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**MEDIA RESOURCES FROM THE GET THE MATH **

- The Setup
**(video)***Optional*

An introduction toand the professionals and student teams featured in the program.*Get the Math* - Math in Fashion: Introduction
**(video)**

This video segment introduces Chloe Dao as she shares her path to becoming the*Project Runway*Season 2 winner. The mathematics used in fashion design is explained to viewers and a challenge is presented. - Math in Fashion: Take the challenge
**(web interactive)**

In this interactive activity users try to solve the challenge posed by Chloe Dao in the video segment, Math in Fashion: Introduction. - Math in Fashion: See how the teams solved the challenge
**(video)**

The teams use algebra to solve a mathematical fashion challenge presented by Chloe Dao. - Math in Fashion: Try other fashion challenges
**(web interactive)**

In this activity students are challenged to use mathematical reasoning and skills to modify original designs (cargo pants, a jacket and a dress) to meet specified price points.

**MATERIALS/RESOURCES**

*For the class:*

- Computer, projection screen, and speakers (for class viewing of online/downloaded video segments)
- One copy of the “Math in Fashion: Take the challenge” answer key (download DOC | PDF)
- One copy of the “Math in Fashion: Try other fashion challenges” answer key (download DOC | PDF)

*For each student:*

- One copy of the “Math in Fashion: Take the challenge” handout (download DOC | PDF)
- One copy of the “Math in Fashion: Try other fashion challenges” handout (download DOC | PDF)
- One calculator for use in Learning Activities 1 and 2 (Optional)
- Grid paper, chart paper, whiteboards/markers, overhead transparencies or other materials for students to display their math strategies used to solve the challenges in the Learning Activities.
- Computers with internet access for Learning Activities 1 and 2. (Optional)

(Note: These activities can either be conducted with handouts provided in the lesson and/or by using an online simulation on thewebsite.)*Get the Math*

**BEFORE THE LESSON**

Prior to teaching this lesson, you will need to:

- Preview all of the video segments and web interactives used in this lesson.
- Download the video clips used in the lesson to your classroom computer(s) or prepare to watch them using your classroom’s internet connection.
- Bookmark all web interactives you plan to use in the lesson on each computer in your classroom. Using an online bookmarking tool (such as delicious, diigo, or portaportal) will allow you to organize all the links in a central location.
- Make one copy of the “Math in Fashion: Take the challenge” handout for each student.
- Make one copy of the “Math in Fashion: Try other fashion challenges” handout for each student.
- Print out one copy of the “Math in Fashion: Take the challenge” and “Math in Fashion: Try other fashion challenges” answer keys.

**THE LESSON**

** **

**INTRODUCTORY ACTIVITY**

- Begin with a brief discussion about clothing and fashion. For example, ask if any of the students make their own clothes.
- Let students know that today’s lesson will focus on the world of fashion and will include mathematical challenges related to fashion. Ask students to brainstorm where they think mathematics may be used in fashion.
*(Measuring clothing, calculating costs, etc.)* - Explain that in today’s lesson they will be watching video segments and using interactives from
, a program that highlights how math is used in the real world. If this is your first time using the program with this class, you may choose to play the video segment The Setup, which introduces the professionals and student teams featured in*Get the Math*.*Get the Math* - Introduce the video segment Math in Fashion: Introduction by explaining that you are about to show a video segment which highlights how fashion designer and
*Project Runway Season 2*winner Chloe Dao uses algebraic reasoning in her work. Ask students to watch for the math the designer uses and to write down ideas to share with the class. - Play Math in Fashion: Introduction. After showing the segment, ask students to discuss the different ways Chloe Dao uses math in her work. (
*Sample responses: order of operations with whole numbers, decimals, and fractions; measurement, percents, inequalities.)* - Ask students to describe the challenge that Chloe Dao posed to the teams in the video segment.
*(Chloe designed a beaded top which has a retail cost of $40.65. The price needs to come down to $35 or less. Chloe challenged the teams to change the original design hit that price point, keeping in mind that there is a 220% markup from wholesale to retail.)*

**LEARNING ACTIVITY 1**

- Let students know that they will now have an opportunity to solve the problem. Explain that when Chloe’s designs are sold, the wholesale cost of her item is increased to 220% of the original amount to determine the retail price.
- Ask students to think of other situations in real life where a total amount of an item might be increased or decreased by a certain percentage. (
*Ask the following questions to spark discussion:*When you go shopping, if you total the prices listed on the items you want to buy is that the total amount you will pay as you leave the store?*(Not always.)*What additional costs may be needed to figure this out?*(Sales tax or a percent of increase of the original amount must be included.)*Discuss what you can do if you realize the total cost is too high and over your target for how much you wanted to spend.*(You would have to change what was in your cart and decide on the best choices given the target amount you want to spend.)* - Review the following terminology with your students:
**Wholesale cost:***the total cost of materials and labor needed to create a garment.***Retail price:***the price of the garment that includes the total cost of materials and labor, increased by a percent of this original amount.***Markup:***percent of increase compared to the original cost.***Labor cost:***the cost of the work needed to produce a garment, which might include cutting, grading, and sewing the garment.***Percent:***a ratio that compares a number to 100.*

- Distribute the “Math in Fashion: Take the challenge” handout (including the cost sheet) to each student. Ask students to work together to complete the handout. As they complete the challenge, encourage students to examine the cost sheet to see the original costs and Chloe Dao’s suggestions for alterations.

