Unit 2, Lesson 5
Graphs, Tables, and Equations
Extra Support Materials for Algebra 1
5.1
Warm-up
Standards Alignment
Building On
Addressing
HSA-REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Building Toward
Instructional Routines
Worked ExampleMaterials
NoneActivity Narrative
The purpose of this activity is for students to study and make sense of one way to graph a linear: equation from slope-intercept form.
This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.
This is the first Worked Example activity in the course. See the Launch for extended instructions for facilitating this activity successfully. During the Synthesis, students answer three questions, always in the same order, to:
- Justify the first step.
- Analyze one or more specific details in the process.
- Identify or explain the answer in the final step.
Launch
This is the first time students do the Worked Example instructional routine in this course, so, before starting, it is important to explain how it works.
Explain that a Worked Example has a prompt followed by a set of problem-solving steps, revealed one at a time. After each reveal, students have time to quietly read the step. This quiet contemplation continues through to the last step, which is also the answer to the prompt.
Depending on where students have struggled in the past with similar problems, it may be necessary to pause and discuss a step before revealing the next step. If, during this pause, a question similar to an Activity Synthesis question arises, it’s okay to briefly discuss the question now and return to it later to see if students have any additional responses. If students ask “what if” questions, save them to discuss at the end of the Activity Synthesis.
Consider establishing a small, discreet hand signal that students can display when they are ready to move on to the next step. Signals might include a thumbs-up or a certain number of fingers. Using such subtle signals is a quick way to see if students have had enough time to read the step. It also keeps students from being distracted or rushed by hands being raised around the class.
Arrange students in groups of 2. Tell them to close their books or devices (or to keep them closed). Reveal the prompt and the first step. Give students a brief quiet think time, and ask them to give a signal when they have read the step and are ready to see the next. Once most students have given the signal, reveal the next step. Repeat until all steps have been revealed.
If previous work indicates that most students will struggle to make sense of a step, pause and give students 1 minute to discuss with their partner and formulate a question about the step. Ask 1–3 groups to share their questions, inviting other groups to answer. Record responses next to the step for all to see. Once questions have been answered, continue to the next reveal.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneActivity Synthesis
The purpose of this discussion is for students to understand the steps that the solver took to graph an equation from slope-intercept form.
Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.
- “Why did the solution start at ?” ( is the vertical intercept, where the line crosses the -axis.)
- “How are the dashed lines related to the equation?” (The dashed lines represent the change in and change in of the slope of the line.)
- “Where can we see the final answer?” (In step 5, the black line connecting the two points, and is the graph of the equation .)
Ask partners to compare their responses to each question and to decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.
If time allows, consider displaying a second worked example next to the first that either:
- Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7).
- For example, show a horizontal line segment from to in Step 2 then a vertical line segment from to in Step 3.
- Shows the same method with an error that students can critique and correct (MP3).
- For example, draw a dashed line segment from to in Step 2 and from to in Step 3.
5.2
Activity
Instructional Routines
MLR1: Stronger and Clearer Each TimeMaterials
To Gather
Graphing technologyActivity Narrative
The purpose of this activity is to recall the connection between equations and graphs. This will be useful when students create an equation to represent a situation and graph it in an associated Algebra 1 lesson.
In this partner activity, students take turns sharing their initial ideas and first drafts. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). As students revise their writing, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6).
This activity uses the Stronger and Clearer Each Time math language routine to advance writing, speaking, and listening as students refine mathematical language and ideas.
Launch
5.3
Activity
Materials
To Copy (from Blackline Masters)
Graphs, Tables, Equations, and Situations Cards
Activity Narrative
In this partner activity, students take turns to practice applying their skills at connecting multiple representations of the same linear relationship.
As students analyze different representations, they practice reasoning quantitatively and abstractly (MP2). In making connections across representations, they practice looking for and making use of structure (MP7).
The practice will pay off in the associated Algebra 1 lesson when they create graphs and equations to describe the relationship between two quantities from a situation.
Launch
Tell students that the cards contain a situation, an equation, a table, or a graph and that they will take turns matching the cards. Explain how to set up and do the activity. If time allows, demonstrate these steps with a student as a partner:
- Mix up the cards, and place them face up.
- One person selects one card of each type and explains to their partner why the cards match.
- The partner’s job is to listen and make sure they agree. If they don’t agree, the partners discuss until they come to an agreement.
- When both partners agree on the match, they switch roles.
Consider demonstrating productive ways to agree or disagree, for example, by explaining mathematical thinking or asking clarifying questions.
Arrange students in groups of 2. Give each group a set of 32 slips cut from the blackline master. (Note that the slips from the “Set the Table” lesson should be reused, and the graphs should be included this time.) Ask students to redo the matches from the “Set the Table” lesson. Tell students the correct matches to expedite the process.