Maths Year 5/6 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. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Column addition with whole numbers (suggested as 2 days)

Objectives

Formal column addition with whole numbers
Unit 1: ID# 56150

Y5: Use column addition to add 4-digit then 5-digit numbers.
Y6: Use column addition to add 5-digit numbers (5-digit answers).

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

Y5 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.

Y6 Hamilton Objectives
6. Consolidate: Add several large numbers using written addition, including ‘piles of numbers’ with different numbers of digits.

Teaching and Group Activities for Understanding

Day 1 Teaching
Practise rounding to the nearest 100. Then round to the nearest 1000 and the nearest 100 to approximate totals of pairs of 4-digit numbers. Use column addition to find the exact totals, revising leaving an empty row for extra 10s, 100s etc.
Further Teaching with Y6
Use the same method to add pairs of 5-digit numbers (answer less than 100,000).
Group Activities
Y5 -- Use column addition to add pairs of 4-digit numbers, recognising that some calculations produce an extra 10, 100, or 1000. Some children will add pairs of 5-digit numbers.
Y6 – Create pairs of 5-digit numbers; use column addition to add them. Some children will aim for a target range for the total.

Day 2 Teaching
Using a table of hits on a website, find totals, modelling how to use column addition of 5-digit numbers (answers less than 100,000, then greater than 100,000).
Group Activities
Use the in-depth problem-solving investigation ‘Giant domino addition’ as today’s group activity.
Or, use these activities:
Y5 -- Use column addition to add pairs of 5-digit numbers. Some children will aim for a target range for the total of two 4-digit numbers.
Y6 -- Create pairs of 5-digit numbers with totals between 50,000 and 100,000 or totals close to 100,000 or 150,000, using given digits.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pens
  • Place value equipment
  • 1s to 10,000s place value chart (see resources)
  • Blue and red counters
  • Blue and red pens
  • A table to show the numbers of hits on a website (see resources)
  • 0–8 digit cards

Short Mental Workouts

Day 1
Round to the nearest multiple of 100

Day 2
Add pairs of 2-digit numbers

Procedural Fluency

Day 1
Y5: Add 4-digit then 5-digit numbers.
Y6: Practise adding 5-digit numbers (5-digit answers).

Day 2
Y5: Approximate then add pairs of 4-digit numbers. Add pairs of 5-digit numbers from a table of hits on a website.
Y6: Practise adding 5-digit numbers (5-digit and 6-digit answers).

Mastery: Reasoning and Problem-Solving

Y5

  • Fill in the missing digits:

384
+798
522
  • Write an addition of two 5-digit numbers using the digits 4, 5 and 6 where the answer is 70,000.

Y6

  • Write the missing digits:
    3 4 7 1 9 + ☐ 6 5 ☐ ☐ = 7 ☐ ☐ 0 8
  • Write an addition where the two 5-digit numbers add to 55,555. Neither number has a 0 and you must use 6, 7, 8 and 9 as digits somewhere. You can use other digits too!

In-depth Investigation: Giant Domino Addition
Children convert arrangements of dominoes to numbers and then perform a giant addition. They then create their own domino additions.

Extra Support

Y5: Addition Mission
Adding pairs of 3-digit numbers using expanded addition

Y6: Colossal Column
Using column addition to add pairs of 4-digit numbers with 4-digit and 5-digit answers

Unit 2 Column addition: decimals and money (suggested as 2 days)

Objectives

Formal column addition with decimal numbers and with money
Unit 2: ID# 56166

Y5: Column addition with money.
Y6: Column addition with money and decimal numbers.

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

Y5 Hamilton Objectives
31. Add 2-place decimal numbers in the context of money, mentally or using column addition.
10. Use rounding to check answers and determine levels of accuracy.

Y6 Hamilton Objectives
30. Add several decimal numbers using mental or written addition.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use expanded and compact column addition to find the cost of two 4-digit money amounts, e.g. £14.79 + £12.49. Then write an addition that will have an answer between £20 and £30 (no zeroes allowed).
Group Activities
Use the in-depth problem-solving investigation ‘Adding even and odd amounts’ as today’s group activity.
Or, use these activities:
Y5 -- Add two or more amounts of money, using expanded then compact column addition.
Y6 -- Add two amounts of money using compact column addition. Some children will write three amounts with a total in a given range.

Day 2 Teaching
Show a variety of money additions and ask children to estimate a total for each using rounding. Children find exact answers.
Further Teaching with Y6
Use the distance that snails crawl to generate decimal additions. Round distances to the nearest metre to estimate a total. Model column addition, showing how to align decimal points; recognise similarity to adding money amounts.
Group Activities
Y5 -- Find pairs (or trios) of items with a total price of under £50.
Y6 -- Add two or three distances in metres with 2 decimal places. Round and find the total.

You Will Need

  • Two DVDs, one with a price label of £14.79 and the other with a price label of £12.49
  • Mini-whiteboards and pens
  • Whole class practice (see resources)
  • Flipchart and pens
  • Under £50 (see resources)
  • Sets of 2–7 and 4–9 digit cards

Short Mental Workouts

Day 1
Round to the nearest whole number

Day 2
Count on and back in steps of 0.01

Procedural Fluency

Day 1
Y5/6: Practise using column addition to add two then three amounts of money.

