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Activity Synthesis

The goal of this discussion is to emphasize the difference between elevation and distance from sea level. Begin by displaying the vertical number line from the Task Statement for all to see. Invite students to share possible elevations for each person and to share their reasoning about how the elevation satisfies each part of the given description. Record student responses on the display for all to see. If possible, record responses for Clare, Andre, Han, and Lin in different colors.

Then display this table for all to see.

	possible elevation	compare to submarine	distance from sea level
Clare	150 feet		or 150 feet
Andre
Han
Lin

Explain how the first row for Clare has been filled in with one possible elevation of 150 feet. Fill in the rest of the table as a class, emphasizing the language of “greater than” and “less than” when completing the middle column and “absolute value” when completing the right column.

If time allows, ask students if it would be possible for a person to have an elevation less than the submarine’s and also be closer to sea level. (No, it would not be possible because any elevation less than that of the submarine would be below the submarine and must also be farther away from sea level.)

7.2

Activity

Standards Alignment

Building On

Instructional Routines

MLR4: Information Gap Cards

Materials

To Copy (from Blackline Masters)

Points on the Number Line Cards

Activity Narrative

This activity gives students an opportunity to determine and request the information needed to determine the location of points on a number line.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

This activity uses the Information Gap math language routine, which facilitates meaningful interactions by positioning some students as holders of information that is needed by other students, creating a need to communicate.

Launch

Tell students they will be locating points on a number line. Display the Infomation Gap graphic that illustrates a framework for the routine for all to see.

Remind students of the structure of the Information Gap routine, and consider demonstrating the protocol if students are unfamiliar with it.

Arrange students in groups of 2. In each group, give a problem card to one student and a data card to the other student. After reviewing their work on the first problem, give students the cards for a second problem, and instruct them to switch roles.

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to rephrase directions in their own words. Keep a display of the Information Gap graphic visible throughout the activity, or provide students with a physical copy.
Supports accessibility for: Memory, Organization

Activity

None

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

Silently read your card, and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me ?”
Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning, and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

Student Response

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Building on Student Thinking

If some students struggle to make sense of the abstract information they are given, rather than specifically instructing them to draw a number line, consider asking:

"What information do you know about the points?"
“How could you keep track of the information you've learned about the points so far?”

Activity Synthesis

After students have completed their work, share the correct answers, and ask students to discuss the process of solving the problems. Here are some questions for discussion:

“What strategies were helpful in determining the location of the point?” (Drawing a number line.)
“Which clues were most helpful? Least helpful?”

Highlight for students the following glossary and vocabulary terms that were used in this activity and how they are related but different: “absolute value,” “sign,” “opposite,” “greater than,” “less than.”

7.3

Activity

Optional

Standards Alignment

Building On

Addressing

Instructional Routines

Materials

None

Activity Narrative

The purpose of this activity is to give students additional practice comparing rational numbers. In this partner activity, students take turns writing a true statement using numbers and symbols and translating that statement into words. Students must attend to precision as they communicate precisely with their partner (MP6).

Launch

Arrange students in groups of 2. Display the task for all to see. Tell students that they will work with their partner to write true comparison statements. If time allows, choose a student as a partner, and demonstrate how to do the activity. Otherwise, share these steps:

One partner selects two numbers and one comparison symbol and uses them to write a true statement.
The other partner listens and makes sure they agree with the statement.
If they don’t agree, the partners discuss until they come to an agreement.
The other partner then uses one of the following phrases to write a sentence with the same meaning:
- "Is equal to"
- "Is the absolute value of"
- "Is greater than"
- "Is less than"
For the next statement, the students swap roles.

Activity

None

Here are some numbers and symbols. Take turns with your partner to write true comparison statements. One partner will use 2 numbers and 1 symbol to write a true statement. The other partner will use one of the following phrases to write a sentence with the same meaning:

"Is equal to"
"Is the absolute value of"
"Is greater than"
"Is less than"

-0.7

1

4

-2.5

2.5

8

-4

0

For each statement that you write, explain your reasoning to your partner.
For each statement that your partner writes, listen carefully to their explanation. If you disagree, discuss your thinking, and work to reach an agreement.

Student Response

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Building on Student Thinking

Activity Synthesis

Much discussion takes place between partners. Invite students to share how they wrote their true statements comparing two numbers or how they translated the statement into words. Consider discussing the following questions:

“What were some ways you handled disagreements?”
“Describe any difficulties you experienced and how you resolved them.”