Unit 6, Lesson 16
Over and Over
Extra Support Materials for Algebra 1
16.1
Warm-up
Standards Alignment
Building On
Addressing
7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Building Toward
HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Instructional Routines
MLR7: Compare and ConnectMaterials
To Gather
Scientific calculatorsActivity Narrative
The purpose of this task is to help students develop (or remind them of) shortcuts for computing percentages of a number and percentages off of a number. When students interpret their calculations in context, they have an opportunity to reason abstractly and quantitatively (MP2).
Monitor for students who use these different strategies:
- Tape diagrams
- Double number lines
- Numerical expressions
This activity uses the Compare and Connect math language routine to advance representing and conversing as students use mathematically precise language in discussion.
Launch
Provide access to calculators. Select work from students with different strategies, such as those described in the Activity Narrative, to share later.
Activity
NoneA phone is on sale. Which sale results in the lowest price? Explain your reasoning.
- a \$200 phone that is 35% off
- a \$200 phone for sale at 60% of its original price
- a \$150 phone for sale at 87.5% of its original price
- a \$140 phone that is 8.5% off
Student Response
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Activity Synthesis
The goal of this discussion is to connect the visual representations of percent change with numerical expressions to complete calculations.
Display 2–3 approaches from previously selected students for all to see. If time allows, invite students to briefly describe their approach, then use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:
- “Did anyone solve the problem the same way but would explain it differently?”
- “How does the percent change show up in each method?”
- “Are there any benefits or drawbacks to one representation compared to another?”
To prepare for the next activity, mention that 8.5% of 140 can be computed by multiplying 140 by 0.085.
16.2
Activity
Instructional Routines
NoneMaterials
To Gather
Scientific calculatorsActivity Narrative
The purpose of this task is to introduce the idea of interest, and show through example how the balance is different if someone earns interest on their interest, versus someone who withdraws the interest every year. The activity asks a question without much scaffolding, which offers an opportunity for students to make sense of the problem and persevere in solving (MP1).
In addition to “interest,” students may need help interpreting other terms, like “deposit” and “withdrawal.” Use the Launch to gauge how much time to spend on helping students understand the terms associated with bank accounts.
Monitor for different ways students organize their work.
Launch
Ask students if they have ever heard of earning interest on a bank account. After one or more students share their understanding, clarify that, for some types of bank accounts, the bank gives you a percentage of the amount in the account every year. For example, if an account gives 2% interest and you deposit \$100 in the account, you would earn an additional \$2 from the bank after 1 year. The reason banks do this is because the money in your account doesn’t just sit there. The bank uses it to accomplish other things, like giving loans to other customers.
The interest that the bank deposits in your account is now yours. If you leave this money alone, you also earn interest on the new money. So, if you left your \$102 alone, after 1 year, you would earn 2% of that amount in interest. 2% of 102 is 2.04, so you would earn \$2.04, and your new balance would be \$104.04.
Provide access to calculators.
Engagement: Provide Access by Recruiting Interest. Invite students to share their experience with saving money in a bank account.
Supports accessibility for: Conceptual Processing, Memory
Supports accessibility for: Conceptual Processing, Memory
16.3
Activity
Instructional Routines
NoneMaterials
To Gather
Tools for creating a visual displayActivity Narrative
In this practice activity, students have an opportunity to solve a problem in which a percentage change is applied repeatedly. After students have had a chance to make a visual display, conduct a gallery walk or invite one group for each problem to present their solution. When students explain why they agree or disagree with a character’s statement, they are justifying their reasoning and critiquing the reasoning of others (MP3).
Launch
Arrange students in groups of 2–3, and distribute tools for making a visual display. Either assign one problem to each group or allow them to choose a problem. Encourage students to make a rough draft of their solution before making their visual display, and make sure that their work is organized, clear, and easy to understand.