Math Story : Commutative Property Of Addition

The Ice Cream Eating Challenge

“I feel like eating those delicious ice creams on the Ice Cream Land”, says Cirho. “Me too!” say Cirha, Squarho, and Triho. “Let us go and ask Uncle Math to take us there”, suggests Triho. “Perfect idea”, others agree. All the kids immediately leave for Uncle Math’s house.

“Hello, Uncle Math! We want to go to Ice Cream Land and have those delicious ice creams. Please take us there”, says Cirha. “I have a lot of work, children”, he replies. But the kids do not listen to him and force him more. “Alright! Let’s go”, he says.

Soon, they board their spacecraft and land on Ice Cream Land.

“Hurrah! The ice creams look so delicious and yummy! I can’t wait to eat them”, say Cirho and Squarho. They immediately run to grab some ice creams. “Wait! Let us make this more fun. How about an ice cream eating challenge? Whoever wins, will get to take these yummy ice creams back home”, says Uncle Math.

“Wow! That’s amazing. I definitely want to take these ice creams back home”, says Squarho. The kids are delighted. Cirho and Triho team up. Squarho and Cirha team up. They are all set for the ice cream eating competition.

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“Alright! Listen to the rules carefully. There will be 2 rounds. In each round, one of the team members will go and grab one ice cream at a time and give it to the other team member to eat. This will repeat in Round 2 also, but this time the roles will get reversed. That is, in the first round who ate the ice cream will now run and grab the ice cream to give it to another team member”, explains Uncle Math.

“Awesome! This is going to be fun”, says Triho. The kids are all clear. They are ready to begin the challenge.

Soon the competition begins. In Round 1, Cirha and Triho choose to run and grab the ice creams. Squarho and Cirho will be eating them. “Ready, steady, go!” screams Uncle Math, and kids run to grab ice creams.

Cirha has been really quick. She has already got 2 ice creams for Squarho. Triho has got just one ice cream yet. They continue running. Squarho and Cirho continue eating. Uncle Math is keeping track of the score. Who do you think will win this round?

“Time up!” announces Uncle Math. Round 1 ends here. It is time to announce the results of round 1. Uncle Math quickly checks his scoreboard and says, “Squarho has eaten 5 ice creams and Cirho has eaten 3. Clearly, Squarho and Cirha win this round.” Hearing this, Squarho and Cirha jump with joy. Triho and Cirho decide to perform well in the next round.

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Soon Round 2 begins. This time Triho and Cirha are eating, whereas Squarho and Cirho are getting the ice creams. Having got less score in the previous round, Cirho puts his all efforts to be really quick in grabbing the ice creams. Triho is quickly finishing them up.

Both the teams have been performing well. “Time up!” announces Uncle Math. It is time to announce the results of this round. Uncle Math quickly checks his scoreboard and says, “Cirha has eaten 3 ice creams and Triho has eaten 5. Clearly, Triho and Cirho win this round”. Hearing this, Triho and Cirho jump with joy. “Yayy! We won the challenge”, they celebrate.

Squarho gets furious. “We had eaten more ice creams in Round 1. We are the right winners”, he says. “We ate more ice creams in Round 2, we are the winners”, says Cirho. This initiates a fight between them. Both the teams are furious.

“Stop it all of you. I will decide who won the challenge”, says Uncle Math. “After both the rounds, Cirha and Squarho ate 5+3 ice creams, which is 8 ice creams in total. Similarly, Triho and Cirho ate 3+5 ice creams, which is 8 again”, he says.

“What a coincidence. 5+3 gave 8 as the result. When you reversed the order to 3+5, even that gave 8 as the result. Awesome”, says Triho. “Yes! That is because of the order property of addition. Whenever we add two or more numbers, even if we change their orders, the final result will still be the same”, explains Uncle Math.

“Wow! That means we can add numbers in any order. This is such a good trick”, says Cirha. “What about our prizes?” says Cirho. “Haha! Since both the teams have won, all of you can pick your favorite ice creams to take back home”, says Uncle Math. The kids are delighted.

The kids happily pick their favourite ice creams.

It is time to head back home. A day with a challenge, delicious ice creams, and an addition trick. Indeed a delightful day.

We Learnt That…

  • When adding, the numbers can be swapped. The result will still be the same. This is called the Order Property of addition.
  • For example: 3+5 = 5+3 = 8
  • The properties of addition help us calculate addition problems faster.

Let’s Discuss

  • Where were we going today?
  • What type of challenge did Uncle Math keep for us?
  • Who won the challenge? How?
  • What is the order property of addition? Explain with an example.

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