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Unit 8, Lesson 2

Equations and Graphs

Extra Support Materials for Algebra 1

2.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

Notice and Wonder

Materials

None

Activity Narrative

The purpose of this Warm-up is to connect student interpretations of a graph and equation to a situation, which will be useful when students write functions that represent situations in a later activity. While students may notice and wonder many things about these representations, the connections to the actual situation are the important discussion points.

This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how the graph and equation are connected.

Launch

Arrange students in groups of 2. Display the prompt, equation, and graph for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.

Activity

None

A group is asked to memorize a list of 20 words and then to recall as many as possible later. An equation that models the relationship between the position of the word on the list, , and the number of people in the group who remembered the word, , is .

<p>Function on a coordinate grid with 20 points, origin O.</p>

What do you notice? What do you wonder?

Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the prompt. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the connections between the equation, graph, and situation do not come up during the conversation, ask students to discuss this idea.

2.2

Activity

Instructional Routines

MLR6: Three Reads

Materials

To Gather

Graphing technology

Activity Narrative

In this activity, students work to solve linear equations and recognize the solution in graphs. This skill will help students when they examine quadratic equations and their solutions in the associated Algebra 1 lesson. Students reason abstractly and quantitatively (MP2) when they interpret the meaning of solutions in the context of situations.

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

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 about hiking, without revealing the questions.

For the first read, read the problem aloud, and then ask, “What is this situation about?” (A person hiking from the top of a mountain into a valley.) 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 expression represents the hiker’s elevation minutes after the hike started.)
After the third read, reveal the question: “What does a solution to the equation mean?” 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 start by thinking about what the expression represents and what a value of 0 would mean for the expression.)

After Three Reads, tell students to open their books or devices and complete the task. Graphing technology is needed for every student.

2.3

Activity

Instructional Routines

None

Materials

To Gather

Graphing technology

Activity Narrative

In this activity, students practice solving equations and seeing the solution in graphical form. The questions in this activity are not restricted to problems where the equation is equal to zero. Students must recognize that solutions to these equations may involve either rewriting the equation to equal zero before graphing or solving a system of equations with each side of the equation representing a function to be graphed. As students interpret the meaning of their solutions in the context of each situation, they reason abstractly and quantitatively (MP2).

Launch

Graphing technology is needed for every student.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. For example, one situation at a time. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Social-Emotional Functioning

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Audience

Assessment Access

Lesson 2

Equations and Graphs

Warm-up

Standards Alignment

Building On

Addressing

HSA-CED.A.3

HSA-SSE.A.1

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Activity Synthesis

Activity

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Student Response

Building on Student Thinking

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

Addressing

HSA-CED.A.3

HSA-SSE.A.1

Building Toward

HSA-REI.B.4

Standards Alignment

Building On

Addressing

HSA-CED.A.3

HSA-SSE.A.1

Building Toward

HSA-REI.B.4