Divide and Conquer Division Strategies Lucky Dip? We are learning to practise divisibility rules. 15 18 400 99 108 87 300 35 63 90 70 64 200 45 24 12 93 125 75 Exercise 1 Find the numbers from above that are: 1) Divisible by 100 2) Divisible by 10 3) Divisible by 5 4) Divisible by 2 5) Divisible by 3 AC EA AA AM AP
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Divide and ConquerDivision Strategies
Lucky Dip?We are learning to practise divisibility rules.
15 18400 99
108 87 300
35 6390 70
64 20045 24
12 93 12575
Exercise 1Find the numbers from above that are:
1) Divisible by 100
2) Divisible by 10
3) Divisible by 5
4) Divisible by 2
5) Divisible by 3
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Division Strategies
Pick a PairWe are learning to make correct division sentences.
Exercise 2Use the numbers written below to make a correct maths sentence.
3 4 5 6 7 8 9 40 60 70 80
Do all the work in your head.Show them like the example below.
Question: 90 ÷ 10 = Answer: 90 ÷ 10 = 5
1) 80 ÷ 10 = (2) ÷ = 16
3) 120 ÷ 20 = (4) 4,900 ÷ =
5) ÷ 20 = 3 (6) ÷ = 2
7) 72 ÷ = 8 (8) 120 ÷30 =
9) ÷ 10 = 3 (10) 420 ÷ = 60
11) 180 ÷ 60 = (12) ÷ = 8
13) 32 ÷ 8 = (14) 560 ÷ = 80
15) 210 ÷ 70 = (16) 450 ÷ = 50
17) 160 ÷ = 4 (18) 240 ÷ = 40
19) 60 ÷ = 15 (20) 4,800 ÷ = 60
Division Strategies
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Find the FamilyWe are learning to link multiplication and division facts.
Exercise 3For each of the following groups of numbers write as many division facts as you
can
For example, using {10, 2, 30, 120, 4, 5} 120 30 = 4 10 2 = 5 4 2 2
Multiplication SquaresWe are practising using reversibility and factors of numbers up to 100.
Exercise 4Fill in the gaps in these multiplication squares.
1) x 2
18
40 16
4 16
35 42
(2) x 10 3
15
8 32
9 45
24
(3) x 4
6 18
24 8
12
20 45
4) x 4 3
36
14 6
6 36
20
(5) x 7
15 10
28 16
9
32 24
(6) x 6
35
2 14 20
12
63 27
7) x
8 9
18 48
4 36
21 28
(8) x
64 16
56
8 40
18 12
(9) x
15 12
12 16
25
42 28
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Division Strategies
DividagonsWe are practising to use factors.
Exercise 5Complete the triangle. The number in each square is the product of the two numbers in the circles on either side.
1) (2)
3) (4)
5) (6)
7) (8)
12
15
4
618
12
2420
30
820
40
2436
6
1248
16
4228
24
2045
36
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9) (10)
11) (12)
13) (14)
15) (16)
2432
12
28
16
610
15
6328
36
616
24
1230
40
4830
40
818
36
Division Strategies
Multiples and Factors
We are learning divisibility rules.
Exercise 61) Using a hundreds board do the following:
a) Place a single coloured counter over the multiples of two.
b) Take another coloured counter and place over the multiples of four.
c) Describe what you notice?d) What is the lowest common multiple of two and four?e) What is the highest common factor of two and four?
2) On another hundreds board repeat all of question one for the multiples of three and nine. Use different coloured counters.
3) On a third hundreds board repeat question one for the multiples of two and nine. Use different coloured counters.
4) Using a hundreds board do the following:f) Place a single coloured counter over the multiples of
three.g) Take another coloured counter and place over the
multiples of six.h) Describe what do notice?i) What is the lowest common multiple of three and six?j) What is the highest common factor of three and six?
5) On another hundreds board repeat all of question five for the multiples of four and eight. Use different coloured counters.
6) On a third hundreds board repeat all of question five for the multiples of three and eight. Use different coloured counters.
7) Explore the relationship between the lowest common multiple and the highest common factor for each pair of numbers.
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8) Use the four digits in part a) and b) to make the answer to the following division problem a whole number.
÷ a) 1, 3, 5, 9 (b) 2, 4, 6, 8
Division Strategies
Fun with Factors We are practicing using division facts to solve problems.
Exercise 7Solve the following problems:
1) Find some numbers that have all their factors except 1, even. Describe the set of numbers.
2) Find some numbers that have exactly half their factors even. Describe the set of numbers.
