Unit 2, Lesson 2
Words and Symbols
Extra Support Materials for Algebra 1
2.1
Warm-up
Standards Alignment
Building On
Addressing
6.RP.A.3.c
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Building Toward
Materials
NoneActivity Narrative
This Math Talk focuses on calculating percentages mentally. It encourages students to think about expressions or diagrams and to rely on what they know about properties of operations to mentally solve problems. The strategies elicited here will be helpful later when students reason about sales tax and write expressions for situations involving percent calculations in an associated Algebra 1 lesson.
In this activity, students have an opportunity to notice and make use of structure (MP7) as well as repeated reasoning (MP8), because they can exploit the proportional structure of percents to use previous answers to help them answer more-difficult questions—for example, using the value of 75% of a number to find the value of 7.5% of the same number.
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:
- 50% of 80
- 75% of 80
- 1% of 80
- 7.5% of 80
Student Response
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Activity Synthesis
The goal of this discussion is to review students’ strategies for working with percentages.
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?”
Monitor for students who lack conceptual understanding of percent as a rate per 100, or students who lack strategies for evaluating percentages mentally. Check in with these students individually to see if they can use a calculator to evaluate percentages. If many students are struggling to understand percent as a rate per 100 (and therefore why 50% is half of a number, for example), consider illustrating each of these examples using a double number line or tape diagram.
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
2.2
Activity
Instructional Routines
Aspects of Mathematical ModelingMaterials
NoneActivity Narrative
The goal of this activity is to help students practice identifying and representing pertinent information in a word problem. In the associated Algebra 1 lesson, students create equations that represent relationships between two or more variables in contexts. This activity prepares students to be successful in the Algebra 1 lesson by helping them interpret word problems (MP4) before they write equations to represent the relationships. As students discuss the pertinent information and how to represent it, they are constructing viable arguments and critiquing the reasoning of others (MP3).
Launch
Demonstrate how to identify important values and variables using this example: At a department store, t-shirts are on sale for \$5 each and shorts are on sale for \$8 each. A customer plans to buy several t-shirts and shorts.
Ask students questions about the example that will guide their thinking about what is important in the problem and how to represent the important quantities. Here are sample questions to help guide students' thinking:
-
"What information would be important for customers to know?" (The cost of each item and how many of each item they can get.)
-
"What values might be important for purchasing purposes?" (\$5 and \$8)
-
"If you were the customer, what things would you make sure to keep in mind as you shop?" (The cost of each item, the total of everything I want to buy, and the amount of money I have to spend on the items.)
Tell students that they are not solving a problem here, but identifying useful information and describing what each thing represents. Through a class discussion, students should identify some information from the word problem:
- \$5 is the cost of a t-shirt.
- \$8 is the cost of a pair of shorts.
- represents the number of t-shirts bought.
- represents the number of shorts bought.
- represents the total cost.
Remind students that the letters they choose are not as important as knowing what quantities the variables represent. As demonstrated in the solution to the example, it is common, but not required, to use the initial letter of the thing they wish to represent.
2.3
Activity
Materials
To Copy (from Blackline Masters)
Matching Expressions Cards
Activity Narrative
In this partner activity, students take turns matching expressions to situations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
Monitor for students who may match the two blank cards, which will lead to the remaining two unmatched cards not going together. Ask students, “Is it possible to match all of them by using the blanks differently?”
Monitor for students drawing pictures or other representations to help them figure out the relationships.
Launch
Tell students that the cards contain either an expression or a situation and that they will take turns matching the cards. Explain how to set up and do the activity. If time allows, demonstrate these steps with a student as a partner:
- Mix up the cards, and place them face up.
- One person selects one card of each type and explains to their partner why the cards match.
- The partner’s job is to listen and make sure they agree. If they don’t agree, the partners discuss until they come to an agreement.
- When both partners agree on the match, they switch roles.
Consider demonstrating productive ways to agree or disagree, for example, by explaining mathematical thinking or asking clarifying questions.
Arrange students in groups of 2. Give each group a set of 16 slips cut from the blackline master.