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# Maths Year 3 Summer 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 Add/subt multiples of 10, near multiples (suggested as 3 days)

### Objectives

Add/subtract multiples of 10 and near multiples
Unit 2: ID# 3739

National Curriculum

Hamilton Objectives
8. Mentally add or subtract any pair of 2-digit numbers, e.g. 75 + 58 or 75 – 58.
9. Mentally add and subtract multiples of 1s, 10s and 100s to/from 3-digit numbers.
14. Solve problems, including missing number problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 346 + 50. Which digit will change? Confirm it is just the 10s digit; model counting on in 10s from 346 to answer. Repeat with 231 + 30 and 636 + 20.
Write 376 + 50: Which digit will change? Count on in 10s to show how both 100s & 10s digits change. Repeat for 346 + 500, 336 – 50 and 846 – 500.
Group Activities
-- Solve addition or subtraction word problems by counting on or back in 1s, 10s or 100s; cross multiples of 10 and 100.
-- Make up calculations that result in the 10s and/or the 100s digit changing.

Day 2 Teaching
Show a grid from 301 to 400. Demonstrate adding or subtracting 10s by moving up or down the grid. What happens when we add a ‘nearly number’ like 39 instead of 40? We need to add 40, then adjust by subtracting 1. Repeat for adding and subtracting other nearly numbers, e.g. 356 + 41, 356 + 39, 356 – 39, 382 – 59, 338 + 29.
Group Activities
-- Add and subtract near multiples to 3-digit numbers with the same 1s digit.

Day 3 Teaching
Display ‘Word problems’ one at a time; ask children to work on them in pairs. Think carefully about the maths that is needed – write a number sentence; then answer the question. Discuss their thoughts and clarify any misunderstandings as you work through each question. Choose one of the following to create a new word problem: 268 + 30, 583 – 40, 355 + 200, 632 – 400, 346 + 19, 475 – 21.
Group Activities
Use the in-depth problem-solving investigation ‘Place value puzzles’ as today’s group activity.
Or, use these activities:
-- Solve word problems by adding or subtracting multiples, or near multiples, of 10 and 100.
-- Use spinners to create word problems involving adding or subtracting multiples, or near multiples, of 10 and 100.

### You Will Need

• ‘Word problems’ sheet 1 (see resources)
• ‘Addition and subtraction word problems’ sheets 1 and 2 (see resources)
• Whiteboards and pens
• ‘Adding and subtracting multiples of 10 and 100’ (see resources)
• ‘301-400 grid’ (see resources)
• ‘Number cards’ Set A and B (see resources)
• ‘1-100 grid’ (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Count on in steps of 10 and 100 from 3-digit numbers (pre-requisite skills)

Day 2
Count back in steps of 10 and 100 from 3-digit numbers (pre-requisite skills)

Suggested for Day 3
Revise the 3 times table (simmering skills)

### Procedural Fluency

Day 1
Solve word problems by counting on or back in 10s or 100s from 2-digit and 3-digit numbers.

Day 2
Add and subtract near multiples of 10 from 2-digit and 3-digit numbers.

Day 3
Create word problems for addition and subtraction of multiples of 10s and 100s and near multiples of 10.

### Mastery: Reasoning and Problem-Solving

• Add 40 to each of…
216, 159, 608
• Subtract 50 from each of…
117, 349, 608
• Complete each pair of calculations:
 436 + 40 = 436 + 39 = 573 - 30 = 573 - 29 = 773 - 40 = 773 - 41 = 105 + 51 = 105 + 49 =
• Solve these word problems:
-- Sam’s Dad buys a laptop for £345. Sam buys a game for £39. How much did they spend in total?
-- Bella has measured the shelf and it is 253cm long. She saws off two pieces that are each 29cm long. How long is the shelf now?

In-depth Investigation: Place Value Puzzles
Solve the place value subtraction puzzles.

### Extra Support

Hops to Sevens
Bridging 10 when subtracting 1-digit numbers from 2-digit numbers, e.g. 42 - 5

## Unit 2 Subtract large numbers using counting up (suggested as 5 days)

### Objectives

Subtract larger numbers using counting up (frog)
Unit 4: ID# 3769

National Curriculum

Hamilton Objectives
12. Subtract larger numbers with confidence, using 'Frog' for counting up.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
14. Solve problems, including missing number problems.