3) What is the smallest number that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6, 8, 10 but no remainder when it is divided by 11?
4) What is the smallest number that leaves a remainder of 1 when it is divided by the first three prime numbers but no remainder when it is divided by the fourth prime number?
5) Two numbers multiply to give an answer of 1 000 000. Neither of the numbers contains any zeros. What are the two numbers?
6) There are some rabbits and some rabbit hutches. If one rabbit is put in each rabbit hutch, one rabbit is left over. If two rabbits are put in each rabbit hutch, one hutch is left empty. How many rabbits and how many hutches?
7) There are some rabbits and some rabbit hutches. If seven rabbits are put in each rabbit hutch, one rabbit is left over. If nine rabbits are put in each rabbit hutch, one hutch is left empty. How many rabbits and how many hutches?
8) Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form five 2 digit numbers which are all multiples of three.
Division Strategies
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Do it in your headWe are practising doing division mentally and recognising
‘nice’ numbers.
Exercise 8LOOK at the example and SAY the answer.
1) 248 ÷ 2 (2) 180 ÷ 6
3) 999 ÷ 9 (4) 250 ÷ 5
5) 482 ÷ 2 (6) 405 ÷5
7) 369 ÷ 9 (8) 246 ÷ 6
9) 497 ÷ 7 (10) 480 ÷ 8
11) 728 ÷ 8 (12) 842 ÷ 2
13) 357 ÷ 7 (14) 300 ÷ 6
15) 560 ÷ 8 (16) 720 ÷ 9
17) 963 ÷ 3 (18) 300 ÷ 3
19) 108 ÷ 2 (20) 355 ÷ 5
21) 368 ÷ 4 (22) 642 ÷ 2
23) 888 ÷ 8 (24) 484 ÷ 4
25) 639 ÷ 3 (26) 486 ÷ 6
27) 816 ÷ 4 (28) 369 ÷ 3
29) 129 ÷ 3 (30) 648 ÷ 8
Division Strategies
Division by PartitioningWe are learning to use the distributive property for division.
Exercise 9Ruwani knows she can work out the answer to 72 ÷ 4 by breaking 72 into two parts that can be easily divided by 4.72 ÷ 4 = 40 ÷ 4 + 32 ÷ 4
= 10 + 8= 18
What number goes in the ?1) 36 ÷ 3 + 60 ÷ 3 = ÷ 3 (2) 60 ÷ 6 + 18 ÷ 6 = ÷ 6
Use Ruwani’s method to calculate the following:1) 68 ÷ 4 (2) 128 ÷ 4 (3) 145 ÷ 5
4) 102 ÷ 6 (5) 117 ÷ 9 (6) 184 ÷ 8
7) 76 ÷ 4 (8) 87 ÷ 3 (9) 108 ÷ 6
10) 48 ÷ 3 (11) 90 ÷ 6 (12) 168 ÷ 7
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Division Strategies
Division Using Tidy NumbersWe are learning to divide by rounding to a tidy number and then compensating.
Exercise 10Jenna is putting tulip bulbs into bags for sale at the market. She has to put three bulbs into each bag. She has 84 bulbs and wants to know how many bags she will need.Jenna knows that if she had 90 bulbs she would need 30 bags since 90 ÷ 3 = 30.
So 84 ÷ 3 = 90 ÷ 3 – 6 ÷ 3
Use Jenna’s method to calculate the following:
1) 54 ÷ 3 (2) 72 ÷ 4 (3) 114 ÷ 6
4) 76 ÷ 4 (5) 111 ÷ 3 (6) 291 ÷ 3
7) 392 ÷ 4 (8) 495 ÷ 5 (9) 594 ÷ 6
10) 145 ÷ 5 (11) 87 ÷ 3 (12) 133 ÷ 7
Division Strategies
For 84 bulbs I need to take off 6 bulbs which is 2 bags so I need 28 bags.
She then thinks
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Dividing and Dividing We are learning to divide by dividing by a pair of factors of the divisor.