*Note: Students can either complete this activity by using the student handout provided in this lesson and/or by completing the challenge on the***Get the Math website.****If you have multiple computers***, ask students to work in small groups to explore the interactive and complete the handout.***If you only have one computer**, conduct the activity with your students as a group, or students may work in small groups off-line by using the student handout.

- As students complete the challenge, encourage them to use the following 6-step mathematical modeling cycle to solve the problem:
*Step 1:**Understand the problem:*Identify variables in the situation that represent essential features*(For example, let “w” represent the wholesale cost and “r” represent the retail price).**Step 2:**Formulate a model by*creating and selecting multiple representations*(For example, students may use symbolic representations such setting up a proportion or an inequality).**Step 3:**Compute*by analyzing and performing operations on relationships to draw conclusions*(For example, operations include multiplication and algebraic transformations used to determine cross products as they solve a proportion or inequality).**Step 4:**Interpret*the results in terms of the original situation*(The results of the first three steps should be examined in the context of the challenge to change the garment to meet the maximum retail price point).**Step 5:*Ask students to*validate*their conclusions by comparing them with the situation, and then either improving the model or, if acceptable,

**Assess**the reasoning process and product by asking students to articulate how they are solving the challenge:- What strategy are you using to find the maximum wholesale cost?
- How will your strategy for selecting changes to the design help you to meet the retail target price? Why did you select these choices?

- After students have completed the handout, ask each group to share their solutions and problem-solving strategies with the class using whiteboards, overhead transparencies, chart paper, or other tools. Refer to the “Math in Fashion: Take the challenge” answer key, as needed, to provide more details about possible strategies and solutions.
- As students present their solutions, ask them to discuss the mathematics they used in solving the challenge. (
*Possible responses: fractions, proportions, ratios, percents, inequalities, multiplication, division, rounding.)* - Introduce the Math in Fashion: See how the teams solved the challenge video segment by letting students know that they will now be seeing how the teams in the video solved Chloe Dao’s challenge. Ask students to observe what strategies the teams used and whether they were similar to or different from the strategies presented by the class.
- Play Math in Fashion: See how the teams solved the challenge. After showing the video, ask students to discuss the strategies the teams used and to compare them to the strategies presented by the class. During the discussion, point out that the teams in the video solved the challenge in two distinct ways. Discuss the strategies listed in the “Math in Fashion: Take the challenge” answer key, which you have not yet discussed.

**LEARNING ACTIVITY 2:**

- Go to Math in Fashion: Try other fashion challenges.
- Let your students know that they will now use a web interactive to solve additional fashion challenges. They will be able to redesign cargo pants, a prom dress, and a jacket to hit specific price points.

*Note: You can conduct this activity with one computer and an LCD projector in front of the entire class or, if you have multiple computers, your students can work in small groups on computers to complete the activity. If you are using one computer, examine each garment as a group and have your students determine the wholesale price and the changes they would make in order to hit the retail price point. If you are using multiple computers, encourage students to brainstorm strategies and solutions with each other. This activity can also be assigned to students to complete as an independent project or as homework using the “Math in Fashion: Try other fashion challenges” handout as a guide.* - Distribute the “Math in Fashion: Try other fashion challenges” handout. Clarify and discuss the directions.
- As in Learning Activity 1, encourage your students to use the 5-step mathematical modeling cycle as they develop their strategies to solve the challenge.
- After students have completed the activity, lead a group discussion where they can share their strategies and solutions. Refer to and discuss the strategies and solutions presented in the “Math in Fashion: Try other fashion challenges” answer key, as desired.

**CULMINATING ACTTIVITY**

- Assess deeper understanding: Ask your students to reflect upon and write down their thoughts about the following:
- How did you determine an effective strategy for solving the problem? What are your conclusions and the reasoning behind them?
- Compare and contrast the various numerical and algebraic representations possible for the problem. How does the approach used to solve the challenge affect the choice of representations?
*(Sample answers: some approaches use numerical operations in a sequence or order; another approach is to use symbols or variables to represent what is unknown and then write a proportion to solve the problem.)*Are all equivalent?*(Yes.)*Why do you think this is the case?*(There are many different ways to represent and solve a problem; a proportion is an equation that can be written using ratios that are equivalent but in a different order as long as some common element ties the numerators together and a common element ties the denominators together, such as dollars and cents.)* - Why is it useful to represent real-life situations algebraically? (Sample responses: symbols or variables can be used to represent missing values to set up and solve equations to find a solution; using algebra can be a simpler and efficient way to set up and solve problems by using ratios, rates, or proportions.)
- What are some ways to represent, describe, and analyze patterns that occur in our world?
*(Sample responses: patterns can be represented with numbers, symbols, expressions/equations, words, and pictures or graphs.)*

- How did you determine an effective strategy for solving the problem? What are your conclusions and the reasoning behind them?
- After students have written their reflections, lead a group discussion where students can share their thoughts. During the discussion, ask students to discuss how math in general and algebra in particular can be applied to the world of fashion. Ask students to brainstorm other real-world situations which involve the type of math and problem solving they used in this lesson to calculate the target price point and to select and calculate changes to the garments.

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