board. Subtractions with lots of zeroes are probably best done with Frog, not column subtraction. Finding change (£10 – £7.46) is also best-done using Frog,
Group Activities
-- Choose column subtraction or Frog to subtract 4-digit numbers and amounts of money.
-- Subtract amounts of money from £100; find differences between lengths, in metres, with two decimal places.

• Mini-whiteboards and pens
• Flipchart and pens
• ‘Subtracting 5-digit numbers’ (see resources)
• Small blank cards to write on
• ‘Choose which way to subtract’ (see resources)
• Number cards 0–9

Day 1
Quick subtraction facts to 20 (pre-requisite skills)

Day 2
Complements to 1000s (pre-requisite skills)

Suggested for Day 3
Negative numbers (simmering skills)

Day 1
Use column subtraction to subtract pairs of 4- or 5-digit numbers.

Day 2
Choose counting up (Frog), counting back or column subtraction to subtract.

Day 3
Choose to use column subtraction or counting up (Frog) to work out subtractions. Reason about strategy choices.

• Complete the subtraction by finding ☐, ✜ and ⯂.
  7 8 ☐ 1 2
  − 9 3 8 ✜
  6 ⯂ 2 2 5
• Find Sam’s change from £100 if he spends £45.79.
• Say whether each statement is: Never, Sometimes, or Always true. Give an example to illustrate each one.
  -- It’s best to use Frog rather than column subtraction to help you find change.
  -- Subtracting a 4-digit number from a 5-digit number gives a 4-digit answer.
  -- The difference between two 5-digit near multiples of 1000 is a near multiple of 1000.

In-depth Investigation: Durer’s Magic Square
Children complete ‘Durer’s Magic Square’, then use it to create 2- or 3-digit numbers and find the difference between different pairs. They identify patterns.

Faithful Frog
Using counting up (Frog) to subtract 4-digit numbers either side of multiples of 1000, e.g. 5003 – 4984

Frazzled Frog
Using counting up (Frog) to subtract 4-digit numbers, with ‘larger gaps’, either side of multiples of 1000, e.g. 5214 – 4867