Short Blocks

# Maths Year 3/4 Spring Addition & Subtraction (B)

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

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The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 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 2 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