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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