In this partner activity, students take turns matching situations to terms that describe applications of percent increase and decrease: sales tax, interest, gratuity/tip, markdown/discount, markup, commission, and depreciation. The situations are written on slips of paper and the terms are listed on a sorting mat.

It is not necessary for students to memorize the meanings of all these financial terms. The goal is for students to see that there are many different ways that percent increase and decrease are applied to money in the real world. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Invite students to share which situations they sorted under each word. Ask them:

• “What made you decide to put these situations under this descriptor?”
• “Were there any situations that you were really unsure of? What made you decide on where to sort them?”

Invite students to share their sentences describing what the percent increase or decrease told us about the situation. If they do not specify what amount corresponds to 100%, ask them to revise their sentence to add in that information. For example, if a student says “Andre’s interest was 3%,” they could rephrase this as “Andre’s interest was 3% of his starting balance.”

Answer students’ remaining questions about any of these contexts. Tell students there is a chart at the end of the lesson that they can use as a reference tool during future lessons. The key takeaway is that these are all different ways that percent increase or percent decrease are applied to money in the real world.

Math Community
Conclude the discussion by inviting 2–3 students to share a norm they identified in action. Provide this sentence frame to help students organize their thoughts in a clear, precise way:

• “I noticed our norm ‘’ in action today, and it really helped me/my group because .”

In this activity, students apply their understanding of percent increase and decrease to a context involving markup and markdown. They see that a 32% increase followed by a 10% decrease of that new amount does not result in a 22% increase of the original amount. As students relate the percentages to the quantities they represent, they reason abstractly and quantitatively (MP2).

Monitor for students who use these different strategies to calculate the discounted price of the car:

• Create a diagram to represent the situation.
• Multiply the retail price by 0.1, and then subtract this amount.
• Multiply the retail price by 0.9.
• Multiply the wholesale price by 1.22.

Plan to have students present in this order to support moving them from the more concrete to the more abstract and efficient. Note that the last strategy on the list incorrectly oversimplifies the situation.

The purpose of this discussion is to compare different strategies for finding the sale price after both a markup and a markdown. Invite previously selected students to share how they found the price the customer pays for the car. Sequence the discussion of the strategies in the order listed in the Activity Narrative. If possible, record and display the students’ work for all to see.

Connect the different responses to the learning goals by asking questions, such as:

• “How does the 10% discount show up in each method?”
• “Why do the different approaches lead to the same outcome?”
• “Are there any benefits or drawbacks to one strategy compared to another?”

The key takeaway is that finding 90% of the retail price is equivalent to—and more efficient than—calculating the 10% discount and then subtracting that amount from the retail price.

If a student tried to find the sale price by calculating 122% of the wholesale price, ask “Why does this approach lead to a different outcome?” If no student tried to find the sale price by calculating 122% of the wholesale price, consider asking “Jada thought that the final markup percentage would be 22%, because . Why is this incorrect?”