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Unit 6, Lesson 1

Matching Up to Data

Algebra 2

1.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Which Three Go Together?

Materials

None

Activity Narrative

This Warm-up prompts students to compare four data sets. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the data sets for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, tell each student to share their response with their group, and then together find as many sets of three as they can.

Activity

None

Which three go together? Why do they go together?

(hours)	0.03	0.12	0.22	0.3	0.93	1.02	1.28	1.55	2.17	2.77	5.7
(degrees Fahrenheit)	69	67.8	67.4	66.3	59.9	59.1	57.5	57.3	55	52.3	47.1

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

Invite each group to share one reason why a particular set of three goes together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use, such as “increasing” or “decreasing.” Also, press students on unsubstantiated claims.

1.2

Activity

Instructional Routines

MLR8: Discussion Supports

Materials

None

Activity Narrative

The purpose of this activity is to build on the work of the Warm-up as students determine which of the given functions is a better fit for the data. For this activity, students should use any language that makes sense to them to describe why a function is or is not a good fit and how they would change the function to be a better fit for the data. Since both functions offer reasonably good fits for the data, students have the opportunity to make an argument about why they think a particular function is a better fit (MP3).

Monitor for students using different explanations of what makes a function fit the data, such as by focusing on the general shape of the graph, the accuracy of individual points, or the average error for all the points.

In the digital version of the activity, students use an applet to check their initial response to the question about which function better fits the shape of the data. The applet allows students to zoom out on the graph and see the part of the rational function that is not visible in the initial graphing window.

This activity works best when each student has access to devices that can run the Desmos applet because students will benefit from seeing the relationship in a dynamic way. If students don't have individual access, projecting the applet will be helpful during the Activity Synthesis.

1.3

Activity

Instructional Routines

MLR2: Collect and Display Take Turns

Materials

To Copy (from Blackline Masters)

What Happened to the Graph Cards

Activity Narrative

In this partner activity, students take turns describing transformations of a graph and sketching the transformed graph from the description. As students trade roles explaining their thinking and listening, they have opportunities to refine and use more precise language when describing transformations (MP6).

This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.

Launch

Arrange students in groups of 2. Tell students that they are going to take turns. One partner will describe the transformation of graph A to graph B that they see on their handout, and the other will draw the transformation based on the description. Each partner will draw 3 graphs and describe 3 transformations.

Ask students to be specific in their descriptions, but note that the goal is for their partner to draw the transformation correctly without needing to name specific points.

Distribute 2 half sheets to each group from the blackline master, 1 to each student. Remind students to keep their sheet hidden from their partner.

Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to describe the transformations. Display words and phrases, such as “translate up or down,” “translate right or left,” “reflect,” “stretched,” “squashed,” "vertex," "intercept," or "maximum."

Action and Expression: Internalize Executive Functions. To support development of organizational skills in problem-solving, chunk this task into more manageable parts. For example, give students a subset of the cards to start with, and introduce remaining cards if time allows.
Supports accessibility for: Organization, Attention

Lesson Synthesis

<p>Graph on grid. 2 data points.<br>
</p>

Display the three graphs. Invite students to describe how to transform each graph to fit the points.

Here are some questions for discussion:

“Which graph fits the data the best?” (All three can fit perfectly, for example, by translating the parabola up 2 and right 1.)
“What would be a situation where each graph—linear, quadratic, and exponential—would be the best choice to model the relationship?” (Any explanation works so long as the rate of change in the scenario matches the graph chosen. For example: The exponential would be best if the situation was population growth over time. The line would be best if the situation was price per pound.)
"When we fit a curve to data points, will the curve always go precisely through all of the points?" (Not always, but the shape of the curve should fit the general shape of the data.)

to access Cool-down.

Student Lesson Summary

The data in the graph show the temperature , in degrees Fahrenheit, of a can of soda hours after it was put into the refrigerator.

<p>Graph of a decreasing exponential function.</p>

What if we want to build a function that fits this data set? One way to find a function that fits the data well is to start with a simpler function that has the same general shape as the data when graphed and transform it. What shape does this data form?

Let’s try an exponential decay function. We can get the right shape using a simpler equation like , but the graph doesn't fit where the data is. The graph of the function given by isn't represented by a simple equation, but it does fit the data. (What did multiplying by 45 and adding 36 do to the graph?) In this unit we will learn how to translate, reflect, and stretch graphs to fit data.