# Maths Year 3/4 Spring Addition and Subtraction

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

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## Unit 1 Mental addition and subtraction (suggested as 4 days)

### Objectives

Unit 1: ID# 34492

National Curriculum

Y3 Hamilton Objectives
8. Mentally add or subtract any pair of 2-digit numbers.
10. Recognise that there are two ways of completing subtractions, either by counting up or by counting back.

Y4 Hamilton Objectives
10. Mentally add and subtract any pair of 2-digit numbers or 3-digit multiples of 10.
12. Subtract numbers from 3-digit numbers using counting up (Frog).
32. Solve simple money problems involving decimals to two decimal places.
36. Estimate, compare and calculate money in pounds and pence.

### Planning and Activities

Day 1 Teaching
Discuss what strategies we can use to add two 2-digit numbers, and then how we can use those same strategies to add a 2-digit number to a 3-digit number. Use the same strategies to add pairs of 3-digit numbers where a mental strategy would be quicker than column addition.
Group Activities: T with Y3
Use the ‘Make 100’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Use spinners to generate 2-digit numbers to add. Children discuss which strategy they used each time.
Y4 -- Decide when additions can be efficiently solved using a mental strategy rather than column addition. Some children will find trios with a total of 100, then 200.

Day 2 Teaching
Children subtract 20p, then 21p and 19p from prices.
Further Teaching with Y4
Use Frog to find out how much further cyclists need to cycle from 625 to 874 miles. Sketch a bar model to represent this.
Group Activities: T with Y4
Y3 -- Reduce prices by near multiples of 10p; Reduce prices by 32p and 29p.
Y4 -- Use counting up to find the difference between two 3-digit numbers.

Day 3 Teaching
Show children items with prices tags less than £5 and a £5 note. Together calculate the change using Frog. Repeat, finding the change from £10.
Further Teaching with Y3
Revise using Frog to subtract pairs of 2-digit numbers.
Group Activities: T with Y3
Y3 -- Frog investigation: think of a 2-digit number, 1st digit greater than 2nd, reverse and subtract, e.g. 85 – 58.
Y4 -- Count up to find change from £5 and £10.

Day 4 Teaching
Discuss choosing Frog or counting back to subtract 2-digit numbers. Begin to recognise what it is about the numbers that informs this choice.
Further Teaching with Y4
Show a table of items with their ‘old’ and ‘sale’ prices. Demonstrate how to use Frog to count up to find the difference between each pair of prices.
Group Activities: T with Y4
Y3 -- Choose Frog or counting back to subtract; explain choices.
Y4 -- Count up to find the difference between two amounts of money; use addition to check answers to subtractions.

### You Will Need

• Large 100-square
• Plastic or card spider and fly
• ‘2-digit number spinners’ sheets 1 and 2 (see resources, enlarge to A3)
• ‘1 to 100 number grid’ (see resources)
• Tens and one place value cards
• ‘Subtracting near multiples’ sheets 1 and 2 (see resources) or label actual items with the tags
• Items with price tags less than £5, between £5 and £10, a £5 note and a £10 note
• Toy frog
• 0–100 beaded and landmarked number lines to display on the IWB (see resources)
• ‘0–100 landmarked number lines’ (see resources)
• ‘Number cards’ sheet 1 and 2 (see resources)

Day 1

Day 2

Day 3
Change from £1

Day 4
Pairs to 100

### Procedural Fluency

Day 1
Y3: Use Spider and Fly to add pairs of numbers which don’t cross 10s. Add pairs of amounts of money.
Y4: Complete missing numbers in an addition grid; add 3-digit and 2-digit numbers.

Day 2
Y3: Subtract 2-digit numbers by taking away 10s and 1s, or by subtracting a multiple of 10 and adjusting.
Y4: Use empty number lines to subtract pairs of 3-digit numbers by counting up.

Day 3
Y3: Practise using Frog to subtract pairs of 2-digit numbers.
Y4: Find change from £5 and £10 by counting up.

Day 4
Y3: Choose Frog or counting back to calculate given subtractions.
Y4: Draw empty number lines and find the difference between two amounts of money by counting up.

