Math Story : Commutative property of multiplication

Visit To The Juice Factory

“The visit is going to be amazing. I am super excited”, says Cirha. The kids are curious as Uncle Math is taking them for a factory visit. Wow! Let us join them in their factory visit too. Come on!

“This is the biggest juice factory in Samper town. They manufacture and pack the juice cans in smaller, medium and larger packets for the convenience of the buyers. Children, are you ready?” says Uncle Math. The kids are exhilarated and cannot wait to enter the factory.

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The factory is huge and has many automatic machines. There are also three different sections for small, medium and large packaging. First, the kids enter the small section to understand the manufacturing process.

“Wow! First, the empty cans are placed under the machine. Later they are filled with juice, and finally, they are packed in trays. So quick and smooth”, says Triho. They explore the machines and suddenly hear a strange voice.

“Hello, children. I am Bob, the manager of this factory. It looks like you are enjoying the visit. Come on, let us make it more fun. How about a questionnaire? If you answer all the questions right, I shall gift you juice cans”, says the manager. A return gift? Of course, the kids are ready for the questionnaire.

Showing a small tray of cans, Bob asks, “How many total cans are there in this tray?” Wanting to have the juice soon, Cirho immediately answers without even looking at the cans properly. He says, “6”. Cirha loses her calm and asks him to keep quiet. He dislikes this behaviour of Cirha.

Triho observes the tray and says, “There are 2 cans in each row and there are 5 such rows. So the smaller tray has 10 cans.” Do you think he is right?

“Correct answer!” says Bob. “Let us move ahead. Here is your next tray. How many cans are in this tray?” he questions. Cirha looks delighted. Has she got the answer? Does her answer match your answer? Let us find out.

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“So there are 5 cans in each row and there are 2 such rows. So to find the total cans in this tray we need to multiply 5 and 2. So the answer is 10 again”, she says.

“Hey the previous tray also had 10 cans and this also has 10 cans. But their arrangement looks so different. What a coincidence”, says Squarho. He is a good observer indeed. “Haha! So smart”, say Uncle Math and Bob.

“This is just the same tray. I flipped it horizontally to confuse you”, says Bob. “Exactly! Even when the tray was flipped, the total number of cans in it remained the same. Just the numbers 5 & 2 got flipped. So we got the same answer 10. Children, what does this mean?” questions Uncle Math.

“Oh, I know! That means when we change the order of numbers in the multiplication, the answer will still be the same. Initially, we multiplied 2✖5 and later 5✖2. The digits are the same here, just the order has changed”, says Cirho. He is a genius too, right?

Uncle Math agrees with him and pats his back. “Exactly. It is called Order Property of Multiplication. Just like how the order of numbers does not matter when we add the digits, similarly, the order of numbers does not matter when we multiply the digits too,” he says.

Cirha is shocked to see Cirho answering so well. She feels guilty for her rude behaviour and apologizes to him. But Cirho has a big heart. He immediately forgives her.

“Now do we get the juice?” says Cirho as they have answered all the questions correctly. “Not yet! Here is your bumper question,” says Bob as he smiles and takes them to the larger packets area. Is he going to give them a difficult question now? Will the kids get the juice?

“Haww! This is so big!” says Squarho. There are 20 rows of cans in this large tray, and each row has 2 cans. “To find the total cans we need to multiply 2 and 20. Oh no! That means we need to add 2 twenty times. This will be time taking”, says Squarho. He looks disappointed. But Triho looks happy.

“Haha! Squarho, why add twenty times. Let us flip the numbers. This will make the multiplication as  2✖ 20. So we will have to add 20 twice”, says Triho. Squarho smiles now as he realizes that they can use the order property here.

“There are 40 cans in this large tray”, says Triho. Bob is impressed. He loves the effort and teamwork. “You guys are geniuses! You deserve more cans now”, he says. Cirho and Squarho are elated as they will get more cans now.

Bob gives 3 juice cans to each of them. The kids are joyful. Such a wonderful day it was. But wait, can you find the total juice cans 4 of them got in total?

We Learnt That…

  • When we multiply two or more numbers, the order does not matter. 
  • The order property of multiplication states that the answer remains the same when multiplying numbers, even if the order of numbers is changed.
  • Never underestimate anybody’s potential.

Let’s Discuss

  • Where were we going today?
  • Explain the order property of multiplication with an example. 
  • Cirha was mean when Cirho could not answer. Was she right? Why or why not?

Please refer this guide by Fun2Do Labs for teaching properties of multiplication to kids :