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# Equations in Geometry

Lesson 20 of 29

## Objective: Students will be able to apply equations to solve basic geometry problems involving expressions by using properties of geometry learned in previous grades.

## Big Idea: Give context to multi-step equations while also reviewing basic geometry properties of two dimensional figures - it's a two-fer!

*50 minutes*

Today’s activity follows the Bubbles Lesson and is therefore the day the solutions are mixed. Since the solution is better after a few days of sitting, the only portion of the activity completed today is the mixing stage. Mixing the solution should not take much time and the activity today can be completed in cooperative groups without much explanation. Therefore, groups can complete the mixing stage and begin the activity at their own pace.

Prepare students for the entire class period by telling them that the solution works best when allowed to sit for a few days after mixing. Therefore, after creating solutions today, we will be working in our collaborative groups (or partnerships) to complete an application of equations activity. This activity reviews some geometry facts students should already know, but at an 8^{th} grade level as expressions and equations are required to answer the questions. As groups complete mixing solutions, they are to begin working on the geometry activity. (I planned this type of self-guided activity for today on purpose because with hands-on activities students always finish at different times and classroom management can become an issue when most of the room is finished and you are trying to help the slowest groups catch up.

Mixing Solutions Suggestion

It is my suggestion that you pass out solution containers first and ask students to put group names on the lid with a permanent marker or by a post-it note with names written on it. Then allow groups about two minutes to discuss their recipe and make a group decision about quantities. As groups are discussing their homework and making decisions, bring the water around and pour two cups into each group’s container. Next, set out the dawn dish liquid and measuring devices for students to measure their own soap. Allow sections of the room at a time to come up and measure soap. Then rinse the measurement tools and allow the groups to come up again and measure glycerin. It would be very helpful to use a science lab with sinks to do this measuring. If you are choosing to add paint, then set that out last and again in an organized fashion, allow groups to come up and add the paint color of their choice. By only using one ingredient and only a few groups at a time you risk less chaos and more mistakes because of goofy students you can see at all times. Then stir all ingredients (pop cycle sticks work well for this) and put the lids on for storage. Pick a safe place to store these solutions for a few days. If you can get a few bubble blowing sticks great, straws also work find for blowing bubbles.

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#### Beginning the New Activity

*25 min*

After the solutions are safely stored, allow students the rest of the class period to work on Solving Equations in Geometry. As student work, move about the room assessing student entry points into the work and providing feedback that moves their learning forward. As you notice multiple methods of answering the questions ask students to present one particular idea during the wrap-up session. Some of these equations will be challenging for the students because of multi-step equations and others will be difficult because of the fractions. Still other students may struggle to remember their geometry facts. If you have multiple approaches to the problems - great! Ask students from each approach to present and then have the class discuss the merit of each approach (only select correct approaches not incorrect thinking).

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#### Wrapping Up the Lesson

*5 min*

You may have time to hold a wrap up over the first question all four problems but students may not finish all problems in time for a full discussion of the entire page. Any problems not finished or not discussed should be assigned for homework.

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