Lesson 11

The purpose of this warm-up is to help students connect their current work with percentage contexts to their prior work on percent increase and efficient ways of finding percent increase.

Consider telling students that these questions may have more than one correct answer. Students in groups of 2. 2 minutes of quiet think time followed by partner and then whole-class discussion. 

For each expression, ask a few students to explain whether they think it represents: the total bill, the tip, or neither. For each expression, select a student to explain their reasoning.

The purpose of this activity is to introduce students to a context involving markups and markdowns or discounts, and to connect this to the work on percent increase and percent decrease they did earlier. The first question helps set the stage for students to see the connection to markups and percent increase. Look for students who solve the second question by finding 90% of the retail price, and highlight this approach in the discussion.

Tell students that a mark-up is a percentage that businesses often add to the price of an item they sell, and a mark-down is a percentage they take off of a given price. If helpful, review the meaning of wholesale (the price the dealership pays for the car) and retail price (the price the dealership charges to sell the car). Sometimes people call mark-downs discounts.

Provide access to calculators. Students in groups of 2. Give students 5 minutes of quiet work time, followed by partner then whole-class discussion.

It is important throughout that students attend to the meanings of particular words and remain clear on the meaning of the different values they find. For example, "wholesale price," "retail price," and "sale price" all refer to specific dollar amounts. Help students organize their work by labeling the different quantities they find or creating a graphic organizer.

For the first question, help students connect markups to percent increase.

Select students to share solutions to the second question. Highlight finding 90% of the retail price, and reinforce that a 10% discount is a 10% decrease.

Ask them to describe how they would find (but not actually find) . . . 

• "The retail price after a 12% markup?" (Multiply the retail price by 0.12, then add that answer to the retail price. Alternatively, multiply the retail price by 1.12.)
• "The price after a 24% discount?" (Multiply the retail price by 0.24, then subtract that answer from the retail price. Alternatively, multiply the retail price by 0.76.)

The purpose of this activity is to introduce students to the concept of a commission and to solve percentage problems in that context. Students continue to practice finding percentages of total prices in a new context of commission.

Monitor for students who use equations like \(c = r \boldcdot p\) where \(c\) is the commission, \(r\) represents the percentage of the total that goes to the employee, and \(p\) is the total price of the membership.

Tell students that a commission is the money a salesperson gets when they sell an item. It is usually used as an incentive for employees to try to sell more or higher priced items than they usually would. The commission is usually a percentage of the price of the item they sell.

Provide access to calculators. Students in groups of 2. Give students 2 minutes of quiet work time. Partner then whole-class discussion.

Students may find the percentage of an incorrect quantity. Ask them to state, in words, what they are finding a percentage of.

Students may not understand the first question. Tell them that a membership is sold for a certain price and the money is split with \$42 going to the gym and \$8 going to the employee.

Select students to share how they answered the questions.

During the discussion, draw attention to strategies for figuring out which operations to do with which numbers. In particular, strategies involving equations like \(c = r \boldcdot p\) where \(c\) is the commission, \(r\) represents the percentage of the total that goes to the employee, and \(p\) is the total price of the membership.

This activity gives students an opportunity to practice various vocabulary terms that come along with percentages. Students are asked to sort scenarios to different descriptors using the images, sentences or questions found on the scenario cards. The questions found on the scenario cards are intended to help students figure out which descriptor the scenario card belongs under.

As students work on the task, identify students that are using the vocabulary: tip, tax, gratuity, commission, markup/down, and discount. These students should be asked to share during the discussion.

Arrange students in groups of 2. Distribute the sorting cards, and explain that students will sort 8 scenarios into one of 6 categories. Demonstrate how students can take turns placing a scenario under a category and productive ways to disagree. Here are some questions they might find useful:

• Which category would you sort this under?
• What do you think this word means?
• What words can we use as clues about where to sort this card?

Students should use the question at the bottom of the card to help them if they get stuck sorting the scenarios.

Ask identified 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?"

Consider asking some groups to order the situations from least to greatest in terms of the dollar amount of the increase of decrease and asking other groups to order them in terms of the percentage. Then, have them compare their results with a group that did the other ordering.

Answer students’ remaining questions about any of these contexts. Tell students there is a copy of this chart at the end of the lesson that they can use as a reference tool during future lessons. Allow them a space to take notes on their own to remember it or details from one of the activity examples.