### Teaching and Group Activities for Understanding

Although column subtraction is specified for Year 3 in the National Curriculum, Hamilton believe that teaching column subtraction in Year 4 will be more successful. The National Curriculum Guidance specifies that teachers can teach areas of study in different year groups than those mentioned in the Curriculum, so long as they are taught within the same Key Stage. If you would like to teach column subtraction in Year 3 please see Year 4 Addition and Subtraction autumn Unit 7, spring Unit 4 and summer Units 2 and 3.

Day 1 Teaching
Write 137 – 72. Agree we can use Frog to find this difference, by, counting up from 72 to 137. Draw an empty number line jotting to show this and model each of Frog’s jumps (72 to 80, 80 to 100 and 100 to 137). Explain that we can do 1 big jump to 100. Repeat to model using Frog to do £1.46 – 83p. Children try £1.23 – 88p.
Group Activities
-- Use Frog to calculate the amount left in a purse after buying an item.
-- Use Frog to calculate differences.

Day 2 Teaching
Display a word problem resulting in the calculation 476 – 438. How can Maths Frog help us to work this out? Frog will start on 438, jump to the next 10 (440), then jump to 470, then 476. Remind children that we could do one big jump of 36 from 440 to 476 if we are confident but we don’t have to! Children try 873 – 837.
Group Activities
-- Investigate reversing the last 2 digits of a 3-digit number, then use Frog to find the difference between them.

Day 3 Teaching
Show a toy priced £4.67. Give a child a £5 note and ask them to use this to pay for the toy. You’ve given the shopkeeper too much money. How will she work out how much change to give you? Maths Frog can help us! Sketch a line from £4.67 to £5. Model using Frog to hop to £4.70 and then to £5. Repeat, to find change from £10 and £20.
Group Activities
Use the ‘Step Change’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Practise finding the change from £5, £10 and £20.
-- Play online checkout/ change games, finding change from £1, £5 and £10.

Day 4 Teaching
Show a game and say that it costs £18. So far Katie has saved up £7.55. How much more does she need? Maths Frog can help! Sketch a line from £7.55 to £18. Model the hops from £7.55 to £7.60, then to £8, then to £18. Ensure children add hops accurately to find the answer: £10.45. Repeat as necessary for finding the difference between £8.43 and £14, then £6.55 and £19.
Group Activities
-- Calculate how much more money is needed to pay for a range of items.
-- Calculate how much more money is needed to pay for a more expensive version of an item.

Day 5 Teaching
A family have £100 and so far have spent £67.73. How much money is left? Use Frog to model the hops. Ask children to add the jumps, adding the £s first then the pence, then put them together. Some children may draw 3 hops, others draw 4. It doesn’t matter as long as we get the right answer! Repeat for a family who have spent £62.41 out of their £100.
Group Activities
-- Practise finding change from £100 (or £20) for a range of items.
-- Play ‘Change from £100’ pairs, ‘Change from £20’ pairs.

### You Will Need

• Whiteboards and pens
• ‘At the charity shop’ (see resources)
• ‘Purses’ (see resources)
• Bead string and real coins
• 0-9 cards and place value cards
• Representational notes (£5, £10, £20)
• ‘Finding change’ (see resources)
• Additional activity sheets (see resources)
• Internet access
• Picture of a console/computer game
• Calculators

### Mental/Oral Maths Starters

Day 1
Pairs with a total of 10 (pre-requisite skills)

Day 2
Pairs with a total of 100 (pre-requisite skills)

Day 3
Subtraction facts (pre-requisite skills)

Suggested for Day 4
Adding to the next 10 (simmering skills)

Suggested for Day 5
Match digital and analogue times (simmering skills)

### Procedural Fluency

Day 1
Subtract 2-digit numbers from 3-digit numbers, by counting up - using ‘Frog’.

Day 2
Subtract a pair of 3-digit numbers, using Frog.

Day 3
Calculate change from £5, £10 or £20 by counting up.

Day 4
Calculate admission price differences by counting up.

Day 5
Calculate the change from £20 or £100 by counting up.

