Unit 5, Lesson 7
Slopes of Segments
Extra Support Materials for Algebra 1
7.1
Warm-up
Standards Alignment
None
Building On
Addressing
Building Toward
Materials
NoneActivity Narrative
This Math Talk focuses on subtraction and division. It encourages students to think about the order of each step and to rely on the structure of complex problems to mentally solve problems. The strategies and understandings elicited here will be helpful later in this lesson when students will need to be able to find the slope of the line through 2 given points.
To solve each problem, students need to look for and make use of structure (MP7).
Launch
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
- Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
- Invite students to share their strategies, and record and display their responses for all to see.
- Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem. Keep all previous problems and work displayed throughout the talk.
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
NoneEvaluate mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for subtracting two sets of numbers and dividing the differences, as is often done when calculating the slope. To involve more students in the conversation, consider asking:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to ’s strategy?”
- “Do you agree or disagree? Why?”
- “What connections to previous problems do you see?”
MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. Examples:
Advances: Speaking, Representing
- “First, I because .”
- “I noticed , so I .”
Advances: Speaking, Representing
7.2
Activity
Instructional Routines
MLR2: Collect and DisplayMaterials
NoneActivity Narrative
In this activity, students find the slope of a line that goes through 2 given points. In the associated Algebra 1 lesson, students find the average rate of change over an interval. By finding a slope using 2 coordinate pairs, students are focusing on the mechanics of computing the value and can focus more fully on the context and meaning in the Algebra 1 lesson. As students develop the skill of calculating slope or average rate of change, they look for and express regularity in repeated reasoning (MP8).
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 they will be working on problems about slope. Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to calculate the slope of each line. Display words and phrases, such as “slope,” “rate of change,” “first point,” “second point,” “subtract,” and “divide.”
7.3
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students consider the slope of segments in a situation. Students interpret the meaning of slope in the situation, then find the segments where the slope is greatest and least. As students interpret the values in the context of this situation, they reason abstractly and quantitatively (MP2). In the associated Algebra 1 lesson, students examine the average rate of change in situations. The work of this activity supports students by allowing them to consider only segments between two points connected by a segment so they can focus on greater trends in the Algebra 1 lesson.
Launch
If necessary, explain the meaning of the unemployment percentage.