Unit 6, Lesson 19
Adjusting Windows
Extra Support Materials for Algebra 1
19.1
Warm-up
Standards Alignment
Building On
Addressing
Building Toward
HSF-LE.A.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Instructional Routines
NoneMaterials
To Gather
Graphing technologyActivity 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
NoneUse graphing technology to create a graph of . Here are some different graphing windows to try:
- and
- and
- and
- and
- Identify the graphing window that makes the graph look:
- the steepest
- 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.
Student Response
Loading...
Building on Student Thinking
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
Materials
To Gather
Graphing technologyActivity 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.
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.)
19.3
Activity
Instructional Routines
Aspects of Mathematical ModelingMaterials
To Gather
Graphing technologyActivity 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
Supports accessibility for: Organization, Memory, Attention