Maths Year 5 Autumn Addition and Subtraction

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.

Unit 1 Column addition (4- and 5-digit numbers) (suggested as 2 days)

Objectives

Column Addition with 4- and 5-digit numbers
Unit 1: ID# 5153

National Curriculum
Add/Sub (i) (iii)

Hamilton Objectives
8. Confidently add numbers with up to 4 or 5 digits using column addition, including ‘piles’ of numbers.
10. Use rounding to check answers and determine levels of accuracy.

Teaching and Group Activities for Understanding

Day 1 Teaching
Write 3458 + 2477, 3478 + 2827 and 3455 + 2327. Children arrange by estimation from biggest to smallest answers. Take feedback. Draw out rounding to nearest 1000 to approximate. Model column addition/find exact answers.
Group Activities
-- Discuss which additions of 4-digit numbers are easy/quick to do and which are harder/slower to do and why. Children then work out the answers.
-- Teach children how to add pairs of 5-digit numbers.
Day 2 Teaching
Using a table of hits on a website, find totals, modelling how to use column addition and reminding children to leave a line before the answer so that they can record the ‘carry’ digits.
Group Activities
Use the ‘Exasperating 80 Grand’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use a place value chart to generate pairs of 5-digit numbers to add.
-- Use digits 1 to 8 to create two 4-digit numbers, aiming to have a total between 6000 and 8000.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pen
  • Table of hits on a website (see resources)
  • Place value chart (see resources)
  • Red and blue counters
  • Red and blue pens
  • 0 to 8 digit cards

Mental/Oral Starters

Day 1
Place value in 4-digit numbers (pre-requisite skills)

Suggested for Day 2
Add 3 single digit numbers spotting bonds to 10 and doubles (simmering skills)
or
Pairs to 100 (simmering skills)

Procedural Fluency

Day 1
Practice using compact column addition.

Day 2
Children use column addition to add pairs of 4-digit numbers, and are prompted to make some estimates first.
Children find the total number of hits on a website each day (5-digit numbers).

Mastery: Reasoning and Problem-Solving

  • Fill in the missing digits:
    ☐ ☐ 3 8 4
    + 7 9 8 ☐ ☐
    ☐ 5 2 2 ☐
  • Write an addition of two 5-digit numbers using the digits 4, 5 and 6 where the answer is 70,000.
  • What mistake has Tom made in this addition?
  • 36,842 + 8543 = 3,141,385

In-depth Investigation: Exasperating 80 Grand
Children use all of the digits 0 to 9 once only to create pairs of five-digit numbers, with a total as close to 80,000 as possible.

Extra Support

Addition Mission
Adding pairs of 3-digit numbers using expanded addition

Unit 2 Decimal and money calculation (suggested as 4 days)

Objectives

Decimal and money calculation
Unit 2: ID# 5167

National Curriculum
Add/Sub (iv)
Decimals (x)

Hamilton Objectives
31. Add 2-place decimal numbers in the context of money, mentally or using column addition.
32. Subtract 1- and 2-place decimal numbers in the context of money by counting up.
10. Use rounding to check answers and determine levels of accuracy.
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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Add amounts of money using column addition. Use the context of adding prices and demonstrate column addition, if appropriate using expanded form to show what is happening.
Group Activities
Use the ‘Adding Odd or Even Amounts’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
- -Add amounts of money, progress from expanded column addition to compact column addition.

Day 2 Teaching
Show a variety of additions and ask children to estimate a total for each using rounding. Then parcel the additions out to the class and find exact answers.
Group Activities
-- Add amounts of money; estimate totals first.

Day 3 Teaching
Use Frog to find change from £20, giving a clear demonstration of the hops that Frog makes on an empty number line. Use a bar model to show change from £50 and £100, solving by counting up using Frog.
Group Activities
-- Find the change from £20, £30, and then £50 by counting up (Frog).
-- Add 2 amounts of money and find the change from £100.

Day 4 Teaching
Use Frog to find differences between amounts of money, e.g. I went shopping and to start with had £37.28 in my purse. I spent £18.98. How much did I have left? Model on an empty number line.
Group Activities
-- Whole class problem solving activity. Finding the difference between two 4-digit numbers by counting up. Notice and describe patterns.

You Will Need

  • Two DVDs, one with a price label of £14.79 and the other with a price label of £12.49
  • Whole class on board (see practice sheets)
  • Priced items ‘Under £50’ (see practice sheets)
  • Catalogues with age appropriate games and toys
  • Finding change from £100 (see resources)

Mental/Oral Starters

Day 1
Mixed addition facts bingo (pre-requisite skills)

Suggested for Day 2
Time – converting between units of time (simmering skills)

Day 3
Bonds to £1 (pre-requisite skills)

Day 4
Change from £1 (pre-requisite skills)


Procedural Fluency

Day 1
Add amounts of money using column addition and after some initial practice also add 3 amounts.

Day 2
Find pairs of items with a total price of under £50.

Day 3
Find the change from £50.

Day 4
Finding a difference between 2 amounts of money by counting up (Frog).

Mastery: Reasoning and Problem-Solving

  • Write an addition of 3 amounts each containing pounds and pence where the total is £50.
  • Create an addition of 2 amounts less than £10 where only the digits 8 and 9 are used. What is the lowest total possible? And the highest?
    ☐ – £56.72 = £53.28
  • What is the change from £100 if you buy yourself and a friend a meal for £36.32 each?
  • 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?
    £54.23 – ☐ = £18.76
    What amount is missing?


In-depth Investigation: Adding Odd and Even Amounts
Children create two amounts of money – one with even digits, one with odd digits – and add these. They look for patterns of even/odd in the totals.

