Short Blocks

Maths Year 5/6 Autumn Addition & Subtraction (B)

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 Money: counting up, change, differences (suggested as 2 days)

Objectives

Use counting up (frog) to find change and differences between amounts of money
Unit 3: ID# 56182

Y5: Use counting up (Frog) to find change and the difference between amounts of money
Y6: Find totals and use counting up (Frog) to find change and the difference between amounts of money

National Curriclum
Y5: Add/Sub (ii) (iv)
Y6: Add/Sub (iv) (vii)

Y5 Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers in the context of money by counting up.
7. Add/subtract mentally with confidence, where numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value, e.g. giving change.

Y6 Hamilton Objectives
5. Consolidate: Add and subtract mentally with confidence, where numbers are < 100 or it relies upon simple addition/ subtraction and place value.
8. Solve addition/subtraction multi-step problems in context, deciding which operations to use and why.

Planning and Activities

Day 1 Teaching
Use counting up (Frog) to find change from £20. Use a bar model to show change from £50 and then change from £100 for a pair of items.
Group Activities
Y5 -- Find change from £20 and £50 by counting up (Frog).
Y5/6 -- Add two or three amounts of money and find the change from £100.

Day 2 Teaching
Use counting up (Frog) to find differences between amounts of money.
Group Activities
Y5/6 - Whole class investigation: Find the difference between two money amounts by counting up. Notice and describe patterns in answers.

You Will Need

  • Mini-whiteboards and pens
  • Catalogues with age appropriate games and toys
  • Finding change from £100 (see resources) or real items with similar price labels

Short Mental Workouts

Day 1
Pairs to £1 ping-pong

Day 2
Finding change

Worksheets

Day 1
Y5 Find the change from £50.
Y6 Work out totals and calculating change: ‘Shopping in Town’.

Day 2
Y5/6 Find differences between prices on two websites.

Mastery: Reasoning and Problem-Solving

Y5

  • Frog is counting up from £5.61 to £20. First, he hops 49p to £6. Then he hops £15 to £20. What has he done wrong? Can you correct him?
  • Laila’s Dad buys some groceries for £38.14. He pays with a £50 note and gets £12.86 change. Just about to leave the shop, Laila says ‘Stop Dad, you’ve got too much change!’ Do you agree with her?
  • What is the change from £100 if you buy yourself and a friend a meal for £36.32 each?
  • £54.23 – ☐ = £18.76
    What amount is missing?

Y6

  • True or false?
    -- Buying 3 things each less than £30, and each priced at a number of pounds and 99p, will result in 3p and some pounds change from £100.
    -- Three amounts totalling £10 can be written without any being more than £3.40.
  • When estimating how much change we will get, is it better to round up to the next pound or down to the previous pound? Give a reason for your answer.

In-depth Investigation: Day 2 Group Activity
Children explore differences between 4-digit money amounts in the form £☐☐.☐☐.

Extra Support

Y5: DVD Decisions
Using counting up (Frog) to calculate change from £10

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

Unit 2 Subtract nums with 1/2 decimal places (suggested as 3 days)

Objectives

Subtract numbers with 1 or 2 decimal places
Unit 5: ID# 56206

Y5: Subtract numbers with 1 decimal place then 2 decimal places then a mix.
Y6: Subtract numbers with 2 decimal places then a mix of 1 and 2 decimal places.

National Curriculum
Y5: Frac/Dec (ix) (x)
Y6: Add/Sub (viii)
Frac/Dec (vii)

Y5 Hamilton Objectives
32. Subtract 1- and 2-place decimal numbers by counting up: 6.2 – 3.5, 13.1 – 9.45.

Y6 Hamilton Objectives
31. Subtract decimal numbers using mental strategies or written counting up.
29. Find the complement to 1, or to next whole number, for a number < 10 with up to 3 decimal places.

