Tables and SharesEach 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. Jars in the Shelf Bheema made a shelf for 30 jars. This is a long shelf with two 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 Children will enjoy building new multiplication tables for themselves instead of only memorising them. How Many Cats? Some of Gayatri's cat s were playing in a box. W hen she tried to count, all she could see were legs. She counted 28 legs. How many cats are there in the box? 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. 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. ✽ ✽If he is at 42, he has taken _______ jumps. Starting from 0, a rabbit jumps 5 steps at a time. ✽ many jumps does he reach 25? ______________ In how ✽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. 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. 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. was left with So he ✽ ________ shells. many necklaces How✽ 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. 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 ✽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? 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 20 70 – 50 So, I have distributed 5 × 10 20 rupees are still left. = 50 rupees. 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. 128 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)472 f )9108 g)232 ÷ 2 h) 2428 129 i) Meera made 204 candles to sell in the market. She makes packets of 6. How many packets will she make? If she packs them in packets of 12, then how many packets will she make? j) On Sport s Day, 1 61 children are in the school playground. They are standing in 7 equal rows . How many children are there in each row ? Story Problems Srishti's grandma is asking her to make problems. Now you look at the other pictures and make questions like Srishti. There are 8 packets of rakhis. Each packet has 6 rakhis in it. There are 10 packets of sugar. number of students.