### Mastery: Reasoning and Problem-Solving

Y3

• Use a different strategy for each of these additions:
45 + 29
45 + 34
65 + 35
78 + 28
• Write the missing numbers:
(a) ☐ + 30 = 55
(b) 100 - 79 = ☐
(c) ☐ + 19 = 65
(d) 73 – ☐ = 58
(e) 50 – ☐ = 43
(f) ☐ + 47 = 62
• Hassan spends 39p on a drink. He uses a 50p coin to pay. How much change does he get?
• Sam has 76 cards. Tom has 92. How many more does Tom have than Sam?

Y4

• Tim buys a DVD and Frog finds the change from £10. He says it is £3.46. How much was the DVD?
• Complete each diagram:
 £10 £6.83 ?
 £5 ? £2.27
 £10 £3.58 ?
• Write a list of ‘Top Tips’ for how you would find the difference between these two prices: £4.52 and £6.18.

In-depth investigation: Make 100
Given a pattern of four 1-digit numbers, children attempt to make a total of exactly 100.

### Extra Support

Y3: Hop, Jump and Hop
Subtracting pairs of 2-digit numbers either side of a multiple of 10, e.g. 54 – 37, using counting up (Frog)

Y4: Winter Warmers
Finding the change from £5 (answers less than £1)

Are We Nearly There Yet?
Using counting up (Frog) to subtract numbers either side of 100, e.g. 102 – 97 and 102 – 78

## Unit 2 3-digit +/– 1-digit numbers (suggested as 2 days)

### Objectives

3-digit +/– 1-digit numbers
Unit 2: ID# 34508

Y3: Mentally add/subtract 1-digit numbers to/from 3-digit numbers.
Y4: Mentally add/subtract 1-digit numbers to/from 4-digit numbers.

National Curriculum

Y3 Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15.
14. Solve problems, including missing number problems.

Y4 Hamilton Objectives
16. Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

### Planning and Activities

Day 1 Teaching
What is 5 + 2? 25 + 2? 425 + 2? 3425 + 2? Point out that we can use the fact that 5 + 2 = 7 to answer each of these questions. Use a counting stick to show additions that bridge 10/100/1000.
Group Activities: T with Y3
Y3 -- Play games adding 1-digit numbers to 3-digit numbers.
Y4 -- Repeatedly add a 1-digit number to a 4-digit number; notice the pattern in the 1s digit.

Day 2 Teaching
Write 8 – 5? 38 – 5? 738 – 5? 3738 – 5? Point out that we can use the fact that 8 – 5 = 3 to answer each of these questions. Use a counting stick to show subtractions that bridge 10/100/1000.
Group Activities: T with Y4
Use the ‘Magical subtractions’ in-depth problem-solving investigation below as today’s group activity. Or, use these activities:
Y3 -- Play games involving subtracting 1-digit numbers from 3-digit numbers.
Y4 -- Repeatedly subtract a 1-digit number from a 4-digit number.

### You Will Need

• Counting stick
• Number cards 3–9
• Counters
• Sets A, B, C and D 3-digit number cards (see resources)
• 0–9 dice and 1–6 dice

### Short Mental Workouts

Day 1
Count on and back in steps of 1

Day 2
Subtract 1-digit numbers from teens numbers

### Procedural Fluency

Day 1
Y3: Add 1-digit numbers to 3-digit numbers using number facts and bridging through 10s and 100s.
Y4: Add 1-digit numbers to 3- and 4-digit numbers.

Day 2
Y3: Subtract 1-digit numbers from 3-digit numbers using number facts and bridging: through 10s and 100s.
Y4: Subtract 1-digit numbers from 3- and 4-digit numbers.

### Mastery: Reasoning and Problem-Solving

Y3

• How many times can 7 be subtracted from 232 before the answer is less than 200?
• Kit says ‘If I keep adding 6 to 152, I’ll eventually reach exactly 200’. Is he correct?
• Complete the bar models:
 ? 347 7
 ? 8 555
 442 ? 7

Y4

• A 3-digit number had 5 added to it. The answer then has 4 digits and ends in 1. What was the number?
• How many times can 7 be subtracted from 1111 before the answer is less than 1000?
• Ally says ‘If I keep adding 8 to 1904, I’ll eventually reach exactly 2000’. Is he correct?

