11 Tables and Shares
Shyama's Garden
Shyama has planted sunflower,
rose and marigold plants in her
garden. She has planted them in
three flower-beds. Her garden
looks like this.
See, how I planted
18 plants in each
flower bed!
Each flower- bed has a different arrangement.
See how the roses are planted.
18 = 6 × 3 So there are 6 rows with 3 plants each.
What are the ways in which the sunflower and marigold are
planted?
18 = _____ × ______ So there is ___ row with ___ plants.
18 = _____ × ______ So there are ___ rows with ___ plants each.
You too can make your own garden. Draw a garden, showing
flower-beds with 48 plants. Each row should have the same
number of plants.
The concept of multiplication can be related to the arrangement of things in an array. Some
other problems, based on contexts like the arrangement of chairs, children in the school
assembly, etc., can also be discussed.
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Jars in the Shelf
Bheema made a shelf for 30 jars. This is a long shelf with two
rows. Each row has the same number of jars.
Can you think of other ways to make a shelf to keep 30 jars?
✽ Draw a shelf. Show how many jars you will keep in each
row. How many rows are there?
Have your friends drawn it in different ways?
Easy Tricks
I do not know the
multiplication table
of 7.
I know the tables till 5 but
there is an easy trick.
I can make the table of 7 with
the tables of 2 and 5.
Bunty
Guddu
Children will enjoy building new multiplication tables for themselves instead of only
memorising them.
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Table of 2 4×2 10×2
3×2 5×2 6×2 9×2
2×2 8 8×2 20
1×2 6 10 7×2 18
4 12 16
2 14
Table of 5 4×5 10×5
3×5 5×5 9×5
2×5 20 6×5 8×5 50
1×5
10 15 25 7×5 45
30 40
5 35
Table of 7 28 70
14 21 35 63
42 56
7 49
See, how I added the
two numbers in the
yellow boxes to get
the table of 7.
Aha... it is easy.
I can also make the
table of 7 with the
tables of 4 and 3.
Help Bunty to make the table of 7, using tables of 4 and 3.
Table of 4 4×4 10×4
3×4 5×4 6×4 9×4
2×4 8×4
1×4 8 7×4
4
Table of 3 4×3 10×3
3×3 5×3 6×3 9×3
2×3 8×3
1×3 7×3
6
3
Table of 7
7
Which two tables will you use for writing the table of 12?
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How Many Cats?
Some of Gayatri's cats were playing in a box. When she tried to
count, all she could see were legs. She counted 28 legs. How
many cats are there in the box?
8 legs mean 2 cats.
12 legs mean _____ cats.
How many legs? 4 8 12
How many cats? 1 2
So 28 legs mean __________ cats.
✽ Billo has kept his chickens in a box. He counted 28 legs. How
many chickens are there?
✽ Leela has not gone to school for 21 days. For how many weeks
was she away from school?
Encourage children to fill in the table and also proceed towards making generalisations. For
example, they should be able to see that 48 legs would mean there are 12 cats, or
vice versa. In fact, this forms the foundation for algebraic thinking in later years.
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Jumping Animals
Do you remember the jumping animals of Class III?
A frog jumps 3 steps at a time starting from 0.
✽ Count the jumps he takes to reach 27.
So, he has taken 27 ÷ 3 = _______ jumps.
43 42
44
41
45
40 1
46 39 25 10 9 2 0
26 24
47 11 8 3
38 37 27
48 36 23 1 20 19
60 59 58 49 28 22 2 12 7 4
18 6 5
57 50 35 13
29
51 17
56 34 30 14
52 16 15
55 31
54 53 33 32
66 67
✽ He has taken _________ jumps, if he is at 36.
✽ If he is at 42, he has taken _______ jumps.
Starting from 0, a rabbit jumps 5 steps at a time.
✽ In how many jumps does he reach 25? ______________
✽ He reaches _________ after taking 8 jumps.
✽ He needs _________ jumps to reach 55.
Practice Time
1) 28 ÷ 2 = 2) 56 ÷ 7 =
3) 48 ÷ 4 = 4) 66 ÷ 6 =
5) 96 ÷ 8 = 6) 110 ÷ 10 =
Children have done similar kinds of exercises for multiplication and division in Class III.
Refer to pages 173-176, Math-Magic Class III, NCERT.
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Sea Shells
Dhruv lives near the sea. He thought of making necklaces for his
three friends. He looked for sea-shells the whole day. He collected
112 sea-shells by evening. Now he had many different colourful
and shiny shells.
