Subject:
Numbers and Operations
Material Type:
Lesson Plan
Level:
Middle School
Grade:
6
Provider:
Pearson
Tags:
6th Grade Mathematics, Absolute Value, Coordinate Plane, Graphing Points, Integers
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Text/HTML

Education Standards (2)

Peer Review and Revise

Peer Review and Revise

Lesson Overview

Students revise their work on the assessment task based on feedback from the teacher and their peers.

Key Concepts

Concepts from previous lessons are integrated into this assessment task: the opposite of a number, integers, absolute value, and graphing points on the coordinate plane. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.

Goals and Learning Objectives

  • Apply knowledge of the opposite of a number, integers, absolute value, and graphing points on the coordinate plane to solve problems.
  • Track and review a choice of strategy when problem solving.

Task 1: Critique

Lesson Guide

Return students’ solutions to the Self Check. 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.

Have students read over the feedback they received and give them a few minutes to think about it.

Mathematical Practices

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

  • Discuss what it means to persevere. Give students an example of when you persevered and succeeded, or have volunteers talk about times when they persevered.
  • Explain that some math problems are hard. Students may not be able to find a solution easily. Encourage students to stick with a problem even if it is difficult. Students may need to revise their work or start again with a new strategy. Tell students not to give up! Explain that making sense of problems and persevering in solving them is part of the math process. Ask students to try this mathematical practice as they revise their work today.

Opening

Critique

Review your work from the Self Check and think about these questions.

  • What is the minimum number of vertices your figure or design needs to have one vertex in each quadrant?
  • What do you know about numbers that have equal absolute values?
  • How do you know your figure or design meets all of the criteria?
  • Does your explanation show how your figure or design meets each of the criteria?
  • Is your work neat and labeled clearly?
  • Can you make a different figure or design that meets the same criteria?

Task 2: Math Mission

Lesson Guide

Discuss the Math Mission. Students will create a figure or design on the coordinate plane that meets certain criteria.

Opening

Create a figure or design on the coordinate plane that meets certain criteria.

Task 3: Revise Your Work

Lesson Guide

Put students in pairs to revise their work. Encourage students to incorporate ideas from their partner in their work.

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 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.

SWD: As you confer with struggling students, try to move them toward efficiency. Scaffold their learning by starting with their strategy and another more efficient strategy. Help them to find the relationship between the two. Have students attempt the more efficient strategy the next time they are finding coordinates of a vertex or solving a reflection problem.

Interventions

Student has difficulty getting started.

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

Student works unsystematically.

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

Student presents his or her work poorly.

  • Is your work clear?
  • Do you have an explanation for how you met the criteria?

Student has a correct solution.

  • Can you find a different way to solve the problem?

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 the feedback.

Possible Answers

  1. Sample answer:
  2. Explanations will vary.

Work Time

Revise Your Work

Work with your partner to revise your work based on the feedback that both of you got on this problem.

  1. Create a figure or design on the coordinate plane that satisfies the criteria below.
    • At least one vertex has coordinates that include a number and its opposite.
    • At least one vertex has coordinates that are both nonintegers.
    • At least one vertex is in each quadrant.
    • At least two vertices have x-coordinates that have equal absolute values.
    • At least two vertices have y-coordinates that have equal absolute values.
  2. Label each vertex with its ordered pair, and explain how your figure or design meets the criteria.

Use the Coordinate Plane Plotter interactive if you find it to be helpful.

INTERACTIVE: Coordinate Plane Plotter

  • What is a noninteger?
  • What is the minimum number of vertices your design needs to have one vertex in each quadrant?
  • What do you know about numbers that all have the same absolute values?
  • How do you know your design meets all of the criteria?
  • Is your work neat and labeled clearly?
  • Can you make a different figure or design that meets the same criteria?

Task 4: Make Sense and Persevere

Task 4: Make Sense and Persevere

Mathematical Practices in Action

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

Have students watch the video. The video shows Jan and Carlos engaged in Mathematical Practice 1: Make sense of problems and persevere in solving them.

Have students talk about the discussion questions. In the discussion, elicit that Carlos and Jan went through the criteria one by one to make sense of the problem. Also bring out in the discussion that when Carlos found that his figure did not meet one of the criteria, he didn’t give up. He and Jan changed the figure so that it would meet that criteria. And at the end, Jan and Carlos ran through the criteria one by one to make sure they had met each one.

Have students talk about what it was like for them to solve this problem and ask them to talk about if they encountered anything like Jan and Carlos did. End the discussion by having students brainstorm things that help them make sense of a problem and that help them persevere in solving a problem.

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

Work Time

Make Sense and Persevere

Watch the video to see how Carlos and Jan make sense of a problem and then persevere in solving it.

  • How did Carlos and Jan make sense of the problem?
  • What did they do that showed they were persevering in solving the problem?
  • Did you encounter anything like what Carlos and Jan encountered when they were trying to solve the problem?
  • What kinds of things help you make sense of a problem and persevere in solving it?

VIDEO: Mathematical Practice 1

Task 5: Prepare a Presentation

Lesson Guide

Students will prepare a presentation with their partner.

Check that students’ presentations clearly reflect the process students went through to solve the problem.

Preparing for Ways of Thinking

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?

Work Time

Prepare a Presentation

  • Prepare a presentation that describes the process you went through to solve this problem. What was easy? What was hard?

Task 6: 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.

Have pairs present their work and discuss how they approached the problem.

Be sure to include students whose strategies did not work, 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 they addressed and how they addressed those questions. Have students ask questions and make observations as they view each other's work.

Focus on the strengths and weakness of the different solution methods.

  • Which approach did you like best? Why?
  • Which approach was most difficult to understand? What was difficult about it?

SWD: Students with disabilities may have difficulty determining what information to review and study in preparation for the Unit Assessment. Create a study guide or template for students with disabilities that outlines the key skills and concepts with which they must be familiar for the Unit Assessment.

Performance Task

Ways of Thinking: Make Connections

  • Take notes about the concepts you learned in this unit:
    • Absolute value
    • Opposite of a number
    • Coordinate plane
    • Coordinates
    • Figures on a coordinate plane

As students present, ask questions such as:

  • How did you approach the problem?
  • How does your approach compare with the other methods mentioned so far?
  • Which method do you like best? Why?
  • How does your figure or design meet the criteria? How can you change your figure or design and still meet the criteria?
  • What was the most difficult part of this problem? The easiest part?
  • How did you incorporate feedback into your final figure or design?
  • What helped you make sense of this problem?
  • Give an example of some really hard work you had to do to solve this problem.

Task 8: Reflect On Your Work

Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to discover what students would do differently if they started the problem now.

Work Time

Reflection

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

What I would do differently if I started the problem now is ...