Planning and Activities

Day 1 Teaching
Use Frog to calculate the likely growth of mice (lengths in cm with 1 decimal place).
Further teaching with Y6
Use Frog to subtract numbers with 2 decimal places from whole numbers, then from numbers with 2 decimal places.
Group Activities
Y5 -- Use counting back/place value and/or counting up (Frog) to calculate subtractions for numbers with 1 decimal place.
Y6 -- Use counting up (Frog) to calculate differences between numbers with 2 decimal places, e.g. measurements of arm spans.

Day 2 Teaching
Use Frog to calculate differences between jumps in metres (2 decimal places). Use a bar model to represent the problem.
Group Activities
Y5 -- Use counting up (Frog) to calculate differences between numbers with 2 decimal places, e.g. measurements of arm spans.
Y6 -- Count up to subtract; explore and reason about the choice between column subtraction and counting up for subtracting numbers with 1 or 2 decimal places.

Day 3 Teaching
Use Frog to find the difference between two numbers, one with 2 decimal places and the other with 1 decimal place.
Group Activities
Use the in-depth problem-solving investigation ‘Talisman squares’ as today’s group activity.
Or, use this investigative activity:
Y5/Y6 -- Whole class investigation. Investigate subtracting numbers with consecutive digits, 9.8 – 7.65, 8.7 – 6.54, 7.6 – 5.43.

You Will Need

  • Mini-whiteboards and pens
  • 1–9 dice
  • Number cards 0–9, one set per pair
  • Measuring tape
  • Paper clips
  • Flipchart and pens

Short Mental Workouts

Day 1
Count on and back in steps of 0.01

Day 2
How much to the next metre?

Day 3
Quick-fire doubles and halves

Worksheets

Day 1
Y5: Work out how much hamsters have grown (in cm, with 1 decimal place).
Y6: Calculate differences in athletics results.

Day 2
Y5: Calculate differences in athletics results.
Y6: Work out how much bamboo grows each day.

Day 3
Y5: Subtract pairs of numbers with 1 or 2 decimal places.
Y6: Choose how to subtract numbers with 1 or 2 decimals places.

Mastery: Reasoning and Problem-Solving

Y5

  • True or false?
    1.5 – 0.75 = 3/4
    6 – 3.38 > 2.5
    When you subtract a number with 2 decimal places from a whole number, the answer must have 2 decimal places.
  • Write the missing numbers.
    7m – 4.38m = ☐
    ☐ + 2.43m = 4m
    8.17m – 4.4m = ☐

Y6

  • Write the missing number in the bar diagram:
4.06
2.68
  • Write two 2-place decimal numbers which add to 6. Write two different 2-place decimal numbers which add to 4.5.
  • Frog subtracts a number from 3.4. He makes 2 jumps: the first is 0.63 and the second is 1. Write the subtraction he is solving.
  • Calculate 7 – 2.89 mentally without writing anything. Check your answer using Frog.

In-depth Investigation: Talisman Squares
Children find differences between adjacent numbers on a 4 × 4 grid and then explore arrangements on a 3 × 3 grid.

Extra Support

Y5: The Hamsters Are Growing!
Rehearsing finding differences between 1-place decimals (coming soon)

Y6: Jump to Success
Counting up (using Frog) from numbers with 2 decimal places to the next whole number

Unit 3 Strategies for +/-; word problems (suggested as 3 days)

Objectives

Use mental/written addition and subtraction strategies; solve word problems
Unit 6: ID# 56214

Y5: Place Use mental/written addition and subtraction strategies; use column subtraction to subtract 5-digit numbers; solve word problems.
Y6: Use mental/written addition and subtraction strategies; solve word problems.

