# Lesson 8

Percentage Situations

### Lesson Narrative

In this lesson, students are introduced to contexts involving markups and discounts as they continue to study contexts involving tax and tips. An optional activity also includes a context of commissions.

Questions about rounding may naturally come up in this lesson. This lesson primarily involves dollar amounts, so it is sensible to round to the nearest cent (the nearest hundredth of a dollar). Percentages may be rounded to the nearest whole percent or fraction of a percent, depending on the situation.

Then, students solve a variety of multi-step percentage problems from a variety of situations including problems involving fractional percentages. They continue to move toward using equations to represent problems, which enables them to see the common underlying structure behind different problems (MP7). For example, $$1.2x$$ can represent

• a 20% increase in $$x$$.
• the total bill when 20% tax is added.
• the total bill when a 20% tip is added.
• the retail price when the wholesale price is marked up by 20%.

This lesson includes 2 optional activities. Consider using the activity Commission at a Gym if this additional context is interesting to students. Consider using the card sort activity if students would like to see more financial math.

### Learning Goals

Teacher Facing

• Comprehend “interest,” “markup,” “markdown,” and “commission” as other contexts that involve adding or subtracting a percentage of the initial amount.
• Determine what information is needed to solve a problem involving sales tax and discounts. Ask questions to elicit that information.
• Explain (orally) how to calculate the new dollar amount after a markup, markdown, or commission.
• Interpret (orally and in writing) tape diagrams that represent situations involving a sales tax, tip, or discount.

### Student Facing

Let's find unknown percentages.

### Required Preparation

Print and cut up slips from the Card Sort: Percentage Situations blackline master. Prepare 1 copy for every 2 students. These may be re-used if you have multiple classes.

It is recommended that students be provided access to four-function calculators so that they can focus on reasoning about how numbers are related to each other, representing those relationships, and deciding which operations are appropriate (rather than focusing on computation.)

### Student Facing

• I can find the percentage increase or decrease when I know the original amount and the new amount.
• I understand and can solve problems about commission, interest, markups, and discounts.

Building On