Application Exercise 4.1: Observing and Responding to Student Thinking

Application Exercise 4.1: Observing and Responding to Student Thinking

Click the link below to watch an eighth-grade student solve the problem, “The dress was originally priced at $90. If the sale price is 25 percent off, how much will it cost on sale?” and then answer the questions that follow.

Percent Increase and Decrease : https://mediaplayer.pearsoncmg.com/assets/chapter_4_p_63_jw_gr7

Questions

Part 1

This eighth-grade student’s initial entry point into solving this problem involved using an algebraic approach (writing a proportion and solving for the unknown, or x). Compare this strategy with your initial strategy. Consider, how might one think about this problem more conceptually.

Part 2. Describe the student’s initial error related to his use of a proportion.

Part 3. In this case, how did using a cross-multiplication approach result in an incorrect solution?

Part 4. How did prompting the student to show a solution involving the use of a diagram, or visual model, enhance his understanding/explanation?

Application Exercise 4.2: A Three-Phase Lesson Format

Apply your understanding of lesson planning that was presented in this chapter.

Question

Part 1:What are the advantages of using a three-phase lesson plan model? How does it compare to how you learned mathematics?

Part 2: You are going to plan a three-phase lesson on partitioning fractions for second grade. Describe what you will do before actually planning the lesson.

Part 3: A teacher finds a task for partitioning fractions: “Using dotty grid paper, draw 4 by 4 squares. Then draw lines to show fourths in as many ways as you can.” How might the teacher develop a three-phase lesson around this task?