In-depth investigation: Magical subtractions
Children subtract the digital root of a 3-digit number from that number.
Magic ensues!

### Extra Support

Y3: Hops to Fours
Bridge 10 when adding 1-digit numbers to 2-digit numbers

Y4: How High Can You Jump? How Low Can You Go?
Add and subtract 1-digit numbers to and from 3-digit numbers

## Unit 3 Column addition (suggested as 4 days)

### Objectives

Unit 3: ID# 34524

Y4: Column addition of 3-digit numbers and money

National Curriculum
Y4: Add/Sub (i); Frac/Dec (x); Meas (iv)

Y3 Hamilton Objectives
11. Add numbers with 3-digits using column addition, first expanded then compact method.
14. Solve problems, including missing number problems.
32. Add and subtract amounts of money; use both £ and p in practical contexts.

Y4 Hamilton Objectives
11. Use column addition to add 3-digit and 4-digit numbers: first expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.
32. Solve simple money problems involving decimals to 2 decimal places.
36. Estimate, compare and calculate money in pounds and pence.

### Planning and Activities

Day 1 Teaching
Remind children how to use expanded addition to calculate 728 + 153, leaving a line above the answer for the extra tens, then modelling 567 + 158 showing how we need to add an extra 10 and 100. Repeat for trios of numbers, first estimating the totals.
Group Activities: T with Y3
Y3 -- Use expanded addition to add two 3-digit numbers. Some children will begin to use compact addition.
Y4 -- Apply compact addition skills to add trios (or pairs) of 3-digit numbers, aiming for given target totals.

Day 2 Teaching
Use both expanded and compact column addition to calculate the same addition. Children try each method, then say which they prefer.
Further Teaching with Y4
Group Activities: T with Y4
Use the ‘Next door additions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Target totals: make additions with a total less than 500 and more than 500. Some children will use expanded addition; others will use compact addition. They then choose their preferred layout to calculate other additions.
Y4 -- Add pairs of amounts of money using expanded and then compact addition.

Day 3 Teaching
Use IWB £1, 10p and 1p coins to show addition of pennies, then 10p coins to amounts on a place value grid, crossing multiples of 10p and £1. Show how to use expanded and compact addition to add amounts of money (1p coins >10p, 10p coins >£1).
Group Activities: T with Y3
Y3 -- Add multiples of 1p and 10p to given prices.
Y4 -- Use expanded addition and compact addition to add amounts of money. Some children will rank calculations in order of difficulty; explain reasoning.

Day 4 Teaching
Use IWB £1, 10p and 1p coins to show addition of 10p, 20p and 4p to prices.
Further Teaching with Y4
Group Activities: T with Y4
Y3 -- Use place value grids to help add multiples of 10p to given prices. Some children will count on in tens to add multiples of 10p.
Y4 -- Apply compact addition skills to add pairs/trios of 3-digit amounts of money.

### You Will Need

• Hundreds, tens and ones place value cards
• ‘Adding two 3-digit numbers’ sheet (see resources)
• Number cards 1–9
• ‘Adding amounts of money’ activity sheet (see resources)
• ‘On board practice 1 and 2’ (see resources)
• 1p, 10p and £1 coins
• ‘Money place value grid’ (see resources)
• IWB coins
• 1–6 dice and 0–9 dice
• ‘On board practice 2’ (see resources)
• ‘Adding money’ sheet (see resources)
• Books with price labels: £4.79, £5.49, £5.25, £4.65, £4.29

### Short Mental Workouts

Day 1

Day 2

Day 3
Count in steps of 20

Day 4
Money place value

### Procedural Fluency

Day 1
Y3: Practise using expanded addition to add pairs of 3-digit numbers, moving extra numbers into the tens and/or hundreds column.
Y4: Use a written method to add pairs, or trios, of 3-digit numbers. Estimate answers by rounding numbers to the nearest 10.

Day 2
Y3: Use expanded and compact addition to calculate two answers, then choose preferred layout to calculate other answers.

