This activity gives students an opportunity to use a graphing calculator to do the same things they will in the associated Algebra 1 lesson, and to draw the same sorts of connections between changing the parameters of a function and a graph representing the function. In this activity, though, the functions are linear instead of quadratic.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

The goal of this discussion is to clarify how changing parts of the equation affects the graphs of linear equations.

• Display this first draft:
  Clare is correct. Since the equation now has a 5 and a 3, the intercepts are 5 and 3.
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Here are some possible questions for discussion:

• “Can you summarize how adding or subtracting a constant term to affected the graph?” (Adding or subtracting a constant term to the equation moved the graph vertically.)
• “Can you summarize how adding or subtracting a constant to (before multiplying by 2) affected the graph?” (Adding or subtracting a constant to moved the graph horizontally.)
• “We can write the equation as a sum or difference (for example, ) or as a product (for example, ). How is each form helpful or unhelpful for graphing?” (The first form shows the -intercept, and the second form shows the opposite of the -intercept.)

In the first part of the activity, students apply what they noticed in the previous activity. In the second part, they practice identifying equivalent expressions. This is in preparation for the associated Algebra 1 lesson, when they will need to rewrite expressions in equivalent forms, including expanding expressions like . When they identify equivalent expressions, students notice and make use of structure (MP7).

The goal of this discussion is to explore strategies for identifying equivalent expressions. When students are demonstrating their processes, encourage them to identify when they are using the distributive property. If students struggled to rewrite any particular expressions, invite them to share their work and identify any errors. Here are some questions for discussion:

• “What strategies did you use to identify equivalent expressions? Demonstrate your process.”
• “In the first problem, each equation was set up to easily see one of the intercepts. How did you figure out the other intercept?” (I used the distributive property to either distribute a number or factor out a number.)
• “In the second problem, all of the equations involved some combination of 2s, 5s, 10s, and ’s. What strategies did you use to keep track of which equations went where?” (I used a graphic organizer and placed the equations into groups in order so I wouldn’t miss any. I color-coded each equation with the group it went with.)