In this lesson, we’ll introduce the concept of modeling equations with clothes hangers for `6`th graders. We use clothes hangers to make connections with equations. These diagrams are helpful for students to see a representation of a relationship between two different quantities. In later concepts and future grade levels, students can use clothes hanger diagrams to develop a strategy for modeling, writing, and solving more complex equations. You can expect this lesson to take one `45`-minute class period.
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Students will be able to model equations with clothes hangers.
Start the students off by having them complete a notice and wonder warm-up. Display the first slide of the clothes hanger diagram on your board:
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Give students a few minutes to jot down some notice and wonders. Notice and wonders allow students to write down anything they see or may have questions about. Any student is able to do this activity!
After students have finished up, go over the noticings and wonderings by listing what students say on the board. This way all students can see what others have written and can write that down as well.
Now we can discuss some deeper questions. Ask students these questions:
Tell students that they can keep crossing off circles until there are only circles on the one side of the hanger. Display slide `5`.
Ask students what one “`x`” is equal to.
Have students do one more similar example on slide `6`.
Then show the example with the total numbers in squares on slide `7`.
Ask students how we could balance the hanger to have `x` by itself here. Ask students the following questions:
This example will prepare students for writing and solving one-step addition equations.
Show a hanger diagram that represents a one-step multiplication equation. Display slide `8`.
Ask students if you can take off an `x` from both sides? Why? Why not? Then ask students if they can take a number from both sides of the hanger? Why? Why not? Some students may think you can. Explain why this does not work.
Display slide `9` for students to see. Tell students that we are going to find what one `x` is equal to.
Tell students that since there are three `x`’s, they will make three equal groups. Ask students how many squares are equal to one circle.
There are two more examples on slides `10` and `11` for you to do as a class.
Work together to express the clothes hanger as an equation. Display slide `12` for students to see.
Show students how both sides of the hanger can be expressed. Practice expressing the clothes hanger as an equation with the next two examples on slides `13` and `14`.
Look at one of the addition equations we already worked on and do the same things to the expression that you did to the hanger. Display slide `15`.
We crossed off two circles from both sides. Ask students what operation this represents. Students should say subtraction. Remind students that taking away, or crossing off is the same thing as subtracting or finding the difference.
Ask students what to do to find the value of `x` when there are addition equations.
Display slide `16` to show how to solve.
Subtracting `2` from both sides gives us `x = 3`. When we crossed off two circles from both sides, we also had three circles left over.
Look at one of the multiplication equations we already worked on and do the same things to the expression that you did to the hanger. Display slide `17`.
We grouped together a circle with two squares. Ask students what operation this represents. Students should say division. Remind students that by making equal groups, we are dividing.
Ask students what to do to find the value of `x` when there are multiplication equations.
Display slide `18` to show how to solve.
Using the strategy of modeling equations with clothes hangers allows students to visualize what is on both sides of the equal side. Students will then be able to solve equations using the clothes hanger.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of modeling equations with clothes hangers activities. Check out the online practice and assign to your students for classwork and/or homework!
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