Short Blocks

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

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

## Written algorithms(suggested as 5 days)

### Planning and Activities

Day 1
Model expanded and compact column addition. Y3 practise adding two 3-digit numbers; Y4 add two 4-digit numbers.
Group Activities: T with Y3
-- Make two 3-digit numbers using dice; add the numbers using compact addition.
Y4 -- Use the digits 6, 7, 8 and 9 (or 3, 4, 5 and 6) to make a 4-digit number. Reverse the digits and find the total, e.g. 7689 + 9867. Find the digit sum of the answer. Describe patterns.

Day 2
Estimate totals by rounding to the nearest 100 or the nearest 10 before solving 3-digit additions.
Further Teaching with Y4
Revise compact decomposition for subtracting 3-digit numbers.
Group Activities: T with Y4
Y3 -- 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.
Y4 – Work towards securing a written method for 3-digit subtractions.
– Consolidate use of compact column subtraction. Consider the most appropriate/efficient method for subtraction.

Day 3
Discuss why and where there will be ‘carries’ in 3-digit additions.
Further Teaching with Y4
Model compact decomposition of 4-digit numbers. Discuss why and where there will be ‘moves’ across columns in 4-digit subtractions.
Group Activities: T with Y4
Y3 -- Investigate addition of pairs of palindromic numbers.
Y4 – Use base-10 equipment in a place value grid to help with expanded column subtraction of 4-digit numbers (1 move).
– Begin to use compact column subtraction of 4-digit numbers (1 move).

Day 4
Further Teaching with Y4
Further use of decomposition to subtract 4-digit numbers: 2 moves across columns.
Group Activities: T with Y3
Y3 -- Add three or four 2-digit numbers, using expanded and compact addition.
-- Estimate the total when adding three or four 2-digit numbers, then find the answer using compact addition.
Y4 -- Begin to secure use of expanded column subtraction to subtract pairs of 4-digit numbers.
-- Secure use of expanded column subtraction to subtract pairs of 4-digit numbers; begin to use compact subtraction. Subtract amounts of money.

Day 5
Consider mental strategies to solve 300 – 256, 678 – 523 and 678 – 199.
Further Teaching with Y3
Estimate and add three or four 2-digit numbers using expanded or compact addition.
Group Activities: T with Y3
Y3 -- Add several 2-digit numbers with a given target total.
Y4 Use the in-depth problem-solving investigation ‘Subtraction Surprise’ from NRICH as today’s group activity.
Or, use this activity:
-- Create subtraction questions that can be solved mentally.

### You Will Need

• Mini-whiteboards and pens
• ‘3-digit number cards’ (cut into cards, see resources)
• Calculators
• 0–9 Dice (3 per child)
• 0–9 Digit cards
• Counters
• 100s, 10s and 1s place value cards/dice
• Flipchart and pens
• A3 paper
• Base-10 equipment (1000s, 100s, 10s, 1s)
• ‘Column subtraction of 4-digit numbers’ (see resources)
• ‘2-digit number cards’ (cut into cards, see resources)
• ‘Addition’ Sheets 1 and 2 (cut into cards, see resources)
• ‘Whole class practice’ (see resources)
• ‘Estimating totals’ Sheets 1 to 3 (see resources)

### Short Mental Workouts

Day 1

Day 2
Add four 1-digit numbers (uses the Number Spinners ITP)

Day 3
Subtract 1-digit numbers from numbers less than 100

Day 4
Subtraction facts to 20

Day 5
Subtraction facts: Multiples of 10

### Worksheets

Day 1

Day 2
Y3 Add numbers to reach a target.
Y4 Subtract 3-digit numbers.

Day 3
Y4 Column subtraction of 3-digit numbers.

Day 4
Y3 Add three and four 2-digit numbers.
Y4 Subtraction practise.

Day 5
Y3 Estimate and add several 2-digit numbers.
Y4 Subtraction strategies.

### Mastery: Reasoning and Problem-Solving

Y3

• Choose a different method to solve each addition:
375 + 567 =
638 + 51 =
24 + 36 + 25 =
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 this the closest possible total to 200?

Y4

• Here is Ali’s homework:
1. 4278 + 2675 = 6842
2. 5678 + 2656 = 7224
3. 7552 + 1995 = 8447
4. 1862 - 7543 = 8305
He is upset as he has them all wrong. Calculate the correct answers, then advise Ali what mistake he has made in each.
• Write these two numbers in expanded form, i.e. as hundreds + tens + ones:
749
321.
Mentally find the difference between them; write the answer.
• Complete these using column subtraction:
(i) 538 – 264
(ii) 783 – 427
(iii) 446 – 382
(iv) 621 – 355
• Write the missing numbers in this calculation:
88☐ – 3☐7 = 535

Y3 In-depth investigation:
Look for patterns when adding numbers with a difference of 11 (Day 5 Working at Greater Depth, Group Activity 2).

Y4 In-depth investigation: Subtraction surprise
Watch a short video of some calculations which lead to a surprising result. What do you notice? Can you describe the steps carried out in each calculation? Subtraction Surprise from nrich.maths.org.

### Extra Support

Y3: Totally investigative
Adding any pairs of 2-digit numbers using partitioning (including 1s greater than 10 and 10s greater than 100).

Y4: Expanded Sums
Using expanded column addition to add pairs of 3-digit numbers (one ‘carry’).

Hops and Jumps
Subtracting numbers either side of a multiple of 100 using Frog, e.g. 624 – 596, 403 – 376 and 512 – 487.