# Maths Year 3 Summer Addition and Subtraction

Each unit has everything you need to teach a set of related skills and concepts.

## Mentally add/subtract 1-digit numbers (suggested as 2 days)

### Mastery

### Worksheets

### Resources

### Catch-up Learning

### Teacher Tips

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

### Planning and Activities

**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*)

### Worksheets

**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

## 3-digit expanded and compact addition (suggested as 5 days)

### Planning and Activities

**Day 1 Teaching**

Write 654 + 567. One child calculates answer using expanded addition, another using compact addition. Remind both children to leave a space before drawing the lines for the answer. When children have finished, compare their workings and answers. Write 478 + 245, and 837 + 367. Use your preferred strategy to calculate the two answers.**Group Activities**

-- Add two 3-digit numbers, using expanded and compact addition methods.

-- Make two 3-digit numbers using dice. Then add the numbers using compact addition.

**Day 2 Teaching**

Write 426 + 217, 742 + 276 and 587 + 278. Children round each to nearest 100, then add to estimate the total. Repeat, this time children round each to nearest multiple of 10; then use addition of 2-digit numbers to estimate total. Give 1 addition to each third of the class to find an exact answer. Compare with estimates.**Group Activities**

-- Think mathematically to use chosen digits to make two (or three) 3-digit numbers with a total as close as possible to 600 (or 1000). Use compact addition.

-- Estimate the total of two 3-digit numbers; find the exact total using compact addition.

**Day 3 Teaching**

Write 48 + 26 + 35. Agree we could do this by adding the larger two numbers (83) and then the smallest. BUT we can also use column addition. This is especially useful if we are adding four 2-digit numbers. Model both expanded and compact addition for 45 + 28 + 63 + 38. Here, we had an extra 20 to add to the 10s! Children have a go with 36 + 45 + 58 + 23.**Group Activities**

-- Add three or four 2-digit numbers, using expanded and compact addition methods.

-- Estimate the total when adding three or four 2-digit numbers, then find the answer using compact addition.

**Day 4 Teaching**

Write 43, 86, 27, 36, 18, 54, 72 and 67. Look for 3 numbers that might have a total close to 100. They check using column addition. How did you choose your numbers? Rounding to the nearest 10 can help. Now choose 3 numbers with a total near 150. Check using column addition. Now choose 4 numbers with a total near 150.

Group Activities

-- Look for 3 or 4 numbers that children estimate will have a total near given multiples of 10.

-- Play ‘missing digits’. Children work out the missing 1s digit in addition calculations.

**Day 5 Teaching**

Add 3 numbers where the digits in each number are the same, e.g. 33 + 44 +55. Share answers; discuss observations. Ask them to choose other trios of similar numbers to check if this is always the case. Can we write a ‘rule’ to describe what happens with additions like these? If one doesn’t work, check! [If the answer is a 3-digit number, the middle digit is the sum of the two digits on either side - a function of this being one of a certain group of multiples of 11; If the answer is a 2-digit number, both digits are the same].**Group Activities**

Use the in-depth, whole-class, problem-solving investigation– Investigating 11– as today’s group activity.

-- Investigate patterns when adding three or four 2-digit numbers that have a difference of 11, e.g. 89+ 78 + 67.

### You Will Need

- Whiteboards and pens
- 3-digit number cards (
*see resources*) - 2-digit number cards (
*see resources*) - Calculators
- 0 – 9 Dice
- Counters
- 0-9 cards
- 100s, 10s and 1s place value cards
- 2-digit number cards
- ‘Addition’ sheets 1 and 2 (
*see resources*) - ‘Estimating totals’ sheets 1 to 3 (
*see resources*) - ITP: Spinners

### Mental/Oral Maths Starters

**Day 1**

Know total of any pair of single-digit numbers (*pre-requisite skills*)

**Day 2**

Round 3-digit numbers to nearest 10 and 100 (*pre-requisite skills*)

**Day 3**

Add 4 single-digit numbers (*pre-requisite skills*)

**Day 4**

Add multiples of 10 (*pre-requisite skills*)

**Suggested Day 5**

Subtract single-digit numbers (*simmering skills*)

### Worksheets

**Day 1**

Use expanded or compact addition to add two 3-digit numbers.

**Day 2**

Choose two 3-digit numbers from those given to target one of several given target numbers. Estimate and find exact totals.

**Day 3**

Use expanded or compact addition to add 3 or four 2-digit numbers.

**Day 4**

Choose three 2-digit numbers from those given to target one of several given target numbers. Estimate and find exact totals.

**Day 5**

Add 3 or four 2-digit numbers using compact addition.

### Mastery: Reasoning and Problem-Solving

- Choose a different method to solve each addition:

375 + 567 =

638 + 51 =

24 + 36 + 25 = - Use column addition to help you to find each missing number:

548 + 175 = ☐

☐ – 356 = 387

635 + 296 = ☐

☐ – 466 = 247 - Sally has 45 Pokémon cards, Bill has 67, Jon has 28 and Parvati has 86. How many do they have altogether?
- Choose four of these numbers likely to give a total close to 200:

73 68 56 75 66 37

Add them using column addition. Is the closest possible total to 200?

