We call it the "switcheroo" and use a "rainbow number line" when a+b=b+a. I'm sure purists would rather I call it the commutative property, though I don't like to do that with first graders. Here is a video to show you a student sample of how we learned the commutative property with what I like to call the rainbow on the number line and characters and settings stories in the math interactive notebooks for facts 1-10. These lessons connect to the math common core standard found here at CCSS.MATH.CONTENT.1.OA.A.2.
Here's a video below to show you how this looks in action!
T: "Show 4 pumpkins on the fence and 1 off the fence (put it under the fence flap)."
T: "Show 3 pumpkins on the fence and 2 off the fence (put it under the fence flap)."
T: "Show 2 pumpkins on the fence and 3 off the fence (put it under the fence flap)."
S: Students manipulate their own interactive pages to show this.
T: "Repeat after me...2 on the fence"...(Ss repeat)
T: "Show 1 pumpkin on the fence and 4 off the fence (put it under the fence flap)."
Rainbow Number Line
We talk about the words all and none as well. The number for "none" is always zero. In this story, "all" is the number we are making, which is 5. This is a very good discussion to have with students so they build their problem solving skills.
What about doubles? Well, 5 is not made with a double because it is odd, but all even numbers are made with doubles. If the one in the middle isn't with a rainbow, then it is a double. We just make a smiley face above the doubled number to designate it as the double.
Why Is This Important?
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them--The making of the interactive notebook.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.--I'm taking the time to show the numbers in the story going up or down by 1, and that is solidifying the concept in the students' brains.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.--Why is it that the word "all" in this story must be 5? We talk about it and review that "none" is always zero.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.--The students have created their own interactive page and may revisit it over and over. We will be sure to revisit when we are ready to talk about subtraction and related facts.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.--Not only are we using a number line, we have created another strategy with the "rainbow", a very memorable concept.
CCSS.MATH.PRACTICE.MP6 Attend to precision.--With students repeating each part of the story as it changes, they learn how to tell a story with detail for understanding.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.--Going through all the stories that make a number helps students see the pattern of the rainbow on the number line and why it always works, no matter what!
CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.--As we end up doing all the ways to make all the numbers between 1 and 10, we will notice the same devices used to make sense of the math work for each and every number.
Check out many more stories to teach the commutative property to you students by clicking the image below!