Monday – Adding 2, 3, and 4 digit numbers mentally.

Remember to count on the ones column first, and then add the tens. You could

also split the ones column to make a number bond to 10. Be sure to look for

patterns!

Fluency

Complete the addition patterns using mental methods.

Problem Solving

A factory outlet sells microwave ovens. It has 235 ovens in stock. A delivery of

57 more ovens arrives. How many ovens do they have in total now?

James has two money boxes. In one is £29 and in the other is £49. James takes

all this money and pays it into his bank account. If he had £573 in the account

already, how much did he have in the account after paying the money in?

Reasoning

Write three calculations where you would use mental calculations and three

where you would use the column method. Explain the decision you made for each

calculation.

3. 38 + 45 =

338 + 45 =

3238 + 45 =

4. 62 + 29 =

862 + 29 =

9562 + 29 =

5. 54 + 37 =

654 + 37 =

8254 + 37 =

4. 19 + 79 =

819 + 79 =

6319 + 79 =

1. 45 + 48 =

745 + 48 =

7445 + 48 =

2. 36 + 58 =

636 + 58 =

9036 + 58 =

Tuesday – Subtracting 3 and 4 digit numbers.

If you use column subtraction to solve these, be extra careful to line your

columns up correctly. Remember to borrow and exchange where needed.

Fluency

Complete these subtractions.

Problem Solving

Claire and Mark are planning their honeymoon. The original price was £2500 but

they found an offer online for £490 off. They have saved £1380 so far. How

much more money do they need?

Gopal and Zuri climbed 167m of a 405m climbing wall. How far away were they

from the top?

Reasoning

Grace says that 5129 – 3372= 2257 because:

‘ 5000-3000= 2000

300- 100=200

70-20 = 50

9-2 = 7

so 5129-3372 is 2257’

Do you agree with Grace? Use an addition calculation to justify your answer.

1. 406 - 263 =

2. 305 - 127 =

3. 702 - 588 =

4. 9003 – 8874 =

5. 7006 - 6439 =

6. 7005 - 3584 =

Wednesday – Using factors to multiply.

Factor pairs are pairs of numbers that multiply together to make a specific

number. Each number at least one factor pair involving 1.

For example –

We can make 5 by multiplying 1 x 5. There are no other whole numbers we can

multiply together to make 5 so it has one factor pair.

To make 10, we can multiply 1 x 10 and 2 x 5 meaning it has two factor pairs.

To solve questions with factors, we can split one number we are multiplying into

the 2 x table allowing us to multiply once, and then double our answer.

For example –

21 x 6 =

We split the 6 into the 2 x table which is 3 x 2. We can then multiply the 21 by

3 and then double the answer.

21 x 3 = 63 63 x 2 = 126 therefore 21 x 6 = 126

Fluency

Split the second number into factor pairs to help you multiply.

E.g. 32 x 4 become 32 x 2 x 2.

1. 35 x 8 =

2. 23 x 6 =

3. 47 x 4 =

4. 115 x 8 =

5. 7 x 16 =

6. 27 x 12 =

Problem Solving

Boxes of eggs contain 6 eggs. A company orders 53 boxes of eggs for shipment

and they are due to arrive in 5 days. How many eggs did the company order?

There are 84 marbles in a bag. The marbles need to be split between James and

his three friends. Use factors to calculate how many marbles each person gets.

Reasoning

Another company buys boxes of eggs. The eggs can be in boxes of 6, 8 or 12.

The company can buy either 10 boxes of 6, 8 boxes of 8 or 5 boxes of 12. What

purchase gives the most eggs?

Thursday – Changing the scale of shapes.

To calculate the area of a quadrilateral, we multiply the two different sides

together. Scale is changing the size of a shape by a certain amount but

whatever change we make; we must do to all sides.

Fluency

Calculate the area of these rectangles mentally, then complete the table.

Rectangle Area Area of rectangle with sides doubled A 36cm2 144cm2

B

C

D

Problem Solving

A rectangle has sides that are 12cm and 5cm. The rectangle is redrawn with its

sides doubled in length. What is the area of the new rectangle?

A square has one side measuring 8cm. It is then redrawn with its sides tripled.

What is the area of the new square?

Reasoning

Jim and Matt are comparing rectangles. Matt says that if he doubles the

lengths of the sides, then the area will also double. Is he correct?

Friday – Calculating number of shape arrangements.

Fluency

Complete this table:

Number of counters Number of

arrangements

Pattern for number of

arrangements

2 2 x 1

3 6

4

5

6 720

Reasoning

Write the rule for arrangements in your own words.

Using your rule, calculate the maximum number of arrangements for 8, 9 and 10

objects,

Monday – Adding 2, 3, and 4 digit numbers mentally. Answers

Fluency

Complete the addition patterns using mental methods.

Problem Solving

A factory outlet sells microwave ovens. It has 235 ovens in stock. A delivery of

57 more ovens arrives. How many ovens do they have in total now?

