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# Rational Numbers and Integers: Practice

# Revise Your Work: Integers and Rational Numbers Self Check

# Self Reflection: Integers and Rational Numbers

# Assess and Revise

## Overview

Students revise their work on the Self Check based on feedback from the teacher and their peers.

# Key Concepts

Concepts from previous lessons are integrated into this assessment task: integers, absolute value, and comparing numbers. 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 your knowledge of integers, absolute value, and comparing numbers to solve problems.
- Track and review your choice of strategy when problem solving.

# Critique

# Lesson Guide

Return students’ solutions to the assessment 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.

## Opening

# Critique

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

- How can you tell which is the lesser of two rational numbers?
- How do you find the opposite of a number?
- How do you find the absolute value of a number?
- How do you find distance on the number line?

Use the Number Line Tool if you find it to be helpful.

HANDOUT: Self Relfection: Integers and Rational Numbers

INTERACTIVE: Number Line Tool

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will explain how to compare positive and negative numbers, find the opposite of a number, and find and use absolute value.

## Opening

Explain how to compare positive and negative numbers, find the opposite of a number, and find and use absolute value.

# Revise Your Work

# Lesson Guide

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

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?

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.

ELL: When students work in pairs, it allows you to monitor individual student progress by listening to and recording student conversations and peer problem solving. This type of collaborative work gives ELLs the opportunity to use mathematical language and to engage in conversation with their peers. Allow them to use their language of origin if they are paired with a student who speaks that language.

# 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 or her work poorly.**

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

**Student has a correct solution.**

- What method did you use to solve this 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.

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

Look for students who successfully critique the reasoning of others when evaluating the work of their peers.

# Answers

- Explanations will vary.
- –6.6
- –2.7
- Yes, −|−7| = −|7| because −|−7| = −7 and −|7| = −7; −7 = −7.
- –6.6 is farther from 1.

## Work Time

# Revise Your Work

Revise your work on the Self Check.

Answer the questions. Explain your thinking.

Use the Number Line Tool if you find it to be helpful.

- Which of these numbers is least? −0.6, −6, −6.06, −6.6, 6.6, or 0.6
- What is the opposite of the opposite of −2.7?
- Do the two expressions below have the same value?

−|−7| and −|7| - Which of these two numbers is farther from 1?

−6.6 or 6.6

# Practice

# Lesson Guide

Students will solve problems similar to the Self Check.

# Interventions

**Student has an incorrect solution.**

- Did you plot your numbers on a number line?
- What is the absolute value of –4?

**Student has difficulty getting started.**

- Can you use a number line to help you?
- Think about the definitions for the terms
*the opposite of a number*and*absolute value*.

**Student has a solution.**

- How could you explain your solution to someone else?
- What is the difference between the opposite of a number and the absolute value of a number?

# Answers

Explanations will vary.

- –12
- 2.7
- –4
- Both –5.4 and 5.4 are the same distance from 0; they are opposite numbers.

## Work Time

# Practice

Answer the questions. Explain your thinking.

Use the Number Line Tool if you find it to be helpful.

Which of these numbers is greater?

−12 or −15What number is the opposite of −2.7 ?

What is the value of this expression?

−|−4|Which of these numbers is closer to 0?

−5.4 or 5.4

Ask yourself:

- How can you tell which is the greater of two rational numbers?
- What does the opposite of a number mean?
- What does absolute value mean?
- How do you find distance on the number line?

# Make Connections

# Lesson Guide

- Organize a whole-class discussion to consider issues arising from students’ revisions. You may not have time to address all these issues, so focus the class discussion on the issues that are most important for your students.
- Have students share their work and discuss how they approached each problem.
- 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.

Ask questions such as the following:

- Which problems were most difficult?
- Did you and your partner ever disagree about an answer? How did you resolve your differences of opinion?

ELL: Write the key points, observations, and common misconceptions on a poster so that students can refer back to them throughout the unit. When working with ELLs, provide supplementary materials, such as graphic organizers, to illustrate new concepts and vocabulary necessary for mathematical learning.

## Performance Task

# Ways of Thinking: Make Connections

Take notes about how to compare positive and negative numbers, find the opposite of a number, and find and use absolute value.

As students present, ask questions such as:

- How can you compare two numbers?
- How can you find the opposite of a number?
- How can you find the absolute value of a number?
- How can you find distance on a number line?
- How does your number line model the math?

# 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 problems now.

## 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.

**What I would do differently if I started the problem now is …**