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60-30-10

By Cooper-Hewitt National Design Museum, October 18, 2006

• Middle School

• Other

• Mathematics

Lesson Time

Two fifty-minute class periods

Introduction

In this activity students will use ratios and proportions to represent quantitative relationships as they investigate the concept of how percentages are used by designers. Students will decorate the same room using three different percentages of colors.

National Standards

Mathematics
Standard 2. Level III. Understands and applies basic and advanced properties of the concepts of numbers
1. Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation
Standard 3. Level III. Uses basic and advanced procedures while performing the processes of computation
1. Adds, subtracts, multiplies, and divides integers, and rational numbers
6. Uses proportional reasoning to solve mathematical and real-world problems (e.g., involving equivalent fractions, equal ratios, constant rate of change, proportions, percents)
8. Selects and uses appropriate estimation techniques (e.g., overestimate, underestimate, range of estimates) to solve real-world problems.
Standard 4. Level III. Understands and applies basic and advanced properties of the concepts of measurement
Common Core State Standards

English Language Arts Standards: Speaking and Listening

Comprehension and Collaboration:

CCSS.ELA-LITERACY.SL.6-8.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade level topics, texts, and issues, building on others' ideas and expressing their own clearly.

CCSS.ELA-LITERACY.SL.6-8.1.A Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.

CCSS.ELA-LITERACY.SL.6-8.2 Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation.

CCSS.ELA-LITERACY.SL.8.3 Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced.

Presentation of Knowledge and Ideas:

CCSS.ELA-LITERACY.SL.6-8.4 Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation.

CCSS.ELA-LITERACY.SL.6-8.5

Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.

CCSS.ELA-LITERACY.SL.6-8.6 Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 8 Language standards 1 and 3 here for specific expectations.)

Objectives

Students will do the following:
• explore how the concept of percentages can be expressed in everyday objects
• create three designs that use different percentages of colors

Materials

• paper and/or graph paper
• paint, markers, or colored pencils
• magazines and catalogs
• rulers

Procedures

Building Background Math and Business Suits
The purpose of this activity is to examine how an everyday object can be described in mathematical terms. 1. Bring in pictures from a clothes catalogue of a man's slacks, jacket, shirt, and tie. 2. Ask students to think about what percentage of the outfit's color is the slacks and jacket, what percentage of its color is the shirt, and what percentage is the color of the tie. 3. Students' answers should fall somewhere in the range of 60% for the suit and slacks, 30% for the shirt, and 10% for the tie. Involve the students in a discussion about why they think suits are often designed in this way.
Steps for Learning
The Percentage Challenge

The purpose of this activity is to provide students with an opportunity to use percentages to examine a real-world design problem.

1. Ask students if they think the same 60%-30%-10% formula used in designing business suits can be transferred to the decoration of a room.

2. Explain to students that they are going to use their knowledge of percent to design the following three rooms:

Room One:

• 60% of a dominant color
• 30% of a secondary color
• 10% of an accent color
Room Two:
• 75% of a dominant color
• 20% of a secondary color
• 5% of an accent color
Room Three:
• 45% of a dominant color
• 35% of a secondary color
• 20% of an accent color
3. Have students draw three empty rooms for this activity. Make three copies of each room the students draw. Provide access to the materials listed in the "Materials" section of this lesson. Have students paint/decorate the three rooms using the percentages listed above. 4. After students have finished decorating their rooms, have them show their rooms to the rest of the class. Ask the class members to choose which of the rooms they like the most. 5. Involve students in a discussion about which rooms students liked the most. Also discuss how they used percentages to investigate a design problem.

Reflection