Short Blocks

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

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

First time using Hamilton Maths?

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 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