I will make a necklace of
28 shells. Will these shells
be enough to make necklaces
for all my friends?
He took 28 shells for one necklace.
112 – 28 = 84
Now he was left with 84 shells. Again he took 28 more shells for
the second necklace.
✽ How many shells are left now? ________
Then he took shells for the third necklace.
✽ So he was left with ________ shells.
✽ How many necklaces can Dhruv make from 112 shells?
________
✽ Are the shells enough for making necklaces for all his friends?
________
Try these
A) Kannu made a necklace of 17 sea-shells. How many such
necklaces can be made using 100 sea-shells?
Encourage children to solve questions based on division with large numbers, for which they
do not know multiplication tables, using repeated subtraction. More problems based on real
life contexts can be given.
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B) One carton can hold 85 soap bars. Shally wants to pack
338 soap bars. How many cartons does she need for packing
all of them?
C) Manpreet wants 1500 sacks of cement for making a house.
A truck carries 250 sacks at a time. How many trips will the
truck make?
A driver charges Rs 500 for a trip. How much will Manpreet
pay the driver for all the trips?
Gangu's Sweets
Gangu is making sweets for Id. He has made a tray of 80 laddoos.
Please pack 4
laddoos in a box.
I need 23 small
boxes.
Rabiya
✽ Are the sweets in the tray enough to pack 23 small boxes?
____________
✽ How many more sweets are needed? ______________
For solving this problem, encourage children to use their own strategies — of making groups
in the tray, using multiplication to do division or repeated subtraction, etc.
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✽ Gangu also has a bigger box in which he packs 12 laddoos.
How many boxes does he need for packing 60 laddoos?
Practice Time
1) Neelu brought 15 storybooks to her class. Today 45 students
are present. How many children will need to share one book?
2) A family of 8 people needs 60 kg wheat for a month. How
much wheat does this family need for a week?
3) Razia wants change for Rs 500.
How many notes will she get if she wants in return —
(a) All 100 rupee notes? _________________
(b) All 50 rupee notes? _________________
(c) All 20 rupee notes? _________________
(d) All 5 rupee notes? _________________
✽ You have to distribute 72 tomatoes equally in 3 baskets. How
many tomatoes will there be in each?
✽ There are 350 bricks in a hand-cart. Binod found the weight of
a brick to be 2 kg. What will be the weight of all the bricks?
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Children and their Grandfather
Rashi, Seema, Mridul, Rohit and Lokesh asked their grandfather
to give them money for the Fair.
I have 70 rupees in my pocket.
Tell me how to share money
equally among all of you . If you
are right, you get this money!
One method
Rashi and Seema thought for a while and said — We know how to
do 70 ÷ 5.
Seema starts writing and says —
10 First I give Rs 10 to each one of us.
5 70
– 50 So, I have distributed 5 × 10 = 50 rupees.
20 20 rupees are still left.
Rashi completes it like this. She says — 10 + 4
5 70
– 50
I give 4 rupees more to each. So I have 20
distributed 20 rupees. – 20
Now nothing is left. And all the money is divided 0
equally.
So, each gets 10 + 4 = 14 rupees.
This method is actually about how children divide when they distribute some objects
repeatedly. In this case, they might first give Rs 10 each to five people and then next
distribute the remaining money in the second round. They could as well distribute it by first
giving Rs 5 to each. Children can, thus, use any way to complete the process of division. This
is the beauty of this method.
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Another Method
Mridul and Lokesh are trying 70 ÷ 5 in a different way.
Lokesh writes —
First, I give Rs 5 to each. 5+6
5 70
I have distributed 5 × 5 = 25 rupees. – 25
Next, I give Rs 6 more to every one. 45
I have distributed 30 rupees more. – 30
Now I am left with ________ rupees. ?
How will Lokesh distribute the rest of the money? Complete it.
So, each child gets 5 + 6 + ________ = ________ rupees.
Check your answer!
Multiply your answer by 5 and
see if you get 70. Is your
answer correct?
Your Method
✽ Now use your own method to divide Rs 70 equally among
5 people. If you want you can start by giving Rs 2 to each.
Or you can even start with Rs 11 to each.
Can you start with
Rs 15 to each?
Try Doing These
a) 5 65 b) 84 ÷ 2 c) 3 69 d) 90 ÷ 6
e) 4 72 f ) 9 108 g) 232 ÷ 2 h) 2 428
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