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# Maths Year 5 Spring 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 Mental and written addition/subtraction (suggested as 3 days)

### Objectives

Unit 1: ID# 5573

National Curriculum

Hamilton Objectives
7. Add and subtract mentally with confidence, where 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.
5. Solve number problems and practical problems involving place value.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Demonstrate how to add 197 to 4735, using an empty number line jotting to show the addition of 200 and a hop back of 3 as we have added 3 too many. Now subtract 197 by subtracting 200 and adding 3 back on. This is our technique to add/subtract nearly numbers (near multiples of 10, 100, 1000). Repeat, adding and subtracting 1995 to/ from 4735.
Group Activities
-- Use place value to add and subtract multiples and near multiples of 100 and 1000.

Day 2 Teaching
Use place value to add and subtract; add and subtract near multiples of 100, 1000 and 10,000. Sketch an empty number line jotting to show subtracting 1000, then subtracting 998, adding 2 back on as we have subtracted too much, etc.
Group Activities
-- Use place value to add and subtract near multiples of 100, 1000 and 10,000.

Day 3 Teaching
Write these additions on the board: 4267 + 2784 + 3832, 8723 + 5265, 23,451 + 18,325 and 67,342 + 8,352. Ask children to discuss in pairs which they think will have the biggest answer and the smallest answer. Give reasons. Model rounding, followed by column addition to check.
Group Activities
Use the ‘Triple trouble’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Use column addition to add a combination of 4-digit and 5-digit numbers.

### You Will Need

• ‘Mental addition and subtraction’ activity sheet (see resources)
• ‘0 to 3 line’ – 1/4s (see resources)
• ‘0 to 3 line’ – 1/8s (see resources)
• ‘Nearly numbers answers’ (see resources, enlarge to A3, then cut up into cards)
• Glue sticks
• ‘Nearly numbers (2) answers’ (see resources, cut up into cards)
• Place value chart (see resources, enlarge to A3)
• Additional activity sheets (see resources)
• Blue and red counters

### Mental/Oral Maths Starters

Day 1
Place value in 4-digit and 5-digit numbers (pre-requisite skills)

Suggested for Day 2
Count in 1/4s and 1/8s (simmering skills)

Suggested for Day 3
Addition facts to 20 (simmering skills)

### Procedural Fluency

Day 1
Add and subtract from 4 and 5-digit numbers:
- using place value
- recognising near multiples of 100, 1000 and 10,000.

Day 2
Use place value to add and subtract near multiples of 100 and 1000 to and from 4-digit numbers.

Day 3
Use column addition to add 4-digit numbers, 5-digit numbers and a mix.

### Mastery: Reasoning and Problem-Solving

• Predict what the 1s digit of your answer will be if you carry out the following sequence:
Subtract 9999
Subtract 999
Subtract 99
Subtract 9
What number are you left with?
• What number must I add to 9998 to get 33,454?
• What mistake has Tom made in this subtraction?
6734 – 997 = 5731
• Fill in the missing numbers.
 4 5 7 ? 8 + 1 ? 4 9 ? ? 2 ? 2 0

In-depth Investigation: Triple Trouble
Write an addition of three 4-digit numbers where the answer is between 28,550 and 28,650.

### Extra Support

Digit Dance
Using place value to add and subtract, e.g. 4582 + 300, 4582 - 50 (not crossing 10s, 100s or 1000s)

Super Scores

## Unit 2 Column subtraction and word problems (suggested as 4 days)

### Objectives

Column subtraction with 4- and 5-digit numbers; word problems
Unit 2: ID# 5581

National Curriculum

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
Remind children how we can use expanded and compact decomposition for 64,723 – 35,387. Model moving 10 to 1s column to subtract the 7, moving 100 to 10s column, and moving 10,000 to the 1000s column. Does this answer seem about right?
Group Activities
-- Investigation to practise subtraction using a chosen method, then discover patterns in the answers.

Day 2 Teaching
Write 86,072 – 32,537 as a vertical subtraction on the board. Can children spot where a 10, 100, 1000 or 10,000 will have to be moved? Discuss. Model first expanded then compact decomposition.
Write 30,008 – 25,783 and agree it’s better to use Frog!
Group Activities
Use the ‘Mobile differences’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Explore expanded and compact decomposition.
-- Explore the relationship between addition and subtraction; solve missing number calculations.

Day 3 Teaching
Write 45,782 – 7356 on the board. Discuss the layout of this calculation so the numbers of common place value line up. Solve 2 word problems using decomposition. Would Frog (counting up) be a less error-prone strategy for either calculation?
Group activities
-- Consolidate written subtraction; create and solve subtraction word problems.

Day 4 Teaching
Write 34,782 – 18,346 both as an expanded vertical subtraction and a compact vertical subtraction on the board. Children discuss how many moves will be required. Demonstrate both versions. Can children write a subtraction that will need 4 moves?!
Group Activities
-- Investigate number patterns arising from column addition and subtraction.

