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# Maths Year 5/6 Autumn Addition & Subtraction (A)

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 Column addition with whole numbers (suggested as 2 days)

### Objectives

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

National Curriculum

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

### Procedural Fluency

Day 1
Y5: Add 4-digit then 5-digit numbers.

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.

### Mastery: Reasoning and Problem-Solving

Y5

• 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.

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!

Children convert arrangements of dominoes to numbers and then perform a giant addition. They then create their own domino additions.

### Extra Support

Y6: Colossal Column

## 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

Y6: Column addition with money and decimal numbers.

National Curriculum
Frac/Dec (viii)
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

### 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

Y6: Take Away Night

## Unit 3 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 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:

 ☐ 0 5 ☐ _ ☐ 3 8 1 2 1 9
• 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:
 3 4 4 ☐ 6 _ ☐ 1 2 ☐ 2 8 ☐ 9 7
• 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