Exercise 11
Task 1
Tevita knows he can work out the answer to 72 ÷ 4 by dividing by 2 and dividing by 2 again.72 ÷ 2 = 36 and 36 ÷ 2 = 18 so 72 ÷ 4 = 18
Use Tevita’s method to calculate the following:1) 300 ÷ 4 (2) 128 ÷ 4 (3) 92 ÷ 4
4) 184 ÷ 4 (5) 500 ÷ 4 (6) 104 ÷ 4
7) 140 ÷ 4 (8) 56 ÷ 4 (9) 42 ÷ 4
10) 90 ÷ 4 (11) 66 ÷ 4 (12) 700 ÷ 4
Carla knows that dividing by 6 is the same as dividing by 3 and then dividing the answer by 2.To work out 90 ÷ 3 she works out 90 ÷ 3 = 30 then 30 ÷ 2 = 15 so 90 ÷ 3 = 15
She wonders if she does the division in a different order whether she will get the same answer.90 ÷ 2 = 45 and 45 ÷ 3 = 15 so 90 ÷ 6 = 15
Task 2
Use Carla’s method to calculate the following:(Sometimes you will find it easier to divide by 3 first and other times it might beeasier to divide by 2 first.) 1) 96 ÷ 6 (2) 150 ÷ 6 (3) 84 ÷ 6
4) 132 ÷ 6 (5) 450 ÷ 6 (6) 336 ÷ 6
Dividing by 2 and then dividing by 2 again is the same as dividing by 4.Dividing by 3 and then dividing by 2 is the same as dividing by 6.Ashley wonders if this rule works for other numbers as well.Ashley knows that 120 ÷ 12 = 10 so he wonders if he will get the same answer if he divides by 3 and then divides by 4 since 3 × 4 = 12.120 ÷ 3 = 40 and 40 ÷ 4 = 10 so it seems to work.He decides to check it out for some other numbers he knows as well.
So dividing by 3 and then dividing by 4 is the same as dividing by 12.
Task 3
What number goes in the box?1) 155 ÷ 5 ÷ 2 = 155 ÷ (2) 114 ÷ 2 ÷ 2 = 114 ÷
7) Marewa knows that 324 ÷ 36 = 9Using this, what is the value ofa) 324 ÷ 18 (b) 324 ÷ 12 (c) 324 ÷ 72d) 324 ÷ 9 (e) 162 ÷ 9 (f) 648 ÷ 36
8) Aloma knows that 240 ÷ 15 = 16Using this, what is the value ofa) 480 ÷ 15 (b) 120 ÷ 15 (c) 240 ÷ 16d) 480 ÷ 32 (e) 240 ÷ 32 (f) 240 ÷ 5
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9) Barnaby knows that 420 ÷ 14 = 30Using this what is the value ofa) 420 ÷ 28 (b) 420 ÷ 7 (c) 210 ÷ 14d) 840 ÷ 14 (e) 420 ÷ 30 (f) 420 ÷ 15
10) Francesca knows that 324 ÷ 54 = 6Using this, what is the value ofa) 324 ÷ 108 (b) 324 ÷ 6 (c) 324 ÷ 27d) 162 ÷ 54 (e) 648 ÷ 54 (f) 648 ÷ 27
Division Strategies
TargetWe are practicing using basic facts to write division
problems.
Exercise 14Place the numbers given in the grid to get an answer as close as possible to the given target number.
1) ÷1, 2 and 3 Target 6
2) ÷2, 3 and 4 Target 7
3) ÷2, 3 and 5 Target 5
4) ÷3, 4 and 5 Target 16
5) ÷4, 5 and 6 Target 8
6) ÷6, 7 and 9 Target 11
7) ÷5, 6 and 8 Target 10
8) ÷6, 7 and 8 Target 9
9) ÷7, 8 and 9 Target 12
10) ÷2, 4 and 6 Target 8
11) ÷1, 3 and 5 Target 6
12) ÷3, 4 and 5 Target 13
Division Strategies
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Number SquaresWe are practising recognising factors of numbers.
Exercise 15Find the missing numbers in each number square. The number at the end of the row is the product of the numbers in that row. The number at the bottom of each column is the product of the numbers in that column.1) 72 Use 1, 2, 3, … 9 once each to fill the 9 spaces.
120
42
70 32 162
2) 5 20 Two of the hidden numbers are 1.Four are chosen from 2, 3, 4, 5, 6 and 7.
2 12
3 30
25 18 16
3) 3 30 Two of the hidden numbers are 1.Four are chosen from 2, 3, 4, 5, 6, 7, 8 and 9.
4 16
2 6
20 9 16
4) 20
12
14
6
4 15 28 12
Seven of the hidden numbers are 1.Five are chosen from 2, 3, 4, 5, 6, 7, 8 and 9.
5) 12
18
30
16
24 10 24 18
Seven of the hidden numbers are 2.The other nine numbers are chosen from 1, 3, 5, 6.
6) 12 14400
14 980
15 450
9 450
900 700 5400 840
Seven of the hidden numbers are 1.Five are multiples of 10 below 100.