First Grade Frame of Mind

Purposeful Resources for Curious Learners

The Switcheroo and Rainbow Number Line (Commutative Property)

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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!

Assembly

Here is how I teach all the ways to make five with this page found in a spooky Halloween or non spooky Fall versions of facts 1-10. We first create the page in our notebooks. The students usually come in and color the b/w page during morning work time. This works for me since our math is first thing in the morning.
Together I show them how to cut, fold and paste each piece into their page. Here I am showing the ways to make 5, but students have had some experience with interactive notebooks when we did all the ways to make 1 and then 2, 3, 4 follows. The first one is usually the easiest one to put together and they get a little more challenging each time and this is where you can really see their problem solving skills flourish! I always walk around the room making sure everyone has their pieces glued so they can do the next activity of creating the stories for each way to make five.
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So after creating the page by cutting and pasting, then we make our stories together.
T: "Show 5 pumpkins on the fence and zero off the fence."
S: Students manipulate their own interactive pages to show this.
T: "Repeat after me...5 on the fence"...(Ss repeat)
T: "...zero off the fence"...(Ss repeat)
T: "...5+0=5"...(Ss repeat)
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T: "Show 4 pumpkins on the fence and 1 off the fence (put it under the fence flap)."

S: Students manipulate their own interactive pages to show this.
T: "Repeat after me...4 on the fence"...(Ss repeat)
T: "...1 off the fence"...(Ss repeat)
T: "...4+1=5"...(Ss repeat)
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T: "Show 3 pumpkins on the fence and 2 off the fence (put it under the fence flap)."

S: Students manipulate their own interactive pages to show this.
T: "Repeat after me...3 on the fence"...(Ss repeat)
T: "...2 off the fence"...(Ss repeat)
T: "...3+2=5"...(Ss repeat)

The "Switcheroo"!

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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: "...3 off the fence"...(Ss repeat)
T: "...2+3=5"...(Ss repeat)
S: "It's a switcheroo!"
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T: "Show 1 pumpkin on the fence and 4 off the fence (put it under the fence flap)."

S: Students manipulate their own interactive pages to show this.
T: "Repeat after me...1 on the fence"...(Ss repeat)
T: "...4 off the fence"...(Ss repeat)
T: "...1+4=5"...(Ss repeat)
T: "We just did the switcheroo, 4+1 and now we just showed 1+4!"
**This is when I say that 4+1 and 1+4 is always 5, whether you're in Australia or China or in outer space...all day, every day, last week, next month, 100 years ago or 1 million years ahead. Five is made with 4 and 1 or we can say 1 and 4.

Rainbow Number Line

I refer them to the "rainbow" number line for all the ways to make 5. Since this is a fall theme, we have the cute pumpkins in line making the number line. The number line goes up to ten, but since we are only making all the ways to make 5 that's all we need to use! This is put on their interactive page as well and the students draw their own rainbows on the number line.
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 The last story we do is zero on the fence and 5 off the fence.

4b166d1a-a99c-4c7a-8109-2152bd9a5194All and None

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.

Doubles

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.

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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.

 

Click the pic to get more info about these printables!

Click the pic to get more info about these printables!

 

Check out many more stories to teach the commutative property to you students by clicking the image below!

 

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Find more math interactive notebook activities! Click the image here!

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