Unit 2, Lesson 18
Putting the Pieces Together
Extra Support Materials for Algebra 1
18.1
Warm-up
Standards Alignment
None
Building On
Addressing
Building Toward
Instructional Routines
Worked ExampleMaterials
NoneActivity Narrative
The purpose of this activity is to identify the slope of a linear equation that is not in 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.
Launch
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 the step with their partner and to formulate a question about the step. Ask 1–3 groups to share their questions, and invite 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
NoneIdentify the slope of the linear equation .
Step 1:
Step 2:
Step 3:
The slope is .
Activity Synthesis
The purpose of this discussion is for students to explore one method of finding the slope from a linear equation that is not in 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.
- “What did the solver do in the first step?” (The solver subtracted from each side of the equation.)
- “Why did the solver isolate ?” (To change the form of the equation into form, which makes it easier to identify the slope of the equation.)
- “How did the solver know which part of the equivalent equation was the slope?” (In form, the slope is the coefficient of .)
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 (next to the first) a second worked example that either:
- Shows a different method of solving a similar problem so that students can compare and contrast it with the first example (MP7).
- Shows the same method with an error so that students can critique and correct it (MP3).
18.2
Activity
Instructional Routines
MLR7: Compare and ConnectMaterials
NoneActivity Narrative
The purpose of this activity is for students to practice writing linear equations given a point on a line and the slope of the line. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5). Graph paper can also be used.
Monitor for students who use these different strategies when given a point that is not the -intercept:
- Use the slope to work from the point they are given to the -intercept
- Graph the line
This activity uses the Compare and Connect math language routine to advance representing and conversing as students use mathematically precise language in discussion.
18.3
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students write linear equations when given two points. Initially students are given the intercepts, then work with points off of the axes. Students make sense of problems and persevere in solving them when they decide on an approach to use based on the information they are given (MP1).
Launch
Keep students in groups of 2. Consider having graphing technology or graph paper available for students to use.