Day 3
Y3: Add 10p or 1p coins to 3-digit amounts.
Y4: Find missing numbers in column additions of money.

Day 4
Y3: Add multiples of £1, 10p and 1p to 3-digit amounts.
Y4: Use expanded and compact column addition to find totals of pairs of amounts of money. Estimate totals.

### Mastery: Reasoning and Problem-Solving

Y3

• Add four hundred and fifty-six to three hundred and seventy-two.
• What is the total of two hundred and sixty-eight and two hundred and eighty-six?
• Write the missing numbers:
643 + 174 = ☐
☐ – 356 = 238
327 + 258 = ☐
☐ – 426 = 247
• Amit uses 346 Lego pieces in building his model X-wing, and his sister uses 287 in building her Millennium Falcon. How many Lego pieces have they used altogether?

Y4

(i) £5.78 + £4.22
(ii) £2.56 + £7.44
(iii) £3.17 + £6.83
• Is a column addition calculation the most efficient way to find:
£4.99 + £7.46
£8.06 + £8.06
£4.31 + £5.69?
• Write the missing numbers in this calculation:
£4.☐7 + £5.6☐ = £☐.45

Children add pairs of 3-digit numbers and look for patterns in the digital roots of the answers.

### Extra Support

Add any pairs of 2-digit numbers using partitioning (including ones >10 and tens >100)

Y4: Pocket Money
Add two prices with a total of more than £1 using partitioning

Expanded Sums
Use expanded column addition to add pairs of 3-digit numbers (one ‘carry’)

## Unit 4 Frog and decomposition (suggested as 5 days)

### Objectives

Frog and decomposition
Unit 4: ID# 34540

Y3: Counting up to subtract
Y4: Column subtraction and counting up to subtract

National Curriculum

Y3 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.

Y4 Hamilton Objectives
12. Subtract numbers from 3-digit numbers using ‘Frog’/counting up, e.g. 426 – 278, 321 – 87.
14. Use column subtraction to subtract 3-digit and 4-digit numbers: first expanded, then compact method.
15. Estimate and use inverse operations to check answers to a calculation.

### Planning and Activities

Day 1 Teaching
Use Frog to calculate 136 – 87, modelling how to draw the steps. Repeat for 143 – 75.
Further Teaching with Y4
Model expanded column subtraction of 3-digit numbers where one, then two moves are necessary, e.g. 725 – 462, then 745 – 367.
Group Activities: T with Y4
Y3 -- Use Frog on landmarked lines to subtract numbers between 50 and 100 from numbers between 100 and 150. Some children will use a bar model to show the link with addition.
Y4 -- Use base-10 equipment to support expanded column subtraction.

Day 2 Teaching
Children use Frog to solve 123 – 76. Write 126 – 73. Do you think this has a bigger or smaller answer? Why? Write 624 – 257 and 624 + 257. Y3 do addition, whilst you remind Y4 how to use expanded column subtraction. Check answers using the inverse operation.
Group Activities: T with Y3
Use the ‘Pattern Subtractions’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Children replace the boxes in a subtraction calculation with different digits to get different answers, including smallest and largest possible answers, looking for patterns.
Y4 -- Use base-10 equipment and place value cards to support expanded column subtraction. Subtract pairs of 3-digit numbers using the most efficient method, including expanded column subtraction.

Day 3 Teaching
Use Frog to subtract numbers within the same century, e.g. 162 – 135.
Further Teaching with Y4
Introduce compact column subtraction alongside expanded (1 move).
Group Activities: T with Y4
Y3 -- Learn to draw empty number line jottings for subtracting by counting up. Use Frog to calculate given subtractions, discussing pattern in answers.
Y4 -- Use base-10 equipment to aid expanded column subtraction. Begin to use compact column subtraction.

Day 4 Teaching
Write 873 – 827. Children solve on whiteboards with Frog. Ask children how we check it. Agree that we use addition, because the inverse of subtraction is addition – addition undoes subtraction.
Further Teaching with Y4
Use expanded and compact column subtraction to calculate 722 – 347. Six children at front of class hold digit cards to create a subtraction.
Group Activities: T with Y4
Y3 -- Investigation: Find different answers to 18⌂ – 12□. Find smallest and largest answers.
Y4 -- Use expanded column subtraction to subtract pairs of 3-digit numbers (with 1 or 2 ‘moves’) using base-10 equipment to help. Some children will consolidate use of compact column subtraction.