### You Will Need

• 1-20 cards (1 set per pair of children)
• Whiteboards and pens
• Flipchart
• A soft ball
• Place value ‘arrow’ cards
• ‘Subtraction Activity’ sheet (see resources)
• 0-9 digit cards
• A set of 10s cards and a set of 1s cards

### Mental/Oral Maths Starters

Day 1
Revise subtraction facts to 20 (pre-requisite skills)

Day 2
Pairs to 100 (pre-requisite skills)

Day 3
Count up to the next 1000 (pre-requisite skills)

Suggested for Day 4
Change from £1 (simmering skills)

### Procedural Fluency

Day 1
Subtract pairs of 4-digit or 5-digit numbers using decomposition.

Day 2
Subtract pairs of 5-digit numbers. Watch out for any calculations where Frog would be a less error-prone strategy than decomposition.

Day 3
Practice subtraction including word problems. Some need 2 calculation steps.

### Mastery: Reasoning and Problem-Solving

• Use just digits 4 and 5 to create a 5-digit – 5-digit subtraction to give an answer with at least two 9s.
Can you get 9091?
What is the smallest answer you can get?
What is the largest?
• Explain why it would be sensible to choose different methods to solve (a) and (b) below.
67,493 – 21,561
50,005 – 44,878
• Find the missing numbers in this subtraction:
1 2 ☐ 6 2 – 9 3 ☐ 8 = 3 1 1 ☐

In-depth Investigation: Mobile Differences
Children use trial and improvement to find the largest and smallest possible differences using numbers selected to given criteria.

### Extra Support

Hops, Skips and Jumps
Using counting up (Frog) to subtract 4-digit numbers from multiples of 1000 (e.g. 4000 - 3786), or when the larger number has zeros (e.g. 4002 - 3987)

## Unit 3 Mental addition & subtraction strategies (suggested as 3 days)

### Objectives

Mental addition and subtraction strategies, including frog
Unit 3: ID# 5591

National Curriculum

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.
9. Subtract larger numbers by counting up.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use spinners to generate pairs of 2-digit numbers. Children add and subtract; briefly share strategies. Write additions and subtractions with related multiples of 10 and 100, e.g. 84 + 36, 84 – 36, 840 + 360, 840 – 360; 8400 + 3600, 8400 – 3600.
Group Activities
Use the in-depth problem-solving investigation ‘Two and two’ from NRICH as today’s group activity.
Or, use these activities:
-- Complete a short subtraction investigation, pattern-spotting in the answers.
-- Identify an appropriate strategy when practising adding pairs of 2-digit numbers.

Day 2 Teaching
Some folk are cycling 4000 miles. So far they’ve gone 2658 miles. Use Maths Frog to find how much further they have to cycle. Choose a child to draw an empty number line jotting. Model Frog subtraction. How far to go once they reach 3452 miles?
Group Activities
-- Practise counting up to find a difference by completing an investigation.

Day 3 Teaching
Write 56 + ☐ = 83; ☐ + 56 = 92; ☐ – 23 = 46; 73 – ☐ = 42. Children discuss in pairs how to work out the missing numbers. Draw out that sometimes we need subtraction to solve an addition or addition to solve subtraction. Using 2 spinners, children work out missing numbers in number sentences with pairs of 2-digit numbers and pairs of multiples of 10.
Group Activities
-- Calculate missing numbers, then write word problems for ‘number triangles’.

### You Will Need

• 0-9 dice (one per pair of children)
• Internet access for ‘Spinners’ from www.topmarks.co.uk
• Mini-whiteboards and pens
• ‘Multiples of 10 and 100: 4-in-a-row’ game board (see resources)
• 6, 7, 8 and 9 digit cards (one set per pair of children)
• ‘Number triangles’ sheet (see resources)
• ‘Blank number triangles’ sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Add pairs of 2-digit numbers (pre-requisite skills)
Subtract pairs of 2-digit numbers (pre-requisite skills)

Day 2
Pairs to 1000 (pre-requisite skills)

Suggested for Day 3
Rounding whole numbers to the nearest 1000 (simmering skills)

### Procedural Fluency

Day 1
Add and subtract 2-digit numbers. Use the same strategies to add and subtract multiples of 10 and 100.

Day 2
Use Frog to count up from 4-digit numbers to multiples of 1000.

Day 3
Use mental strategies to solve addition and subtraction missing number problems and word problems.

### Mastery: Reasoning and Problem-Solving

• Never, sometimes, always true?
Subtracting a 4-digit number from a multiple of 10,000 gives a 4-digit answer.
Adding 2 numbers less than 5000 can give a 5-digit total.
The difference between two 5-digit multiples of 1000 is a multiple of 1000.
• Complete the calculations:
[_____] + 23,478 = 30,000
8100 – [______] = 6600
5999 = [______] – 3578

In-depth investigation: Two and Two
Children investigate possible numerical values for the letters in ‘alphanumeric’ addition calculations. Two and Two from nrich.maths.org.

### Extra Support

Hop to 100s, and Beyond
Using counting up (Frog) to subtract numbers either side of a multiple of 100, e.g. 304 - 297, then 304 - 267