Day 2
Y5: Find pairs (or trios) of items with a total price of under £50.
Y6: Add distances in metres (2 decimal places).

Mastery: Reasoning and Problem-Solving

Y5

  • 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?
  • A jacket costs £34.49 and a pair of trainers costs £57.70. How much do they cost in total?
  • ☐ – £56.72 = £53.28

Y6

  • A coat costs £25.79 and a pair of boots costs £38.29. Use rounding to the nearest £10 and to the nearest £1 to estimate the total cost. What is their exact total cost?
  • Jim runs 13.85 kilometres and Ann runs 12.78 kilometres to meet him. How far have they run in total?

Y5/6

  • Write an addition of 3 amounts each containing pounds and pence where the total is £50.

In-depth Investigation: Adding Even and Odd 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

Y5: Sums of Money
Using expanded addition to add amounts of money

Y6: Take Away Night
Using expanded, then compact addition to add amounts of money

Unit 3 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 4 Whole number column subtraction & frog (suggested as 3 days)

Objectives

Use column subtraction and counting up (frog) to subtract whole numbers
Unit 4: ID# 56190

Y5: Use column subtraction and counting up (Frog) to subtract whole 3-digit and 4-digit numbers.
Y6: Use column subtraction and counting up (Frog) to subtract whole 3-digit, 4-digit and 5-digit numbers.

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

Y5 Hamilton Objectives
9. Subtract larger numbers using expanded or compact column subtraction, or by counting up.

Y6 Hamilton Objectives
7. Consolidate: Subtract large numbers using decomposition or counting up if appropriate.

Teaching and Group Activities for Understanding

Day 1 Teaching
Ask a Y6 child to model compact column subtraction of 5-digit numbers. Y5 children check with addition.
Further Teaching with Y5
Revise how to use expanded and compact column subtraction to subtract pairs of 4-digit numbers.
Group Activities
Y5 -- Use column subtraction methods to subtract pairs of 4-digit numbers with one or more ‘moves’ across columns.
Y6 – Create and solve column subtractions of pairs of 5-digit numbers, given certain criteria. Identify how many ‘moves’ are necessary before calculation.

Day 2 Teaching
Display a table of heights to descend from the Everest summit to base camp. Demonstrate how to perform the compact column subtraction to subtract 3-digit from 4-digit numbers.
Further Teaching with Y6
Subtract 3-digit and 4-digit numbers from 5-digit numbers, stressing correct alignment of digits.
Group Activities
Use the in-depth problem-solving investigation ‘Nine AGAIN’ as today’s group activity.
Or, use these activities:
Y5/6 -- Identify missing digits in column subtractions (4-digit subtract 3-digit numbers).
Y6 -- Identify missing digits in column subtractions (5-digit subtract 3 or 4-digit numbers).

Day 3 Teaching
Choose whether to use counting up (Frog) or column subtraction (decomposition) to calculate subtractions. Explain reasoning.
Group Activities
Y5/6 -- Write five subtractions (pairs of 4-digit or 5-digit numbers) where you would choose to use Frog and five where you would use column subtraction.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pens
  • 1–9 digit cards
  • ‘Subtracting pairs of 4-digit numbers’ (see resources)
  • 0–9 digit cards
  • ‘Heights to descend from Everest summit to base camp’ (see resources)
  • Cards and pens
  • Sticky notes

Short Mental Workouts

Day 1
Subtraction facts

Day 2
Mental subtraction of 2-digit numbers

Day 3
24-hour clock

Procedural Fluency

Day 1
Y5: Use expanded or compact column subtraction to subtract pairs of 4-digit numbers. Check two subtractions with addition.
Y6: Use column subtraction to subtract pairs of 4-digit or 5-digit numbers.

Day 2
Y5: Use counting up (Frog) to work out the difference in heights between base camps on Everest. Use column subtraction to work out the height of base camps on Everest.
Y6: Use column subtraction to calculate the heights of a plane above sea level.

Day 3
Y5: Choose how to subtract.
Y6: Choose how to subtract.

Mastery: Reasoning and Problem-Solving

Y5

  • Write the missing number in this bar model:

4538
3894
  • Find the missing digits in this subtraction:

05
_38
1219
  • Find the answer to 5060 – 4935 using either Frog or column subtraction. Check using the other method. Write which you prefer and why.
  • Write a subtraction of two 4-digit numbers where the answer is the first number in reverse.

Y6

  • How many times must 33,217 be subtracted from 100,000 to leave a number less than 33,217? What is the number left?
  • Find the missing digits in this subtraction:
3446
_12
2897
  • How would you subtract 28,560 from 90,600? Explain why.

In-depth Investigation: Nine AGAIN
Children subtract 4- and 5-digit numbers and look for patterns in the answers’ digital roots.

Extra Support

Y5: Frog’s Ginormous Jumps
Using counting up (Frog) to subtract 3-digit numbers

Y6: Jump to Millennia
Using counting up (Frog) to subtract 4-digit numbers from multiples of 1000

Unit 5 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 6 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