Empty Layer. Show Empty Layer. Empty Layer. Empty Layer. Empty Layer. Empty Layer. Empty Layer. Empty Layer. Empty Layer. Empty Layer. 34 teachers like this lesson Print LessonSWBAT use the commutative property of addition to solve addition problems. My students are learning addition strategies. I want my little ones to learn they numbers can change order and be added and the result will be the same. It's the Commutative Property! We all know that our students are unique and learn in their own way. We need to teach lessons in multiple ways so that students have lots of opportunities to access material. The same goes for math lessons. I like to look at it as the beginning stages of creating an engineer. Engineers solve problems through different means, but we as teachers supply the different possible paths to pick from to solve a problem. Through perseverance with continued practice they will attempt different strategies and master the skill (MP1). Strategies we have focused on are drawing pictures, counting with our fingers, counting on, and using objects. I will have them do a quick review by asking: Class, we have been learning several ways to solve an addition problem, and I would like to create a list on the chalkboard of all the ways to solve. What methods have we used? If any of our methods are left off, I will remind them of the ones we have used. The commutative property teaches them numbers can be added in any order and still get to the same sum. I describe it to my kids that numbers can be flipped into a different order and they will help me discover that we get the same answer even if the numbers have changed position. This strategy is very much a focus on the structure of algebraic thinking. I want them to notice the position of the numbers and how the numbers flipping doesn't change the sum. I will bring my kids to a gathering spot in front of our chalk board and write the following problem on the board: 2+3= I will ask them to help me solve it; then I will ask them, "What if I change it to 3+2=? ...", and I will write this on the board. I expect some of my kids to already know the answer because some of them have their facts memorized, but others will not, so we will solve this problem also. I will point at the answers for both and ask an open ended question: "What do you notice?" My goal is to guide them towards understanding that the answer stayed the same, the addends stayed the same, and the addends just changed positions. After this is achieved, I will write "commutative property" on the board and have them echo the word after me. Then I will share the definition of the commutative property. I will ask them to help me make a list of what strategies have we learned so far in adding and add commutative property to the list. Watch as one student explained the commutative property. Student Mistake I wanted to provide a random method for students to create math problems for their practice. I designed the math sheet for students to add numbers they rolled using dice. They will roll a dice, write the number, then roll again and add that number to the first. When this is complete, the problem will be flipped, written down, and solved. My goal is for them to see the same answer is achieved even if the numbers are in a different position. If they know the answer to the first problem, it can help them reach the same answer for the second problem created from the same numbers. We will do the first two together, and then they are on their own. Watch this video of getting them started. This student is using the Commutative Property. I realized the possibility could arise that the students would roll numbers that could equal 11 or 12 and many of my students are not ready for that at this time. While the CCSS expects a rigorous understanding of addition and subtraction with 2-digit products by the end of the year, I want to build up to that by starting with lower numbers. Once the students have a good grasp of properties with the lower numbers, we can move on to more challenging ones. I chose to not pass out dice for my students to roll; instead, I rolled, and we created the problems together. Then they had to use the strategy to solve their new problems. You can differentiate the lesson by allowing higher students to roll a dice on their own and help your lower students with creating their own problems. I called students back to the rug, and I put a simple problem on the board: 6+3=9. I then asked students to turn to their partners and explain what answer you would get if you changed the problem to: 3+6=? After a few moments of partner talk, I asked a few students to share their thinking with the group. We discussed that the sum would not change, and I asked students to tell me the name of the property that describes this idea in unison. They all called out, "commutative property!"
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division. Let’s see.  The above examples clearly show that the commutative property holds true for addition and multiplication but not for subtraction and division. So, if we swap the position of numbers in subtraction or division statements, it changes the entire problem. So, mathematically commutative property for addition and multiplication looks like this: Commutative Property of Addition:a + b = b + a; where a and b are any 2 whole numbers Commutative Property of Multiplication:a × b = b × a; where a and b are any 2 nonzero whole numbers Use Cases of Commutative Property
Even if both have different numbers of apples and peaches, they have an equal number of fruits, because 2 + 6 = 6 + 2.
Even if both have different numbers of bun packs with each having a different number of buns in them, they both bought an equal number of buns, because 3 × 4 = 4 × 3. Solved Examples on Commutative PropertyExample 1: Fill in the missing numbers using the commutative property.
Solution:
Example 2: Use 14 × 15 = 210, to find 15 × 14. Solution: As per commutative property of multiplication, 15 × 14 = 14 × 15. Since, 14 × 15 = 210, so, 15 × 14 also equals 210. Example 3: Use 827 + 389 = 1,216 to find 389 + 827. Solution: As per commutative property of addition, 827 + 389 = 389 + 827. Since, 827 + 389 = 1,216, so, 389 + 827 also equals 1,216. Example 4: Use the commutative property of addition to write the equation, 3 + 5 + 9 = 17, in a different sequence of the addends. Solution: 3 + 9 + 5 = 17 (because 5 + 9 = 9 + 5) 5 + 3 + 9 = 17 (because 3 + 5 = 5 + 3) 5 + 9 + 3 = 17 (because 3 + 9 = 9 + 3) Similarly, we can rearrange the addends and write: 9 + 3 + 5 = 17 9 + 5 + 3 = 17 Example 4: Ben bought 3 packets of 6 pens each. Mia bought 6 packets of 3 pens each. Did they buy an equal number of pens or not? Solution: Ben bought 3 packets of 6 pens each. So, the total number of pens that Ben bought = 3 × 6 Mia bought 6 packets of 3 pens each. So, the total number of pens that Ben bought = 6 × 3 By the commutative property of multiplication, 3 × 6 = 6 × 3. So, both Ben and Mia bought an equal number of pens. Example 5: Lisa has 78 red and 6 blue marbles. Beth has 6 packets of 78 marbles each. Do they have an equal number of marbles? Solution: Since Lisa has 78 red and 6 blue marbles. So, the total number of marbles with Lisa = 78 + 6 Beth has 6 packets of 78 marbles each. So, the total number of marbles with Beth = 6 × 78 Clearly, adding and multiplying two numbers gives different results. (Except 2 + 2 and 2 × 2. That is, 78 + 6 ≠ 6 × 78 So, Lisa and Beth don’t have an equal number of marbles. Practice ProblemsAttend this Quiz & Test your knowledge. Correct answer is: 8 + 5 = 5 + 8 Correct answer is: 7 × 3 = 3 × 7 Correct answer is: 15 × 3 Correct answer is: 4, 5 Frequently Asked Questions
Can you apply the commutative property of addition/multiplication to 3 numbers?
Yes. By definition, commutative property is applied on 2 numbers, but the result remains the same for 3 numbers as well. This is because we can apply this property on two numbers out of 3 in various combinations.
Which operations do not follow commutative property?
Commutative property cannot be applied to subtraction and division.
What is the associative property of addition (or multiplication)?
This property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands). That is, (a + b) + c = a + (b + c)
For which all operations does the associative property hold true?
The Associative property holds true for addition and multiplication.
What is the distributive property of multiplication?
By the distributive property of multiplication over addition, we mean that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. That is, a × (b + c) = (a × b) + (a × c) where a, b, and c are whole numbers. |
Why is it important for students to understand and be able to apply the commutative property?
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