## Polya's_Steps.png - Section 4: Summary

# Geometric Modeling: Alice's Adventures in Wonderland, Day 2

Lesson 2 of 3

## Objective: SWBAT apply geometric concepts to solve problems.

#### Do Now

*7 min*

Today's lesson again highlights problems written with reference to *Alice’s Adventures in Wonderland* by Lewis Carroll. It is the second of a 3-lesson series reviewing concepts in Geometry and Algebra.

Like yesterday, students are given a slip of paper with a passage from Alice's Adventures in wonderland on it as they enter the room. Once all of the students have arrived, we will read the passage together. Then, the students will answer a question based on information from the reading.

Today's task asks students to find all possible configurations for 12 people sitting at the Mad Hatter's table if opposite sides of the table have the same number of people. When we go over the problem, I will call on different students to give a possible solution. I begin the lesson with this task because it requires skills and thinking needed to solve problems later in the lesson.

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#### Mini-Lesson

*10 min*

In the Mini-Lesson, we review the steps for solving math problems based on George Polya's book, *How to Solve It. *The Common Core Standards require students to apply mathematics to real-world situations and to use problem-based approaches to find solutions. Polya's steps for solving problems relate to the Common Core Mathematical Practices, specifically MP1, MP3, and MP4. Following these steps helps students to solve more complex problems.

After we review these four steps in the context of our current work, we read another passage from *Alice's Adventures in Wonderland*. I show students two problems and ask them what information they need to know in order to solve the problems. Some of the information can be found in the passage and other information is based on prior knowledge. My plan is for the class to solve these two problems together using Polya's steps to guide our work.

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#### Activity

*25 min*

After our collaborative work on the Mini-Lesson Activity, I review the day's task with the students. It is a challenging one, so students will work in groups. Students work to find the fewest or greatest number of doors the hall at the bottom of the rabbit hole could have if it had a volume of 2,700 cubic feet (G.GMG.1, MP4). Using information found in the passage and discussions from the Mini-Lesson, students will first develop a solution then create a poster showing their solution and their problem-solving process. The entire task usually takes my students two lessons, so this activity rolls into Day 3.

As students work, I circulate around the room and answer clarifying questions. I check to see that the students have a plan for solving the problem and are moving towards a correct solution. I listen to hear students discussion and ask guiding questions if they are having difficulty.

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#### Summary

*3 min*

At the end of the lesson, we gather together I have the groups report back on their progress and we discuss next steps for the project. As they make their reports, I add comments that connect back to our brief discussion of Polya's_Steps earlier in the lesson.

- "Oh, it sounds like your group did a great job with Stage 1 of the problem solving process."
- "So, are you confident that you are now ready to carry out your plan?"

#### Resources

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment