“When will we use this stuff?”
Responding to this question can be frustrating for math teachers and students alike, but it presents an excellent opportunity for you. You have the green light to explain the value of developing life skills and how the content is in fact practical.
Connecting some content to real life can be difficult, but that isn’t the case for percentages. Percentages are used to calculate a company’s profits, interest rates on a loan and an athlete’s performance. As all the shopping and discounts during Black Friday highlight, percentages are central to locating the best deals.
Students can use the beginning of the holiday shopping season to better understand the value of percentages and practice applying them to prices. The following lesson is appropriate for grades 5-8. You can upscale the content for older students (see “Reinforcing the Lesson” for ideas).
Students will enhance their understanding of percentages and be better able to use percentages, proportions, decimals and fractions. The lesson will focus on three specific outcomes:
- Calculating sale prices based on common, percentage-based price reductions
- Proficiency using a calculator to calculate sale prices
- Awareness that percentages can be expressed as proportions, decimals and fractions
- Writing utensils (pencils, colored pencils or crayons)
- Advertisements on newspapers or another source
- Worksheets that include columns for item name, retail price, sale percentage, and new sale price
Start the lesson by getting students to think about sales. Have they ever bought something that was more than 50 percent off? What’s the best deal they have ever gotten on an item?
Explain how shoppers can save hundreds of dollars during Black Friday if they know where to look — and how to calculate discounts. For instance, a 4K television may regularly cost $1,000, but after a 25 percent discount, someone can save $250 on the price. Explain how sales can be expressed in different ways. An ad for the television may say something like “save $250,” “25 percent off,” or “take ¼ off the retail price.”
The price tag is not always what consumers pay. Sometimes there is a percentage or fraction given for the sale, which can help gauge how much of a deal is being offered. Students need to know how much they’re saving so they can decide where (or if) to purchase the product. They also need to be comfortable converting figures to and from percentages. If the ad contains the dollar amount, students may still need to know the percentage discount when comparing it to other sales.
- After introducing the topic of percentages, hand out worksheets and advertisements to the class to get started with the lesson.
- Do one example as a class. Take the first item and note the retail price and sale percentage. Go through the steps needed to solve for the new sale price. Make sure you point out how percentages can be represented as decimals and fractions. For instance, 25 percent is the same as 0.25 or ¼. Once the class has figured out the correct answer, ask a follow-up question, making a slight adjustment to the example. If the example was 25 percent off a $50 item, ask someone to calculate the price of the item if it were 15 percent off.
- Split the class into small groups or pairs. Have each group solve the answers on one section of the worksheet. Groups should solve two to four questions (or based on how much time you’d like this step to take).
- Once groups have had enough time to solve the questions, have one member of each group explain their answers to the class. Intertwine follow-up questions with helpful tips and shortcuts. For instance, instead of a calculator for figuring out 25 percent off a $50 item, students can, in their heads, take half of $50 ($25; to obtain 50 percent), half of $25 ($12.5; to obtain 25 percent), and then subtracting that from the original price ($50 minus $12.5).
Reinforcing (or Upscaling) the Lesson
Adding onto the lesson with other activities and games can help students understand percentages even more. It’s also great for upscaling the lesson or for students who need more of a challenge. Here are a few ideas:
- Do additional problems in a group or in class, implementing additional percentages beyond the discount. You could integrate sales tax and a bonus percentage off using store-based reward credit cards.
- Turn it into a shopping game. Give students a certain dollar amount to spend and see who can save the most, but from a list of items that don’t include the percentage discount. Just give the sale price and the normal price, which requires students to figure out the sale percentage.
- Provide students with the cost of sample items, which represents how much a store pays for the items. Would certain items turn a profit if a store pays a certain amount (cost), offers it at a certain amount (retail price), but advertises a deep discount (sale price)? Have students determine the tipping point of profitability from the retailer’s perspective.
There are several more ways to help students learn more about percentages. When you add relevance to teaching mathematics, you help do more than build math skills — your efforts enhance literacy, interest in math and engagement in authentic learning experiences that connect to problem-solving in the real world. Relating mathematics to the real-world inspires students to ask questions, seek answers and develop a passion for the subject.
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