# Solution Strategies (Feedback)

## Overview

In Part 2 of this two-part lesson, students review and revise their work on the Self Check task based on feedback from you and their peers and use what they’ve learned to solve similar problems.

# Key Concepts

Students apply their knowledge, review their work, and make revisions based on feedback from you and their peers. This process creates a deeper understanding of the concepts.

# Goals and Learning Objectives

- Use feedback to refine solution strategies on the Self Check task.
- Deepen understanding of percent change.
- Apply deepened understanding to solve similar problems.

# Critique

# Lesson Guide

Return students’ solutions to the Self Check task. If you have not added questions to individual pieces of work, write your list of questions on the board now. Students can then select questions appropriate to their own work.

Give students a few minutes to read over the feedback and think about the questions shown.

SWD: Make sure that all students have access to and can comprehend the information in the rubric so that they can accurately interpret your assessment of their work.

Students with disabilities may benefit from support in understanding the expectations. Allow multiple means of representing the information in the rubric (visual presentation of text, visual supports, etc.).

Create and provide an enhanced version of the rubric with embedded text structures (labels, highlights, words in bold) to cue students to pay closer attention to particular terms.

## Opening

# Critique

Review your work on the Self Check problems from Lesson 17, and think about these questions.

- Does your answer make sense? Can you check that it is correct?
- What would Marcus’s dad's salary be after a 10% pay raise? How could answering this question help you check your answer to the 6% pay raise problem?
- What does it mean to say that an item is “45% off”? What does “50% off” mean?
- Were you able to solve the problem using only one step?

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will revise their work on the Self Check task and then apply their knowledge of percent change to solve similar problems.

## Opening

Apply your knowledge of percent change to solve problems.

# Revise and Extend Your Work

# Lesson Guide

Have students work in pairs to revise their work. Encourage students to incorporate ideas from their partner in their revisions. Then have students work with their partner to solve all the problems and to prepare a presentation.

Support student problem solving.

- Try not to make suggestions that move students toward a particular approach to this task. Instead, ask questions that help students to clarify their thinking.
- If students find it difficult to get started, these questions might be useful:
- What feedback questions were you asked?
- How could you and your partner work together to address one of those feedback questions?

If several students in the class are struggling with the same issue, you could write a relevant question on the board. You might also ask a student who has performed well on a particular part of the task to help a struggling student.

ELL: As with other discussions, consider presenting some of the intervention questions in writing to support ELLs.

SWD: Some students with disabilities may struggle with self-assessment; use your knowledge of student strengths and vulnerabilities to inform and create interventions you will put into place for this period of class time.

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

Identify students who make sense of problems and persevere in solving them as they review and revise their work based on feedback.

**Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.**

Look for students who successfully critique the reasoning of others, both in the task itself and when evaluating the work of peers.

# Interventions

**Student has difficulty getting started.**

- What feedback did you get?
- How can you use the feedback to revise your work?

**Student works unsystematically.**

- How can you check that you addressed all the feedback?

**Student presents his work poorly.**

- Is your work clear?
- Have you given enough explanation?

**Student struggles to calculate percentage change.**

- If the price of a T-shirt increased by $6, describe in words how you could calculate the percentage change. Give an example. Use the same method used in the first problem.

**[common error] Student subtracts percentages directly.**

- Make up the price of an item and check to see if your answer works.

**Student is confused by a lack of parentheses in the calculations.**

- In your problem, what operation would your calculator carry out first?
- Use parentheses to help you organize your calculations.

**Student misinterprets what needs to be included the answer.**

- If you just entered these symbols into your calculator, would you get the correct answer?

# Answers

- Let
*s*= new salary.*s*= 40.85 • 1.06, or*s*= (40.85 • 0.06) + 40.85

Marcus's dad’s new salary is $43.30 per hour.

- Let
*p*= the sale price of the dress*p*= 56.99 • 0.55, or*p*= 56.99 – (56.99 • 0.45)

The sale price of the dress is $31.34.

## Work Time

# Revise and Extend Your Work

Work with your partner to revise your work on the Self Check problems based on the questions from the Opening and feedback from your partner.

