Short Blocks

Maths Year 5/6 Spring Calculation

Each unit has everything you need to teach a set of related skills and concepts.

Unit 1 Use of brackets in calculation (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Write 4 + 3 × 12. Ask half the class to work from left to right and others work beginning with the 3, i.e. 3 × 12 + 4. Discuss different answers. Introduce the rules: Brackets, then multiplication/division, then addition/subtraction. Repeat with calculations 4 + 16 ÷ 2 and (4 + 16) ÷ 2.
Group Activities: T with Y6
Y5 -- Explore different orders of addition, multiplication and brackets.
Y6 -- Use three or more number cards 2–9 to create calculations; solve using correct order of operations.

Day 2 Teaching
Explore the order of operations using brackets, for example, (15 + 2) × 4 and 15 + (2 × 4). Discuss how putting the brackets in different places can alter the answer to a calculation. Write 12 + 8 ÷ 4 – 3. Children work in pairs to find the (only) correct answer (11), then other possibilities by using brackets.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘All at 6s and 7s’ as today’s group activity.
Or, use these activities:
Y5 -- Use numbers 1, 2 and 3 with any operations/brackets, to make all numbers from 0 to 9. Use just the number 3 repeatedly with any operations/brackets, to make all numbers from 0 to 10.
Y6 -- Use just the number 3 repeatedly with any operations/brackets, to make all numbers from 0 to 10. Use numbers 6, 2, 3, 4 in sequence to make whole numbers.

Short Mental Workouts

Day 1
Mental division

Day 2
Find intervals using 24-hour clock

Worksheets

Day 1
Y5: Solve calculations, observing brackets and the correct order of operations.
Y6: Solve calculations, observing brackets and the correct order of operations.

Day 2
Y5: Place brackets to create correct number sentences.
Y6: Place brackets to create correct equalities.

Mastery: Reasoning and Problem-Solving

Y5 and Y6

  • In relation to multi-part calculations, agree if these statements are true or false:
    -- We leave the part in brackets until last.
    -- It does not matter which order you do the parts of the calculation not in brackets.
    -- We should always do the easiest parts of a calculation first.
    -- 12 + (3 × 4) gives the same answer if the brackets are removed.
  • Put a pair of brackets in three different places in this calculation to give three different answers:
    4 + 5 × 12 – 7 = ☐
  • Write a word problem involving the numbers 5, 6, and 12 and the answer 132. (Hint, you will need to use brackets in the final calculation.)

In-depth Investigation: All at 6s and 7s
Children try to make every number to at least 10 using 6, 7 and sometimes 2 and 3, and any operations.

Extra Support

Y5 and Y6: Order, Order!
Practising ordering calculations involving brackets, +, −, × and ÷.

Unit 2 Addition and subtraction (suggested as 5 days)

Planning and Activities

Day 1 Teaching
Use Frog to work out how far cyclists have to go before cycling 4000 miles across America. Model using frog to calculate 100,000 – 76,459.
Group Activities: T with Y5
Y5 -- Practise counting up to find a difference between 4-digit numbers and 10,000 by completing an investigation.
Y6 -- Practise counting up to find a difference between 5-digit numbers and 100,000 by completing an investigation.

Day 2 Teaching
Round to find an estimate; use column addition to add pairs of 5-digit numbers. Find pairs of numbers which add to 40,000. What do the pairs have in common?
Further Teaching with Y6
Use column addition to add a 4-digit number to a 5-digit number, then find the difference between the total and 100,000.
Group Activities: T with Y6
Y5 -- Work out the mystery digits in 4- or 5-digit column additions.
Y6 -- Work out mystery digits in a range of column additions.

Day 3 Teaching
Use column subtraction to subtract 5-digit numbers, predict numbers of moves, add to check.
Further Teaching with Y6
Discuss how to lay out 61,638 – 4271 and 61,638 – 742, subtract.
Group Activities: T with Y6
Y5 -- Work out mystery digits in 4- or 5-digit column subtractions.
Y6 -- Work out mystery digits in a range of column subtractions.

Day 4 Teaching
Display priced items on the board. Use Frog to find how much change we would have from £100 to buy a chosen item. Calculate a total of two items, then the change from £100.
Group Activities: T with Y5
Y5/Y6 -- Find money totals and change from £100 (or £50, or £200).

Day 5 Teaching
Draw a diagram on the board showing differences between amounts. Use Frog to find which pairs of amounts have which differences.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Pence and pounds reversed’ as today’s group activity.
Or, use these activities:
Y5 -- Explore money differences using Frog.
Y6 -- Investigation involving 4-digit and 5-digit subtractions of money using Frog.

You Will Need

  • 6, 7, 8 and 9 digit cards
  • Sticky notes
  • ‘Room makeover’ sheet (see resources)
  • Number cards 4–9
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Pairs to 1000

Day 2
Rounding whole numbers to the nearest 1000

Day 3
Add pairs of 2-digit numbers

Day 4
Bonds to £1

Day 5
Subtract pairs of 2-digit numbers

Worksheets

Day 1
Y5: Use Frog to count up from 4-digit numbers to multiples of 1000.
Y6: Use Frog to count up from 5-digit numbers to multiples of 10,000.

Day 2
Y5: Add pairs of 4- or 5-digit numbers; find the difference between the total and 10,000 or 100,000.
Y6: Add to find new scores; calculate how many to reach 100,000.

Day 3
Y5: Use column subtraction to subtract 3-, 4- and 5-digit numbers from 5-digit numbers.
Y6: Use column subtraction to subtract pairs of 5-digit numbers.

Day 4
Y5: Find the change from £50 and £100, then find totals and the change from £100.
Y6: Calculate totals and calculating change: ‘Shopping in Town’.

Day 5
Y5: Estimate, then find the difference between amounts of money.
Y6: Calculate the cheapest place to buy new athletics gear by finding the difference.

Mastery: Reasoning and Problem-Solving

Y5

  • Use just digits 4 and 5 to create a 5-digit – 5-digit subtraction to give an answer with at least two 9s.
    -- Can you get 9091?
    -- What is the smallest answer you can get?
    -- What is the largest?
  • Explain why it would be sensible to choose different methods to solve (a) and (b) below.
    (a) 67,493 – 21,561
    (b) 50,005 – 44,878
  • Find the missing numbers in this subtraction:
    1 2 ☐ 6 2 – 9 3 ☐ 8 = 3 1 1 ☐

Y6

  • Add 1998 to 2569.
    Subtract 1998 from 6565.
    Invent another pair of calculations where the same thing occurs (an addition and a subtraction of the same 4-digit number, resulting in the same answer).
  • -- Drinks cost £2.99 each.
    -- An apple is 49p.
    -- Wraps are £4.99 each.
    Find the total of two drinks, a wrap and an apple.
    Find the change from £20.
  • Frog does three hops: 51p, £2 and £10 to find change from £50. How much was the item bought?
  • Write the missing number in this bar model:
£100
£43.25£9.65£14?

In-depth Investigation: Pence and pounds reversed
Children find patterns in the differences when pounds and pence are reversed.

Extra Support

Y5: Hop to 100s, and Beyond
Using counting up (Frog) to subtract numbers either side of a multiple of 100, e.g. 304 - 297, then 304 – 267.

Y6: Phone a Frog
Using counting up (Frog) to calculate change from £100.

Jump to Millennia
Using counting up (Frog) to subtract 4-digit numbers from multiples of 1000 (e.g. 4000 - 2586), or when the larger number has zeros (e.g. 4002 - 3987, 4020 - 3987, 4200 - 3987).