292

James has two money boxes. In one is £29 and in the other is £49. James takes

all this money and pays it into his bank account. If he had £573 in the account

already, how much did he have in the account after paying the money in?

£651

Reasoning

Write three calculations where you would use mental calculations and three

where you would use the column method. Explain the decision you made for each

calculation.

Many possible answers. Children should be using mental methods on numbers

with digits adding to lower than 10 with no carrying and column for numbers

with digits adding to greater than 10 with carrying.

1. 38 + 45 = 83

338 + 45 = 383

3238 + 45 = 3283

2. 62 + 29 = 91

862 + 29 = 891

9562 + 29 = 9591

3. 54 + 37 = 91

654 + 37 = 691

8254 + 37 = 8291

4. 19 + 79 = 98

819 + 79 = 898

6319 + 79 = 6398

5. 45 + 48 = 93

745 + 48 = 793

7445 + 48 = 7493

6. 36 + 58 = 94

636 + 58 = 694

9036 + 58 = 9094

Tuesday – Subtracting 3 and 4 digit numbers. Answers

Fluency

Complete these subtractions.

Problem Solving

Claire and Mark are planning their honeymoon. The original price was £2500 but

they found an offer online for £490 off. They have saved £1380 so far. How

much more money do they need?

£2500 – £490 = £2010

£2010 – £31380 = £630

Gopal and Zuri climbed 167m of a 405m climbing wall. How far away were they

from the top?

405m – 167m = 238m

1. 406 - 263 = 143

2. 305 - 127 = 178

3. 702 - 588 = 114

4. 9003 – 8874 = 129

5. 7006 - 6439 = 567

6. 7005 - 3584 = 3421

Reasoning

Grace says that 5129 – 3372= 2257 because:

‘ 5000-3000= 2000

300- 100=200

70-20 = 50

9-2 = 7

so 5129-3372 is 2257’

Do you agree with Grace? Use an addition calculation to justify your answer.

Grace is incorrect because she has mixed up the order of the columns in the

numbers (she has put the biggest digit first when they are not part of the same

number).

4 10 1

5 1 2 9

3 3 7 2 -

1 7 5 7

Wednesday – Using factors to multiply.

Fluency

Split the second number into factor pairs to help you multiply.

E.g. 32 x 4 become 32 x 2 x 2.

Problem Solving

Boxes of eggs contain 6 eggs. A company orders 53 boxes of eggs for shipment

and they are due to arrive in 5 days. How many eggs did the company order?

53 x 3 = 159 159 x 2 = 318

There are 84 marbles in a bag. The marbles need to be split between James and

his three friends. Use factors to calculate how many marbles each person gets.

4 people altogether

84 ÷ 2 = 42 42 ÷ 2 = 21 each

1. 35 x 8 = 280

35 x 4 x 2

2. 23 x 6 = 138

23 x 3 x 2

3. 47 x 4 = 188

47 x 2 x 2

4. 115 x 8 = 920

115 x 4 x 2

5. 7 x 16 = 112

7 x 8 x 2

6. 27 x 12 = 324

27 x 6 x 2

Reasoning

Another company buys boxes of eggs. The eggs can be in boxes of 6, 8 or 12.

The company can buy either 10 boxes of 6, 8 boxes of 8 or 5 boxes of 12. What

purchase gives the most eggs?

10 x 3 = 30 30 x 2 = 60

8 x 4 = 32 32 x 2 = 64

5 x 6 = 30 30 x 2 = 60

The would want to order 8 boxes of 8.

Thursday – Changing the scale of shapes.

Fluency

Calculate the area of these rectangles mentally, then complete the table.

Rectangle Area Area of rectangle with sides doubled A 36cm2 144cm2

B 36cm2 144cm2

C 65cm2 260cm2

D 36cm2 144cm2

Problem Solving

A rectangle has sides that are 12cm and 5cm. The rectangle is redrawn with its

sides doubled in length. What is the area of the new rectangle?

12 x 2 = 24 5 x 2 = 10 24 x 10 = 240cm2

A square has one side measuring 8cm. It is then redrawn with its sides tripled.

What is the area of the new square?

8 x 3 = 24 24 x 24 = 576cm2

Reasoning

Jim and Matt are comparing rectangles. Matt says that if he doubles the

lengths of the sides, then the area will also double. Is he correct?

Matt is incorrect. If both sides are doubled, it is the same as multiplying by 4

(doubled one side, then the other), so the new area will 4 times bigger.

Friday – Calculating number of shape arrangements.

Fluency

Complete this table:

Number of counters Number of

arrangements

Pattern for number of

arrangements

2 2 2 x 1

3 6 3 x 2 x 1

4 24 4 x 3 x 2 x 1

5 120 5 x 4 x 3 x 2 x 1

6 720 6 x 5 x 4 x 3 x 2 x 1

Reasoning

Write the rule for arrangements in your own words.

Start with the number of counters, and then continue to multiply it by one less

until you reached the number 1.

Using your rule, calculate the maximum number of arrangements for 8, 9 and 10

objects,

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 4320

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 38880

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 388800