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.

Sunflower, rose and marigold plants.

A girl.

See, how I planted 18 plants in each flower bed!

Each flower- bed has a different arrangement.

See how the roses are planted.

18 = 6x3 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.

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.

30 jars kept in 2 rows.

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

A boy named Bunty.
I do not know the multiplication table of 7.

A girl named Guddu.

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.

Children will enjoy building new multiplication tables for themselves instead of only memorising them.

Table of 2

Table of 2 and table of 5 written on stones .

Table of 7

Table of 7 written on different blocks.

Guddu describing table of 7.

See, how I added the two numbers in the yellow boxes to get the table of 7.

Bunty talking about table of 7 made from table of 4 and 3.

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

Table of 4 written on stones.

Table of 3

Table of 3 written on stones.

Table of 7

Space to write table of 7.

Which two tables will you use for writing the table of 12?

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?

28 legs of cats are visible from a box.

A girl calculating the number of cats.

8 legs mean 2 cats.

12 legs mean _____ cats.

How many legs?

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.

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.

Counting from 0 to 67 written on a snake.

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

28 ÷ 2 =
56 ÷ 7 =
48 ÷ 4 =
66 ÷ 6 =
96 ÷ 8 =
110 ÷ 10 =

Children have done similar kinds of exercises for multiplication and division in Class III. Referto pages 173-176, Math-Magic Class III, NCERT.

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.

A boy is collecting sea-shells besides a sea.

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

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.

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?
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 ₹ 500 for a trip. How much will Manpreet pay the driver for all the trips?

Gangu's Sweets

Gangu is making sweets for Eid. He has made a tray of 80 laddoos.

A man is cooking laddoos.

Rabiya : Please pack 4 laddoos in a box. I need 23 small boxes.

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.

Gangu also has a bigger box in which he packs 12 laddoos. How many boxes does he need for packing 60 laddoos?

Practice Time

Neelu brought 15 storybooks to her class. Today 45 students are present. How many children will need to share one book?
A family of 8 people needs 60 kg wheat for a month. How much wheat does this family need for a week?
Razia wants change for ₹ 500.

A 500 rupee note.

Notes of Rupees 100, 50 ,20 and 5.

How many notes will she get if she wants in return-

All 100 rupee notes?______________________
All 50 rupee notes?_____________________
All 20 rupee notes?_____________________
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?

Children and their Grandfather

Rashi, Seema, Mridul, Rohit and Lokesh asked their grandfather to give them money for the Fair.

An old man.

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 —

Dividing 70 by 5.

First I give ₹ 10 to each one of us.

So, I have distributed 5 x 10 = 50 rupees.

20 rupees are still left.

Dividing 70 by 5.

Rashi completes it like this. She says ---

I give 4 rupees more to each. So I have distributed 20 rupees.

Now nothing is left. And all the money is divided 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 ₹ 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 ₹ 5 to each. Children can, thus, use any way to complete the process of division. This is the beauty of this method.

Another Method

Two children discussing the method of dividing 70 by 5. Mridul and Lokesh are trying 70 ÷ 5 in a different way.

Lokesh writes—

First, I give ₹ 5 to each.

I have distributed 5 × 5 = 25 rupees.

Next, I give ₹ 6 more to every one.

I have distributed 30 rupees more.

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 ₹ 70 equally among 5 people. If you want you can start by giving ₹ 2 to each. Or you can even start with ₹ 11 to each.