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# Working Backwards with Formulas - How do I undo a formula?

Lesson 4 of 18

## Objective: Students will be able to determine unknown dimensions when given the area or circumference of a known figure.

## Big Idea: It’s more fun to go in reverse, just ask Mater! This lesson requires students to manipulate formulas to solve for unknown values.

*60 minutes*

#### Launch

*10 min*

**Opener: **As students enter the room, they will immediately begin working on the opener. See my Instructional Strategy - Process for openers clip for more information on how I run openers! This portion of the lesson is a good way to incorporate **mathematical practice 3**, critiquing the reasoning of others.

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended target is, “I can determine unknown dimensions when given the area or circumference of a known figure.”

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#### Explore

*30 min*

**Working Backwards with Formulas Notes: **I will begin the lesson by passing out the notes sheet, and drawing their attention to the first example problem. The first example is a basic formula, and should pull from their prior knowledge of working with formulas in 6^{th} grade. I will ask that students discuss the question with their table groups, and raise their hand to share out only when they can share an equation – not just an answer. During their discussion, I will walk around the room to hear the various conversations taking place. I will take a volunteer to come to the board to work out the first example, and then I will ask that they discuss the next example, following the same procedures they used in the first example. I again will monitor progress by listening in on table conversations, and will ask for another volunteer to work out the second example.

**Table Practice: **Following the second example, I will ask that tables work together to complete the remaining five example exercises – using their knowledge from the first two examples to guide them. I will set the timer for 8 minutes, and then I will call on tables to work and verbally explain the problems at the board. Students will need to pay close attention to precision, **MP 6**, when working backwards with formulas, as the incorrect inverse operation could lead them astray!

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#### Summarize

*20 min*

**Instructional Strategy - How do table challenges work?: **As a way to assess student progress with the concepts learned this week, I will conduct a table challenge using the Smart Clickers. I will not be offering any assistance during this time, giving students an opportunity to grapple with the mathematics, **MP 1**. At the conclusion of the activity I will reward the top scoring group(s). Students will be regrouped for tomorrow’s lesson based on results and teacher observation during the clicker activity. After the clickers, I will summarize the lesson by posing the question, “How can I find unknown side lengths when given the area or circumference of a figure?” We will discuss as a group.

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- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Relationship Between Circumference and Diameter - What is pi?
- LESSON 2: Circumference and Area of Circles
- LESSON 3: Area of Irregular Figures - How do you break up a figure?
- LESSON 4: Working Backwards with Formulas - How do I undo a formula?
- LESSON 5: 2D Figures - Review Time!
- LESSON 6: Composite Figures and Circles Test
- LESSON 7: Intro to 3D Figures and Cross-Sections - What shape do you see?
- LESSON 8: Volume of Prisms - How are base area and volume of a prism related?
- LESSON 9: Volume of Square Pyramids - What is the relationship between and prism and pyramid?
- LESSON 10: Volume of Prisms and Pyramids Fluency Practice
- LESSON 11: Surface Area of a Rectangular Prism - What shapes do you see?
- LESSON 12: Surface Area of a Triangular Prism - What shape is the base?
- LESSON 13: Surface Area of Triangular and Rectangular Prisms Fluency Practice
- LESSON 14: Surface Area of a Square Pyramid - What shapes are the faces?
- LESSON 15: Volume and Surface Area of Prisms and Pyramids Fluency Practice
- LESSON 16: Volume and Surface Area Review
- LESSON 17: 2D and 3D Volume and Area Test
- LESSON 18: Surface Area and Volume Centers -5 Days of Enrichment and/or Remediation