### Mastery: Reasoning and Problem-Solving

78 + ☐ = 125
68 + ☐ = 134
375 – ☐ = 328
571 = 518 + ☐
127 + ☐ = 163
836 = 862 – ☐
• Write two numbers either side of 100 which have a difference of 37.
• Complete these bar model diagrams:
Diagram 1:
 133 78 ?

Diagram 2:

 585 518 ?
• Calculate the change from £10 when buying:
Key ring £5.68
Cards £7.75
Pen £6.43
• Calculate the change from £50 when buying:
Game £34.75
Controller £42.56
Case £28.67
• Calculate the change from £100 when buying:
Game £67.43
Console £85.85
Tablet £73.68

In-depth Investigation: Step Change
Children find change from 2 or 3 notes. They explore patterns in the pence.

### Extra Support

Frog Goes Freestyle
Subtracting pairs of 2-digit numbers with a bigger gap, e.g. 84 – 37, using counting up (Frog)

AND

Finding change from £1

## Unit 3 Efficient strategies for mental add/subt (suggested as 2 days)

### Objectives

Mentally add and subtract numbers using efficient strategies
Unit 6: ID# 3793

National Curriculum

Hamilton Objectives
8. Mentally add or subtract any pair of 2- digit numbers.
9. Mentally add and subtract multiples of 1s, 10s and 100s to/from 3-digit numbers.
13. Estimate answers and use addition to check subtraction, understanding that addition and subtraction are inverse operations.
14. Solve problems, including word problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Write 463 + 306. Discuss that it’s probably more efficient to calculate mentally than with a written method: We add the 100s then the 1s - we’re using place value. Ask children to work out 463 + 205, 463 + 310. Agree answers.
Discuss how to work out 463 + 299. 299 is a ‘nearly number’. Agree that we add 300 and adjust the answer by subtracting 1. Repeat for 463 + 399 and 463 + 198.

Group Activities
-- Add two 3-digit numbers, beginning to recognise when to use each of two different strategies.
-- Pick two cards and decide if using a written method for addition or a mental calculation is more efficient.

Day 2 Teaching
Write 784 – 230. Ask children to discuss how to do this. Point out that we don’t need Frog! We can do it using place value. Ask children to work out 784 – 210 and 784 – 302. Agree answers. Write 784 – 199 and discuss how we can subtract a ‘nearly number’ using the multiple of 100, then adjusting the answer. Repeat for 784 – 299 and 784 – 198.
Group Activities
Use the in-depth problem-solving investigation ‘Super Shapes’ from NRICH as today’s group activity.
Or, use these activities:
-- Subtract two 3-digit numbers, beginning to recognise when to use each of two different mental strategies.
-- Find the mystery missing numbers that have been subtracted from 3-digit numbers.

### You Will Need

• Whiteboards and pens
• Place value cards
• ‘3-digit number cards’ sheets 1 and 2 (see resources)
• ‘Subtracting mentally’ sheet (see resources)

### Mental/Oral Maths Starters

Day 1
Adding multiples of 10 and 100 to 3-digit numbers (pre-requisite skills)

Day 2
Place value subtractions (pre-requisite skills)

### Procedural Fluency

Day 1
Add multiples or near multiples of 100. Choose a method to add a pair of 3-digit numbers.

Day 2
Find the missing ‘nearly number’ in 3-digit subtractions.

### Mastery: Reasoning and Problem-Solving

Complete the bar models:
Diagram 1:

 ? 428 199

Diagram 2:

 854 399 ?

Diagram 3:

 923 ? 498
• Tracy has 381 pennies saved in her ‘penny-jar’. If she takes out 299 to buy a toy, how many pennies will she have left? How much was the toy in pounds and pence?
• Shane has 258 football cards and his mum buys a job-lot of 199 on-line. How many cards does he have now?
• Ahmed gives 5 pounds and 1 penny to his little brother. He realises that he has 399p left. How much did he start with?

In-depth Investigation: Super Shapes
Find the value of the red shape in the addition problems. Super Shapes from www.nrich.maths.org.

### Extra Support

Pattern Spotters
Adding any pairs of 2-digit numbers using partitioning (including 1s> 10 AND 10s > 100)