National Curriculum
Y5: Add/Sub (i) (ii) (iii) (iv)
Mult/div (x)
Y6: Add/Sub (iv) (vii) (viii)

Y5 Hamilton Objectives
7. Add/subtract mentally with confidence, where numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value.
9. Subtract larger numbers using expanded or compact column subtraction, or by counting up.
11. Solve addition/subtraction multi-step problems; decide which operations/methods to use and why.
22. Solve problems involving addition, subtraction, multiplication, division and a combination, including understanding the meaning of the equals sign

Y6 Hamilton Objectives
5. Consolidate: Add and subtract mentally with confidence, where numbers are < 100 or it relies upon simple addition/subtraction and place value.
8. Solve addition/subtraction multi-step problems in context, deciding which operations to use and why.
18. Perform mental calculations, including with mixed operations and large numbers; carry out calculations using knowledge of the order of operations and brackets.
20. Solve problems involving all 4 operations.

Planning and Activities

Day 1 Teaching
Revise mental addition and subtraction using place value and near multiples.
Group Activities
Use the in-depth problem-solving investigation ‘Problem differences’ as today’s group activity.
Or, use these activities:
Y5 -- Add or subtract mentally using place value or near multiples to help.
Y6 – Recognise and reason about pairs of numbers to add or subtract mentally using place value or near multiples to help.

Day 2 Teaching
Show a set of calculations. Ask children to discuss which to work out mentally and which to work out using a written method and why.
Further Teaching with Y5
Revise expanded and compact column subtraction for 4127 – 2258. Then demonstrate expanded and compact column subtraction side by side for 32,457 – 15,829.
Group Activities
Y5 -- Use expanded column subtraction to subtract pairs of 4-digit, then 5-digit numbers … OR … Investigate subtraction of pairs of 5-digit numbers with all odd or all even digits.
Y6 -- Choose mental or written methods to solve calculations that use the four operations; solve several calculations. Some children will create calculations.

Day 3 Teaching
Display word problems. Discuss what needs to be done to the numbers in the problems to solve them.
Group Activities
Y5/Y6 -- Discuss word problems before deciding what calculations are necessary to solve them. Other children will work in pairs to write a 2-step word problem, swap and solve.

You Will Need

  • Mini-whiteboards and pens
  • ‘Mental addition and subtraction’ (see resources)
  • Digit cards 0–9
  • ‘Mystery additions and subtractions’ (see resources)
  • A table to show the numbers of hits on a website (see resources)
  • Flipchart and pens
  • Additional activity sheets (see resources)

Short Mental Workouts

Day 1
Count on and back in steps of 99

Day 2
Add any pair of 2-digit numbers

Day 3
Times tables

Worksheets

Day 1
Y5: Spot pairs of numbers to add or subtract mentally using place value or near multiples to help.
Y6: Spot pairs of numbers to add or subtract mentally using place value or near multiples to help. Guess which number a partner added/subtracted.

Day 2
Y5: Find the difference between pairs of 4-digit or 5-digit numbers of hits on a website.
Y6: Choose mental or written methods to work out a range of calculations.

Day 3
Y5/Y6: Solve word problems involving several steps.

Mastery: Reasoning and Problem-Solving

Y5

  • True or false?
    Subtracting a 3-digit number from a 4-digit number always gives a 4-digit answer.
    Finding a difference between a 4-digit number and its reverse (e.g. 4531 – 1354) always gives an answer whose digit sum is 9.
  • Complete the calculations:
    23,478 + ☐ = 54,142
    8025 – ☐ = 3852

Y6

  • Tommy subtracted 1998 from 5567, and found an answer of 3565. Does he fully understand the ‘subtract and adjust’ strategy for calculating with near multiples?
  • Explain why 348 × (5 + 8) is not the same as 348 × 5 + 8. Find out by how much the answers differ.

Y5 & Y6

  • Amy and her mum are cutting up a large plank to make some shorter shelves. They finish with three shelves measuring 1.55m each, and a piece left over measuring 15cm. How long was the plank they started with?

In-depth Investigation: Problem Differences
Children write word problems incorporating different calculation strategies.

Extra Support

Y5: Frog's New Teacher
Using counting up (Frog) to subtract 3-digit numbers.

Y6: RICA
Solving word problems. Choosing how to work out the answers to calculations