- Marcus’s dad earns $40.85 per hour. He has just learned that his company is giving him a 6% pay raise. What will his new salary be?

- Karen’s sister finds a dress that she wants to buy. The regular price of the dress is $56.99, but it is on sale for 45% off. What is the sale price of the dress?

# Price Increase

# Interventions

**Student presents his or her work poorly.**

- Is your work clear?
- Have you given enough explanation?

**Student struggles to calculate percentage change.**

- If the price of a T-shirt increased by $6, describe in words how you could calculate the percent change. Give an example. Use the same method used in the first problem.

**[common error] Student subtracts percentages directly.**

- Make up the price of an item and check to see if your answer works.

**Student is confused by a lack of parentheses in the calculations.**

- In your problem, what operation will the calculator carry out first?
- Use parentheses to help you organize your calculations.

**Student misinterprets what needs to be included the answer.**

- If you just entered these symbols into your calculator, would you get the correct answer?

# Answers

- Let
*p*be the percent change.*p*= [(450 – 350) ÷ 350] • 100, or (450 ÷ 350 – 1) • 100*p*= 28.6% - The percent change is about a 28.6$ increase.

## Work Time

# Price Increase

Using what you have learned, solve this problem.

Last year the price of an item was $350. This year the price is $450. Lena wants to know what the percent change is.

- Write an equation.
- Write the solution as a complete sentence.

# Decrease and Increase

# Interventions

**Student presents his or her work poorly.**

- Is your work clear?
- Have you given enough explanation?

**Student struggles to calculate percentage change.**

- If the price of a T-shirt increased by $6, describe in words how you could calculate the percentage change. Give an example. Use the same method used in the first problem.

**[common error] Student subtracts percentages directly.**

- Make up the price of an item and check to see if your answer works.

**Student is confused by a lack of parentheses in the calculations.**

- In your problem, what operation will the calculator carry out first?
- Use parentheses to help you organize your calculations.

**Student misinterprets what needs to be included the answer.**

- If you just entered these symbols into your calculator, would you get the correct answer?

# Answers

- There is no overall change in the price: Using 1 (we can choose any number) for the cost of the product:

1 • 0.8 • 1.25 = 1

Thus, the final cost is the same as the original: 1. - Explanations will vary.

## Work Time

# Decrease and Increase

During a sale, the owner of a shop decreased all the prices in the shop by 20%. After the sale, the owner increased all the prices by 25%.

- What was the overall percent change of the prices?
- Explain how you know.

# Prepare a Presentation

# Preparing for Ways of Thinking

While students work with their partners, note different student approaches to the task.

- How do students organize their work?
- Do they notice if they have chosen a strategy that does not seem to be productive? If so, what do they do?

# Challenge Problem

- Answers will vary. Check students’ Money Exchange problems.

## Work Time

# Prepare a Presentation

Prepare a presentation about the types of revisions you made to your work.

# Challenge Problem

Using paper and index cards, create your own version of the Money Exchange problem. Be sure to use different amounts of money. If you prefer, you can change the money exchange situation to some other context.

# Make Connections

# Lesson Guide

Organize a whole-class discussion to consider issues arising from students’ revision work. You may not have time to address all these issues, so focus your class’s discussion on the issues that are most important for your students.

# Mathematics

Have students share the types of revisions they made to their work.

Have students whose strategies did not work share, so they can talk about how and when they realized their strategy did not work and what they did about it.

Have students share the questions from you or the computer that they addressed and how they addressed those questions.

Have students ask questions and make observations as they view each other’s work. Discuss the solutions to the additional problems and the Challenge Problem.

## Performance Task

# Ways of Thinking: Make Connections

Take notes about your classmates’ revisions to the Self Check problems and their solutions to the percent problems.

## Hint:

As your classmates present, ask questions such as:

- How could you estimate an answer?
- Why did you make those changes?
- What is the starting value, the percent change, and the final value?
- Does this situation involve a percent increase or decrease?

# Reflect On Your Work

# Lesson Guide

Have each student write a brief reflection before the end of the class. Review the reflections to find out what students still do not understand about percents.

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Something I still do not understand about percents is …**