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. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are added value for Hamilton Friends and School Subscribers.

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.

Teaching and Group Activities for Understanding

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

Procedural Fluency

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.

Teaching and Group Activities for Understanding

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

Procedural Fluency

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.

Teaching and Group Activities for Understanding

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

Procedural Fluency

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