Unit 2, Lesson 9
Same Situation, Different Symbols
Extra Support Materials for Algebra 1
9.1
Warm-up
5 mins
Math Talk: True Values
Standards Alignment
Building On
Addressing
Building Toward
HSA-REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Materials
None
Activity Narrative
This Math Talk focuses on strategies for manipulating equations while preserving equality. It encourages students to think about expressions or equations and to rely on properties of operations and equality to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students will need to be able to solve complex equations and justify why certain moves preserve equality.
In explaining their strategies, students need to be precise in their word choice and use of language (MP6).
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.
- Before moving to the next problem, use the questions in the Activity Synthesis to involve more students in the conversation.
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
NoneStudent Task Statement
Solve each equation mentally.
Activity Synthesis
The goal of this discussion is to review students’ strategies for solving multistep equations.
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?”
Emphasize that the expressions on both sides of the equals sign should have the same value, and point out strategies that make explicit use of the equivalence. If the following strategies are not mentioned, ask students about these strategies, and demonstrate if necessary:
- Compensation strategies, such as noticing that 25 is 4 more than 21, so the number that goes in the blank should be 4 more than 3.
- “Doing the same thing to each side” strategies, such as subtracting 21 from each side to get the blank alone.
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
9.2
Activity
20 mins
Refreshing Road Trip
Instructional Routines
Materials
None
Activity Narrative
The purpose of this activity is to further remind students of the different forms that equations representing relationships can take, and to begin to focus students’ attention on equivalent forms of equations in two variables. This will be useful in their Algebra 1 class when students learn to solve equations for a variable.
It’s not critical that students justify why the equations are equivalent to one another. It is more important that they connect each equation back to how it relates to the context. By relating each equation to the context, students are reasoning abstractly and quantitatively (MP2).
Monitor for students who notice that the equations are equivalent and the moves that could be used to relate one to another.
Identify students who struggle with connecting contexts to expressions.
9.3
Activity
15 mins
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