Recalling Percent Change
10 min
Narrative
This Warm-up refreshes students' memory of strategies for working with percent-change situations, preparing them to apply this understanding to situations of exponential change.
As students work, look for the different strategies that they use to answer the questions. For example, students might think of the first question as (0.2)⋅160, as 51⋅160, or as, 160÷5 all of which can be calculated mentally. Others might draw a tape diagram to represent the quantities and their relation to each other. Invite students with contrasting strategies to share later.
Also, to help inform the activities ahead, notice the different ways in which students approach and express the percent decrease situations.
Student Task
A scooter costs $160.
For each question, show your reasoning.
- The cost of a pair of roller skates is 20% of the cost of the scooter. How much do the roller skates cost?
- A bicycle costs 20% more than the scooter. How much does the bicycle cost?
- A skateboard costs 25% less than the bicycle. How much does the skateboard cost?
Sample Response
- $32
- $192
- $144
Activity Synthesis (Teacher Notes)
Select students to share how they approached the questions. Record their responses for all to see. Focus the discussion on the last two questions. Note the different ways in which students expressed 20% more than $160 and 25% less than $192 and why the expressions are equivalent. For example:
- 160+(0.2)⋅160
- 160⋅(1.2)
- 160+160÷5
- 160⋅56
- 192−(0.25)⋅92
- 192⋅(0.75)
- 192−192÷4
- 192⋅43
If any students drew representations like tape diagrams and used them to reason, it is worth taking the time to make connections between the diagrams and the numerical expressions.
Standards
- 7.EE.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. <em>For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.</em>
- 7.EE.B.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
10 min
20 min
Knowledge Components
All skills for this lesson
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Recalling Percent Change
10 min
Narrative
This Warm-up refreshes students' memory of strategies for working with percent-change situations, preparing them to apply this understanding to situations of exponential change.
As students work, look for the different strategies that they use to answer the questions. For example, students might think of the first question as (0.2)⋅160, as 51⋅160, or as, 160÷5 all of which can be calculated mentally. Others might draw a tape diagram to represent the quantities and their relation to each other. Invite students with contrasting strategies to share later.
Also, to help inform the activities ahead, notice the different ways in which students approach and express the percent decrease situations.
Student Task
A scooter costs $160.
For each question, show your reasoning.
- The cost of a pair of roller skates is 20% of the cost of the scooter. How much do the roller skates cost?
- A bicycle costs 20% more than the scooter. How much does the bicycle cost?
- A skateboard costs 25% less than the bicycle. How much does the skateboard cost?
Sample Response
- $32
- $192
- $144
Activity Synthesis (Teacher Notes)
Select students to share how they approached the questions. Record their responses for all to see. Focus the discussion on the last two questions. Note the different ways in which students expressed 20% more than $160 and 25% less than $192 and why the expressions are equivalent. For example:
- 160+(0.2)⋅160
- 160⋅(1.2)
- 160+160÷5
- 160⋅56
- 192−(0.25)⋅92
- 192⋅(0.75)
- 192−192÷4
- 192⋅43
If any students drew representations like tape diagrams and used them to reason, it is worth taking the time to make connections between the diagrams and the numerical expressions.
Standards
- 7.EE.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. <em>For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.</em>
- 7.EE.B.3·Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.