Percentage Contexts

5 min

Narrative

The purpose of this Warm-up is to help students connect their current work with percentage contexts to their prior work on efficient ways of finding percent increase.

Launch

Consider telling students that these questions may have more than one correct answer. Arrange students in groups of 2. Give 2 minutes of quiet think time followed by partner discussion. Then hold a whole-class discussion.

Student Task

Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?

15⋅2015 \boldcdot 20

20+0.15⋅2020 + 0.15 \boldcdot 20

1.15⋅201.15 \boldcdot 20

15100⋅20\frac{15}{100} \boldcdot 20

Sample Response

The last expression represents the tip, while the second and third expressions represent the total bill.

Synthesis

For each expression, ask a few students to explain whether they think it represents the total bill, the tip, or neither. For each expression, select a student to explain their reasoning. Invite other students to share whether they agree or disagree and why, or how they might explain it differently.

Standards
Building On
  • 6.EE.2.b·Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. <em>For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.</em>
  • 6.EE.A.2.b·Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. <span>For example, describe the expression <span class="math">\(2 (8 + 7)\)</span> as a product of two factors; view <span class="math">\((8 + 7)\)</span> as both a single entity and a sum of two terms.</span>
  • 6.RP.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.
  • 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
  • 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>

20 min

10 min