Day 5 Teaching
Write 623 + 326 and 623 – 326. Y3 do the addition and Y4 do the subtraction. Point out the reversed digits and explain the investigation to Y4 children.
Further Teaching with Y3
Explain that children will choose addition or subtraction to find the answers to word problems. Reveal word problems one by one. Model using the bar model for the first two questions.
Group Activities: T with Y3
Y3 -- Draw bar models to represent word problems. Some children will write word problems to go with given bar models and use bar models to represent 2-step problems.
Y4 -- Investigate patterns that occur when subtracting reversed 3-digit numbers.

### You Will Need

• Toy frog
• ‘50 –150 landmarked lines’ (see resources)
• ‘Subtract by counting up’ (see resources)
• Base-10 equipment
• Hundreds, tens and ones place value cards
• ‘Subtraction practice’ (see resources)
• 1–6 dice
• 0–9 dice or hundreds, tens and ones place value dice
• Large number cards 1–9
• ‘Word problems’ (see resources)
• ‘Problem cards’ (see resources)
• ‘Make up your own word problems’ (see resources)
• ‘2-step word problems’ (see resources)

### Short Mental Workouts

Day 1
Complements to 100

Day 2
Inverse number sentences

Day 3
Subtract 2-digit numbers

Day 4
Subtraction facts

Day 5
4 and 8 times tables

### Procedural Fluency

Day 1
Y3: Use Frog to subtract numbers < 100 from numbers between 110 and 150.
Y4: Use expanded column subtraction to subtract pairs of 3-digit numbers.

Day 2
Y3: Count up on landmarked lines to subtract. Use Frog to find missing numbers in bar models.
Y4: Use expanded column subtraction to subtract pairs of 3-digit numbers

Day 3
Y3: Use Frog to subtract numbers within the same century.
Y4: Use expanded column subtraction to subtract pairs of 3-digit numbers. Use expanded, then compact column subtraction, to subtract pairs of 3-digit numbers.

Day 4
Y3: Use Frog to subtract by counting up between pairs of numbers within the same century; check using addition.
Y4: Choose an appropriate method to subtract pairs of 3-digit numbers

Day 5
Y4: Find and correct mistakes in subtractions using counting up and column subtraction.

### Mastery: Reasoning and Problem-Solving

• Y3
Count up to find the difference:
64 – 56
72 – 57
122 – 45
272 – 228
581 – 548
875 – 837
• Tracy has 381 pennies saved in her ‘penny-jar’. If she takes out 329 to buy a Shopkins toy, how many pennies will she have left?
• Shane has 258 Pokémon cards and his mum buys a job-lot of 267 on-line. How many cards does he have now?
• In his exercise routines, Ahmed does 78 press-ups during the week. His fitness tutor says he needs to do 125 each week. So how many more must he do each week?

Y4

• Here is Ali’s homework.
1. 403 – 265
2. 648 – 356
3. 752 – 199
4. 812 – 754
Advise him on the most efficient or error-proof subtraction strategy to calculate each one, explaining why you are suggesting that method.
• Fill the gaps in this subtraction:
81☐ – 4☐7 = ☐46
• Complete each diagram:
 604 387 ?
 919 ? 868
 1003 578 ?

In-depth investigation: Pattern subtractions
Y3 Children subtract 2-digit numbers from 3-digit numbers, by counting up, and look out for patterns in the numbers.
Y4 Children subtract pairs of 3-digit numbers.

### Extra Support

Y3: Frog's Brave Big Jumps
Subtract pairs of 2-digit numbers with a bigger gap, using counting up (Frog)

Frog's Ginormous Jumps
Subtract pairs of 2-digit numbers with a bigger gap, using counting up (Frog)

Y4: Are We Nearly There Yet?
Use counting up (Frog) to subtract numbers either side of 100

Hop to 100s, and Beyond
Use counting up (Frog) to subtract numbers either side of a multiple of 100