Unit 6, Lesson 21
Skills for Mathematical Modeling
Extra Support Materials for Algebra 1
21.1
Warm-up
Worked Example: What’s the Line?
Instructional Routines
Worked Example
Materials
None
Activity Narrative
The purpose of this activity is to see a method of developing an equation to model a set of data.
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 with their partner and formulate a question about the step. Ask 1–3 groups to share their questions, inviting other groups to answer while recording 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
NoneWhat is an equation that would be a reasonable model for this data?
Step 1:
Step 2:
Step 3:
Step 4:
Activity Synthesis
The purpose of this discussion is to explore a method of creating an equation to model a set of data.
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 first? Why?” (The solver drew a line that fits the data well. Visualizing the line makes it easier to identify a reasonable
-intercept and slope.) - “In Step 2, the solver identified two new points that are not part of the data. Why did they create those points?” (The points the solver identified are both on the line. One is the
-intercept, and the other is another point on the line. The solver can use the two points to calculate the slope, or they could draw a slope triangle using those points.) - “In the last step, the solver wrote an equation. How can they make sure it is a good model of the data?” (The can check by graphing the line and seeing how well it fits the data or by making a table of values to see if it is similar to the original data.)
Ask partners to compare their responses to each question and 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)
- Shows the same method with an error that students can critique and correct (MP3)
Have feedback on the curriculum?
Help us improve by sharing suggestions or reporting issues.