Lesson 6: Absolute Value of Numbers

Absolute Value of Numbers

5 min

Teacher Prep

Setup

Reveal one problem at a time. 30 seconds quiet think time then whole-class discussion for each problem.

Narrative

This Math Talk focuses on comparing two positive values to determine which is closer to 0. It encourages students to think about distance on a number line and to rely on the structure of factions and decimals to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students find the distance of both positive and negative rational numbers from zero.

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies, and record and display their responses for all to see.
Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

For each pair of expressions, decide mentally which one has a value that is closer to 0.

$\frac{9}{11}$ or $\frac{15}{11}$
$\frac15$ or $\frac19$
$1.25$ or $\frac54$
$0.01$ or $0.001$

Sample Response

$\frac{9}{11}$ . Sample reasoning: $\frac{9}{11}$ is positive and less than 1, while $\frac{15}{11}$ is greater than 1, so $\frac{9}{11}$ is closer to 0.
$\frac19$ . Sample reasoning: Ninths are smaller than fifths, so $\frac19$ is closer to 0.
Neither. Sample reasoning: They are equal, so they are equally close to 0.
0.001. Sample reasoning: 1 thousandth is 10 times smaller than 1 hundredth, so 0.001 is closer to 0.

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

, so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols $>$, =, or $<$, and justify the conclusions, e.g., by using a visual fraction model.
5.NBT.A·Understand the place value system.
5.NBT.A·Understand the place value system.

Building Toward

6.NS.7.c·Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
6.NS.C.7.c·Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of $-30$ dollars, write $|-30| = 30$ to describe the size of the debt in dollars.

15 min

10 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Absolute Value of Numbers

5 min

Teacher Prep

Setup

Reveal one problem at a time. 30 seconds quiet think time then whole-class discussion for each problem.

Narrative

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies, and record and display their responses for all to see.
Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

For each pair of expressions, decide mentally which one has a value that is closer to 0.

$\frac{9}{11}$ or $\frac{15}{11}$
$\frac15$ or $\frac19$
$1.25$ or $\frac54$
$0.01$ or $0.001$

Sample Response

$\frac{9}{11}$ . Sample reasoning: $\frac{9}{11}$ is positive and less than 1, while $\frac{15}{11}$ is greater than 1, so $\frac{9}{11}$ is closer to 0.
$\frac19$ . Sample reasoning: Ninths are smaller than fifths, so $\frac19$ is closer to 0.
Neither. Sample reasoning: They are equal, so they are equally close to 0.
0.001. Sample reasoning: 1 thousandth is 10 times smaller than 1 hundredth, so 0.001 is closer to 0.

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

, so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols $>$, =, or $<$, and justify the conclusions, e.g., by using a visual fraction model.
5.NBT.A·Understand the place value system.
5.NBT.A·Understand the place value system.

Building Toward

6.NS.7.c·Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
6.NS.C.7.c·Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of $-30$ dollars, write $|-30| = 30$ to describe the size of the debt in dollars.

Absolute Value of Numbers

Warm-upMath Talk: Closer to Zero5 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityJumping Bug15 minKCs

ActivityAbsolute Elevation and Temperature10 minKCs

Knowledge Components

Absolute Value of Numbers

Warm-upMath Talk: Closer to Zero5 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityJumping Bug15 minKCs

ActivityAbsolute Elevation and Temperature10 minKCs

5 min

15 min

10 min

5 min

15 min

10 min