Extra Support

Sums of Money
Using expanded addition to add amounts of money

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

Unit 3 Column subtraction; choose strategies (suggested as 3 days)

Objectives

Column subtraction, and choosing a method
Unit 3: ID# 5179

National Curriculum
Add/Sub (i) (iii)

Hamilton Objectives
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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use column subtraction to subtract pairs of 4-digit numbers. Start by revising expanded column subtraction so everyone is totally clear about what is happening. Then rehearse compact version.
Group Activities
-- Use expanded subtraction to subtract pairs of 4-digit numbers where only 1 move is needed.

Day 2 Teaching
Display table of heights to descend from the summit to base camp (see resources). Then demonstrate how to perform the compact column subtraction to take 3-digit from 4-digit numbers.
Group Activities
Use the ‘Persistent Answers’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Identify missing digits in column subtractions (4-digit – 3-digit numbers).

Day 3 Teaching
Choose whether to use counting up (Frog) or column subtraction (decomposition) to work out calculations. Model using Frog for 8000 – 4763. Then give 3457 – 2786, 4005 – 3968, 6021 – 4987, 7356 – 4264 and children do 2 using Frog and 2 using column subtraction.
Group Activities
-- Work in pairs; write 5 subtractions (pairs of 4-digit numbers) where they would use Frog and 5 where they would use column subtraction. Rest of group guess which method was used.

You Will Need

  • Flipchart and pen
  • Table of heights to descend from the Everest summit to base camp (see resources)
  • Mini-whiteboard and pens
  • Post-it notes
  • 1 – 9 digit cards
  • Cards and pens
  • ITP: Tell the Time

Mental/Oral Starters

Day 1
Subtraction facts (pre-requisite skills)

Suggested for Day 2
24 hour clock (simmering skills)

Suggested for Day 3
Place numbers with 2 decimal places on a line (simmering skills)

Procedural Fluency

Day 1
Use expanded or compact column subtraction to subtract pairs of 4-digit numbers. Check two with addition.

Day 2
Use column subtraction to work out height of base camps on Everest.
Use counting up (Frog) to work out difference in heights between base camps on Everest.

Day 3
Choose five subtractions to work out using Frog and five to work using column subtraction.

Mastery: Reasoning and Problem-Solving

  • Write the missing number in the bar model
4538
3894
  • Find the answer to 5060 – 4935 using either Frog or column subtraction. Check using the other method. Write which you prefer and why.
  • Fill in the missing digits:
        8 4 ☐ ☐
    – 4 8 6 ☐
        ☐ 1 2 4
  • Write a subtraction of two 4-digit numbers where the answer is the first number in reverse.

In-depth Investigation: Persistent Answers
Children subtract numbers with consecutive digits from numbers with identical digits and record the different possible answers.

Extra Support

Frog’s Ginormous Jumps
Using counting up (Frog) to subtract 3-digit numbers

Unit 4 Revise addition and subtraction (suggested as 3 days)

Objectives

Revise addition and subtraction
Unit 4: ID# 5189

National Curriculum
Add/Sub (i) (iii) (iv)

Hamilton Objectives
5. Solve number problems and practical problems involving
place value.
7. Add/subtract mentally with confidence, where numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value.
8. Confidently add numbers with up to 4 or 5 digits using column addition, including ‘piles’ of numbers.
9. Subtract larger numbers using expanded or compact column subtraction, or by counting up.

Teaching and Group Activities for Understanding

Day 1 Teaching
Revise mental addition and subtraction using place value and near multiples. Add 401 and subtract 3005 to/from 25,247. Show how add 399 or subtract 2999. Rehearse more like this.
Group Activities
-- Spot pairs of numbers to add or subtract mentally using place value or near multiples to help.

Day 2 Teaching
Add pairs of 5-digit numbers (5-digit answers),
making sure that children estimate first using rounding to get an accurate estimate. Model compact column addition.
Group Activities
Use the ‘Magic Star Additions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Look for pairs of 5-digit numbers with totals within given ranges.

Day 3 Teaching
Use decomposition to subtract pairs of 5-digit numbers. Revise expanded and compact decomposition for 4127 – 2258. Then demonstrate expanded and compact decomposition side by side for 32,457 – 15,829.
Group Activities
-- Use expanded decomposition to subtract pairs of 4- and 5-digit numbers.

You Will Need

  • Mini-whiteboards & pens
  • Mental addition & subtraction (see practice sheets)
  • Table of hits on a website (see practice sheets)
  • Flipchart & pens
  • Digit cards

Mental/Oral Starters

Suggested for Day 1
Count in ¼s and ⅛s along a number line (simmering skills)

Day 2
Revise addition facts to 20 (pre-requisite skills)

Suggested for Day 3
Times tables (simmering skills)

or
Pairs to 100 (simmering skills)

Procedural Fluency

Day 1
Spot pairs of numbers to add or subtract mentally using place value or near multiples to help.

Day 2
Add pairs of 4-digit or 5-digit numbers.

Day 3
Find the difference between pairs of 5-digit numbers of hits on a website.

Mastery: Reasoning and Problem-Solving

True or false?

  • Subtracting a 3-digit number from a 4-digit number always gives a 4-digit answer.
  • Adding two 4-digit numbers cannot give an answer greater than 20,000.
  • Finding a difference between a 4-digit number and its reverse (e.g. 4531 – 1354) always gives an answer whose digits add to 9, 18, 27 or 36.
  • Complete the calculations.
    23,478 + ☐ = 54,142
    8025 – ☐ = 3852
    ☐ – 3,578 = 10,784

In-depth Investigation: Magic Star Additions
Children explore addition patterns on a star derived from a simple magic star. They use mental or written addition to add 4-digit numbers.

Extra Support

Compact Columns
Using compact column addition to add pairs of 3-digit numbers

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