Lesson 8: Percent Increase and Decrease with Equations

Percent Increase and Decrease with Equations

5 min

Teacher Prep

Setup

Display one problem at a time. 30 seconds of quiet think time per problem, followed by partner then whole-class discussion.

Narrative

This Math Talk focuses on finding the factor that scales 50 to another number. It encourages students to think about increase and decrease in terms of fractions, decimals, or percentages and to rely on properties of operations to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students write equations to represent percent increase or decrease situations.

As students use results from the previous equation to help solve the next equation, they are making use of repeated reasoning (MP8).

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 access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Solve each equation mentally.

$a \boldcdot 50 = 10$
$b \boldcdot 50 = 60$
$c \boldcdot 50 = 51$
$d \boldcdot 50 = 49$

Sample Response

Sample responses:

$a = 0.2$ (or equivalent). Sample reasoning: 10 is $\frac15$ of 50, so $a$ can be $\frac15$ , or 0.2, which is the equivalent decimal.
$b = 1.2$ (or equivalent). Sample reasoning: 60 is equal to $50 + 10$ , and by the distributive property, $50 + 10 = 50 (1 + 0.2)$ .
$c = 1.02$ (or equivalent). Sample reasoning: 1 is $\frac{1}{10}$ of 10, and $\frac{1}{10}$ of 0.2 is 0.02. And 51 is equal to $50 + 1$ . By the distributive property, $50 + 1 = 50 (1 + 0.02)$ .
$d = 0.98$ (or equivalent). Sample reasoning: 51 is equal to $50 - 1$ , and by the distributive property, $50 - 1 = 50 (1 - 0.02)$ .

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

If all students give their answers as fractions, encourage them to express the fraction as a decimal. This will help prepare students for working with equations where decimals are used to represent percent increase or decrease.

If any student expresses their reasoning in terms of percentages, for example, by saying that 60 is a 20% increase from 50, highlight this strategy for all to see.

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

, so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Building Toward

7.RP.3·Use proportional relationships to solve multistep ratio and percent problems.
7.RP.A.3·Use proportional relationships to solve multistep ratio and percent problems. <span>Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.</span>

15 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Percent Increase and Decrease with Equations

5 min

Teacher Prep

Setup

Display one problem at a time. 30 seconds of quiet think time per problem, followed by partner then whole-class discussion.

Narrative

As students use results from the previous equation to help solve the next equation, they are making use of repeated reasoning (MP8).

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.

Student Task

Solve each equation mentally.

$a \boldcdot 50 = 10$
$b \boldcdot 50 = 60$
$c \boldcdot 50 = 51$
$d \boldcdot 50 = 49$

Sample Response

Sample responses:

$a = 0.2$ (or equivalent). Sample reasoning: 10 is $\frac15$ of 50, so $a$ can be $\frac15$ , or 0.2, which is the equivalent decimal.
$b = 1.2$ (or equivalent). Sample reasoning: 60 is equal to $50 + 10$ , and by the distributive property, $50 + 10 = 50 (1 + 0.2)$ .
$c = 1.02$ (or equivalent). Sample reasoning: 1 is $\frac{1}{10}$ of 10, and $\frac{1}{10}$ of 0.2 is 0.02. And 51 is equal to $50 + 1$ . By the distributive property, $50 + 1 = 50 (1 + 0.02)$ .
$d = 0.98$ (or equivalent). Sample reasoning: 51 is equal to $50 - 1$ , and by the distributive property, $50 - 1 = 50 (1 - 0.02)$ .

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

If any student expresses their reasoning in terms of percentages, for example, by saying that 60 is a 20% increase from 50, highlight this strategy for all to see.

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

, so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Building Toward

7.RP.3·Use proportional relationships to solve multistep ratio and percent problems.
7.RP.A.3·Use proportional relationships to solve multistep ratio and percent problems. <span>Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.</span>

Percent Increase and Decrease with Equations

Warm-upMath Talk: Starting with 505 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityMatching Equations15 minKCs

ActivityDecorating Fabric15 minKCs

Knowledge Components

Percent Increase and Decrease with Equations

Warm-upMath Talk: Starting with 505 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityMatching Equations15 minKCs

ActivityDecorating Fabric15 minKCs

5 min

15 min

15 min

5 min

15 min

15 min