At this point, you have already introduced the concept of solving one-step equations using algebra tiles, clothes hangers, or balance scales. In this lesson, we’ll review using a clothes hanger to solve for a missing variable. Then, we’ll talk more formally about inverse operations and how we can use them to solve one-step equations. You can expect this lesson with ByteLearn practice to take one `45`-minute class period.
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Start class with a review of a clothes hanger example. Ask students what the value of `x` is. Allow students to work independently or with a partner before discussing as a class.
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Ask for volunteers for students who not only got the answer but can explain how they worked it out. We’re looking for explanations that say things like: we need to remove two circles from the left side, so we should remove them from the right side too so the hanger stays balanced. The key piece that you want to drive home is that what is done to one side of the hanger must be done to the other side as well.
Explain to students that inverse operations are operations that “undo” each other. They’re opposites. Allow them some time to jot down this friendly graphic in their notebook, which will help them to remember that addition and subtraction are inverse operations.
Start with this equation which is similar to what the clothes hanger could represent. Explain that we want to manipulate the equation so that `x` is the only thing on the left of the equal sign. Ask students what is happening to the `x`. They should respond that `6` is being added to `x`. Then you can ask, “what operation would allow us to “undo” the plus `6`?”. Since we’ve already discussed inverse operations, students should recognize that we can subtract `6`. Show students how we need to subtract `6` on both sides to keep the equation balanced.
Approach the next example in a similar way. Students should recognize that since `11` is being subtracted from `x`, they need to add `11` to both sides of the equation.
Now that students are more familiar with inverse operations and how they are used to solve addition and subtraction equations, introduce multiplication and division as inverse operations as well. Explain that just like addition and subtraction, these operations “undo” one another. Have students add this visual to their notes.
For example `3`, ask students what operation is implied when a number is written right in front of a variable. Hopefully students will recognize that it means `4` is being multiplied by `x`. So in order to undo that to isolate `x`, we need to divide both sides by `4`.
For the last type of example, ask students if they remember that operation a fraction represents. If students don’t immediately know, you can write `15/5` as a fraction and ask them what `15` over `5` equals. Students should recognize that it equals `3`, since the fraction bar represents the same thing as a division sign. Once it’s recognized that `x` is being divided by `3` in this example, students will be able to multiply by `3` on both sides to solve.
The slideshow contains a few more examples to do as a class. Give students time to try each one on their own, then go over them together. You can remind students to refer to their notes about inverse operations.
Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!
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