Percentages come in handy in understanding anything from sports to news and of course, shopping. However, around 80% of the population struggle with understanding percentages. Animator Josh Kurz explains the math behind common percentages in three videos clips.

**Find hundreds more engaging math-focused media and integrated activities, all aligned with CCSS at PBS LearningMedia.**

**Class Activity**

**Learning Outcomes**

Students will be able to

- calculate a sale price when given an original price and percent discount
- explain the difference between percent of and percent off a price

**Common Core State Standards:** 6.RP.A.1, 6.RP.A.3c, 7.RP.A.3

**Vocabulary: **Percent off, percent of

**Materials:** Per student: calculator, paper, pencil, two to three copies of attached 10 x 10 grid; for the class: a few large 10 x 10 grids for demonstration

**Preparation:** Make copies of the 10 x 10 grid.

**Procedure**

**1. Introduction (5 minutes, whole group and pairs)**

Distribute the materials. Ask students to solve the following problem with a partner: A jacket is regularly priced at $50. You buy it on sale for 10% off. What do you pay?

As students share strategies with the class, prompt them to point out when they’re finding *percent off* the original price and when they’re finding *percent of* the original price.

If no one has used a 10 x 10 grid, model it for them. First, cross out 10 squares to show 10% off. Prompt students to consider what the whole, the 10 squares crossed out, and a single square represent (Answer: $50, $5, 50¢). Then, ask students to determine what price the remaining 90 squares represent.

In discussion, emphasize the variety of possible solution strategies.

**2. Video and Problem Solving (20 minutes, whole group and pairs)**

Ask students to solve the following problem with a partner: What would a pair of $130 shoes cost at 20% off?

After students work for a few minutes, show them the video, pausing for discussion at these times:

- At 0:10 (optional), help students see the relationship between the blocks (the “chunks”) and the 10 x 10 grid model.
- At 0:57, ask students, Did anyone start by calculating 20%? By finding 1%?
- At 1:15, ask, Did anyone calculate 80% as shown in the video? What other strategies did you use? Suppose you can either use a $20 off coupon or take 20% off. Which would be a better deal? Why?
- At 1:57, ask students to discuss the following problem in pairs: Suppose you are buying items that cost $90. Which would be a better deal, a 20% off coupon or $20 off? How do you know?

After students share a few ideas, play the remainder of the video.

**3. Conclusion (5 minutes, pairs and whole group)**

Ask students to work in pairs to write a story problem in which a 15% discount is a better deal than a $15 discount and another in which the reverse is true.

As time permits, ask a few students to share their story problems with the class.

**Activity Extension:** Ask students to determine what an item would cost if both $20 off and 20% off yield the same discount.

*This activity is based on work developed at TERC.*