Short Blocks

Maths Year 5/6 Spring Calculation

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

First time using Hamilton Maths?
Open Unit 1 and download the PowerPoint from 'Planning and Group Activities': a brilliant and ready-to-use maths lesson for your white board!

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

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

Objectives

Use of brackets in calculation
Unit 3: ID# 56444

Y5: Use of brackets in calculation.
Y6: Use of brackets in calculation.

National Curriculum
Y5: Add/Sub (iv) Mult/Div (x)
Y6: Add/Sub (iv) (vi)

Y5 Hamilton Objectives
22. Solve problems involving addition, subtraction, multiplication, division and a combination, including understanding the meaning of the equals sign.

Y6 Hamilton Objectives
18. Perform mental calculations, including with mixed operations. Carry out calculations using knowledge of the order of operations and brackets.

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)

Objectives

Addition and subtraction
Unit 4: ID# 56460

Y5: Column addition and subtraction: count up to find change/difference.
Y6: Column addition and subtraction: count up to find change/difference.

National Curriculum
Y5: Add/Sub (i) (ii) (iii) (iv)
Y6: Add/Sub (vii) (ix)

Y5 Hamilton Objectives
8.Confidently add numbers with up to 4 or 5 digits using column addition, including adding ‘piles’ of numbers.
9. Subtract larger numbers using expanded or compact column subtraction, or by counting up.
10. Use rounding to check answers and determine levels of accuracy.

Y6 Hamilton Objectives
6. Consolidate: Add several large numbers using written addition, including ‘piles of numbers’ with different numbers of digits.
7. Consolidate: Subtract large numbers using decomposition or counting up if appropriate (200,000 – 196,875).

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).