Lesson | Loading...

Unit 6, Lesson 19

Adjusting Windows

Extra Support Materials for Algebra 1

19.1

Warm-up

10 mins

Enough with the Zooming Already

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Graphing technology

Activity Narrative

In this activity, students try different graphing windows to see how it impacts how a graph looks. As students develop these skills and comfort with using technology, they are able to use appropriate tools strategically.

Launch

Graphing technology is needed for every student. It may be desirable for students to work in groups of four so that they can view all four graphing windows on four different devices at the same time.

If needed, demonstrate using technology to graph the function and to set the graphing window for the first given window. Then allow students to set the remaining graphing windows and answer the questions.

Activity

None

Student Task Statement

Use graphing technology to create a graph of . Here are some different graphing windows to try:

Identify the graphing window that makes the graph look:
1. the steepest
2. the flattest
Come up with a new graphing window that makes the graph look even steeper than the steepest one you identified.
Come up with a new graphing window that makes the graph look even flatter than the flattest one you identified.

Activity Synthesis

The main purpose of this activity is to learn or revisit how to specify a graphing window with the available technology. Once students show proficiency with this, quickly move on to the next activity.

19.2

Activity

20 mins

How to Lie with Graphing Windows

Instructional Routines

Aspects of Mathematical Modeling MLR6: Three Reads

Materials

To Gather

Graphing technology

Activity Narrative

In this activity, students get more practice adjusting their graphing windows. Then they explore why someone might want to choose a different graphing window to tell a different story. As students determine how graphing windows give unique meanings to the same model, students are modeling with mathematics (MP4).

This activity uses the Three Reads math language routine to advance reading and representing as students make sense of what is happening in the text.

19.3

Activity

10 mins

Renting a Car

Instructional Routines

Aspects of Mathematical Modeling

Materials

To Gather

Graphing technology

Activity Narrative

In this activity, students choose a graphing window to tell a particular story. Using a model to tell a story about the data is a part of modeling with mathematics (MP4).

Launch

Graphing technology is needed for every student. Students may be ready to dive into the activity without much assistance, or they may need to engage in a Notice and Wonder to familiarize themselves with the context and the information encoded in the equation and the graph.

Action and Expression: Provide Access for Physical Action. Support effective and efficient use of tools and assistive technologies. To use graphing technology, some students may benefit from access to step-by-step instructions.
Supports accessibility for: Organization, Memory, Attention

Have feedback on the curriculum?

Help us improve by sharing suggestions or reporting issues.

Submit Feedback

Launch

Graphing technology is needed for every student. Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Use Three Reads to support reading comprehension and sense-making about this problem. Display only the problem stem and the 4 graphs, without revealing the questions.

For the first read, read the problem aloud, and then ask, “What is this situation about?” (There is a harmful chemical in drinking water. The amount of the chemical is modeled in the graphs.) Listen for and clarify any questions about the context.
After the second read, ask students to list any quantities that can be counted or measured. (The graphs are all measuring the chemical in parts per billion over time, measured in years.)
After the third read, reveal the question "Here is Graph A, with rectangles approximating the graphing windows of B, C, and D superimposed. Which rectangle matches which graph?" and combined graph, and ask, “What are some ways we might get started on this?” Invite students to name some possible starting points, referencing quantities from the second read. (We can look at the window of each graph and try to match it with parts of the combined graph.)

Activity

None

Student Task Statement

These graphs represent a function modeling the amount of a harmful chemical in drinking water in parts per billion over time in years.

<p>Horizontal axis, time in years, 0 to 80, by 20’s. Vertical axis, amount of chemicals in parts per billion, 0 to 30, by 5’a. Upward curve from about 0 comma 0 to 80 comma 7 graphed</p> — A

<p>Horizontal axis, time in years, 0 to 8, by 2’s. Vertical axis, amount of chemicals in parts per billion, 0 to 30, by 5’s. Line that appears to be horizontal graphed just above x axis </p> — B

<p>Horizontal axis, time in years, 0 to 80, by 20’s. Vertical axis, amount of chemicals in parts per billion, 0 to 8, by 2’s. Upward curve from about 0 comma 0 to 80 comma 7 graphed</p> — C

<p>Horizontal axis, time in years, 64 to 74, by 2’s. Vertical axis, amount of chemicals in parts per billion, 0 to 30, by 5’s. Line from about 64 comma 3 to 74 comma 5 graphed</p> — D

Here is Graph A with rectangles approximating the graphing windows of B, C, and D superimposed. Which rectangle matches which graph?

Horizontal axis, time in years, 0 to 80, by 20’s. Vertical axis, amount of chemicals in parts per billion. Rectangles 1,2,3 graphed. Rectangle 2, starts at origin, base = about 10, height = about 30. Rectangle 3, starts at origin, base = about 80, height = about 10. Rectangle 1, starts at about 0 comma 65, base = about 10, height = about 30.
Use graphing technology to create a graph of . Practice adjusting the graphing window so your graph looks like A, B, C, and D.
Imagine you are a public health official worried about this model, and you want to convince others that they should be worried, too. Which graphing window would you use, and why?
Imagine you are a public relations official for the company responsible for the chemical in the drinking water, and you want to convince others not to worry. Which graphing window would you use, and why?
What questions should a journalist writing about the issue ask each person about their graph, and which graph should she publish with the article?

Student Response

to access Student Response.

Lesson | Loading...

Settings

Audience

Assessment Access

Lesson 19

Adjusting Windows

Warm-up

Enough with the Zooming Already

Standards Alignment

Building On

Addressing

Building Toward

HSF-LE.A.3

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Activity

How to Lie with Graphing Windows

Instructional Routines

Materials

To Gather

Activity Narrative

Activity

Renting a Car

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Have feedback on the curriculum?

Student Response

Building on Student Thinking

Are You Ready for More?

Launch

Activity

Student Task Statement

Student Response

Building on Student Thinking

Are You Ready for More?

Activity Synthesis

Activity

Student Task Statement

Student Response

Building on Student Thinking

Are You Ready for More?

Activity Synthesis

Standards Alignment

Building On

Addressing

HSF-IF.B.5

Building Toward

HSF-LE.A.3

Standards Alignment

Building On

Addressing

HSF-IF.B.5

Building Toward

HSF-LE.A.3