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.
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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.
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.