**In-depth Investigation: Investigating 11**Look for patterns when adding numbers with a difference of 11. See Day 5 group activity 1 for details.

### Extra Support

**Totally Investigative**

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

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

### Planning and Activities

*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*)

### Worksheets

**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

- Use Maths Frog to help you write the missing numbers:

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

**Read It **Finding change from £1

## Revise expanded and column addition (suggested as 4 days)

### Planning and Activities

**Day 1 Teaching**

Demonstrate both expanded & compact written addition: 46 + 27 + 52 + 17. Remind children to leave a space above the answer for ‘carry’ digits.

Write 82 + 32 + 47 + 25. How could we estimate the answer? Recall strategy to round each number to the nearest 10, then add these multiples of 10. Agree estimates, then use expanded or compact addition to find exact answer. Repeat for 63 + 18 + 36 + 55.**Group Activities**

Use the ‘Mobile Towers’ in-depth problem-solving investigation below as today’s group activity.

Or, use these activities:

-- Revise estimating totals and adding three or four 2-digit numbers using compact addition.

-- Estimate the total of four 2-digit numbers; find exact totals using column addition.

**Day 2 Teaching**

Write 378 + 123 + 285. Ask children to estimate the answer by rounding to nearest 100. Check estimate using first expanded column addition then compact. Remind children to leave a line above the answer. Repeat for 416 + 389 + 534.

**Group Activities**

-- Practise adding trios of 3-digit numbers, using either expanded or compact addition. Totals <1000 and >1000.

-- Estimate, then calculate, three costs that add up to <£1000.

**Day 3 Teaching**

Record expanded addition for £3.55 + £2.26. Demonstrate how we add the 1ps, the 10ps, the pounds and then add the 3 amounts together. Repeat with £4.72 + £2.54 pointing out what happens when you add 70p and 50p – a total more than £1. Children have a go at £4.59 + £2.25 and £4.72 + £3.59, choosing to use expanded or compact addition.**Group Activities**

-- Practise using expanded or compact addition to add amounts of money.

-- Estimate then calculate multiple costs that add up to under £10.

**Day 4 Teaching**

Show four holiday items with prices £2.74, £1.43, £8.53 and £5.72. Choose two to buy for less than £5. Find their total, then calculate the change from £5 using Frog. Repeat to choose two for less than £10 & find change. Repeat for a pair under £20.**Group Activities**

-- Choose two items that add up to under £5, £10 or £20 then calculate change.

-- Buy multiple items that add up to under £20, then calculate change.

### You Will Need

- Whiteboards and pens
- Cards with 2 digit numbers on them
- ‘Adding three 3-digit numbers’ sheets 1, 2 and 3 (see resources)
- ‘Bicycles for sale’ sheet (see resources)
- ‘Adding amounts of money’ sheets 1 and 2 (see resources)
- Books with price tags £4.79, £3.14, £6.01, £5.49, £5.88, £5.25, £3.23, £4.65, £4.29, £2.35, £5.17, £2.52
- Items that might be for sale in a seaside shop e.g. sun cream, beach towel, bucket, spade with prices £2.74, £1.43, £8.53 and £5.72
- ‘The beach shop’ sheet (see resources)
- Coins and dice

### Mental/Oral Maths Starters

**Day 1**

Round 3-digit numbers to nearest 100 (*pre-requisite skills*)

**Day 2**

Round amounts of money to the nearest pound (*pre-requisite skills*)

**Day 3**

Say the amount needed to make £1 (*pre-requisite skills*)

**Suggested for Day 4**

Add 3 multiples of 10 (*simmering skills*)

### Worksheets

**Day 1**

Round 2-digit numbers to the nearest 10; choose three or four of them to add up to approximate one of several target numbers.

**Day 2**

Round 3-digit numbers to the nearest 10; choose two or three of them to add up to approximate one of several target numbers.

**Day 3**

Round to the nearest pound to estimate each total. Then use column addition to ﬁnd the exact answer.

**Day 4**

Calculate the price of 2 items, and then the change from £5, £10 or £20.

### Mastery: Reasoning and Problem-Solving

- Choose three of these numbers and write an estimate of their total:

475 386 287 349 248

Add the three numbers and compare the actual answer with your estimate. Repeat, choosing three different numbers. Was your second estimate closer? - Work out the missing numbers in this addition puzzle:

£4 ☐p 8p__£7 80p ☐p__

£☐ 60p 1p

**In-depth Investigation: Mobile Towers**Children create 4 or five 2-digit numbers and add these to get different totals.

### Extra Support

**Addition of Three-digit Numbers **

Using the interactive tool from Harcourt School at http://www.harcourtschool.com, children use base-10 blocks to explore regrouping in addition

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

### Planning and Activities

**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
- ‘Adding mentally’ (see resources)
- 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*)

### Worksheets

**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)