## Perfumania

By Tonya Adison, November 5, 2006

### Grade Level

- High School

### Category

- Product Design

### Subject Area

- Mathematics

### Lesson Time

### Introduction

### National Standards

**Math Standards**

- Understand meanings of operations and how they relate to one another

- Use mathematical models to represent and understand quantitative relationships

- Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

- Understand measurable attributes of objects and the units, systems, and processes of measurement
- Apply appropriate techniques, tools, and formulas to determine measurements

- Build new mathematical knowledge through problem solving;
- Solve problems that arise in mathematics and in other contexts
- Apply and adapt a variety of appropriate strategies to solve problems

- Recognize reasoning and proof as fundamental aspects of mathematics
- Make and investigate mathematical conjectures

- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

- Recognize and use connections among mathematical ideas;
- Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
- Recognize and apply mathematics in contexts outside of mathematics

**Common Core Standards**

Anchor standards for Speaking and Listening:

Comprehension and Collaboration:

CCSS.ELA-LITERACY.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively.

CCSS.ELA-LITERACY.CCRA.SL.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

CCSS.ELA-LITERACY.CCRA.SL.3 Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric.

**Presentation of Knowledge and Ideas:**

CCSS.ELA-LITERACY.CCRA.SL.4 Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

CCSS.ELA-LITERACY.CCRA.SL.6 Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.

Anchor standards for Language:

**Conventions of Standard English:**

CCSS.ELA-LITERACY.CCRA.L.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Vocabulary Acquisition and Use:

CCSS.ELA-LITERACY.CCRA.L.6 Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

### Objectives

- identify various geometric shapes
- apply the given formulas to determine the volume of these shapes and other shapes in relevant situations
- design their own container to conform to specifications provided
- use their knowledge of volume formulas and shapes to compute volumes of other shapes using proportions

### Resources

### Materials

- rulers (one for each student)
- several perfume/cologne bottles (at least one per group)
- calculators
- construction paper
- graph paper
- student handout
- formula handout

### Vocabulary

**Volume**–the measure of the amount of space a solid figure occupies

**Cube**–A solid figure with six square faces

**Rectangular Prism**–A solid figure with six rectangular faces

**Pyramid**–A three-dimensional figure that has a polygon for its base and whose faces are triangles having a common vertex

**Sphere**–A three-dimensional figure with all points in space a fixed distance from a given point, called the center

**Cylinder**–A three-dimensional figure having two parallel bases that are congruent circles

**Cone**–A three-dimensional figure with one vertex and a circular base

### Procedures

**Set-up:**The teacher should predetermine groups of 3-4 students and have a bottle of perfume/cologne for each student group. (Given the safety considerations, if the teacher does not feel comfortable with students handling the usually glass bottles, teacher can use Styrofoam shapes and label them with various perfume/cologne fragrances.)

**Teacher Motivation:**Students are commissioned by Jennifer Lopez to design a bottle for her new fragrance (“Still”). They will use the knowledge gained in this lesson to complete this task.

**Teacher Presentation:**Teacher starts with a question about the students’ favorite fragrances and probes the students to elicit more descriptions of the bottles in which these fragrances are packaged. The teacher then asks the students what these bottles have in common.

**Students in Groups:**

**Wrap-Up:**Teacher/student discussion on what, if anything, surprised the students. Which designs do you like and why?

### Assessment

### Enrichment Extension Activities

**Activity 1: A new shape?**Consider the wedge shaped bottle. How can we determine the volume of this shape using what we already know? (One-quarter of a cylinder!)

**1. Students are asked to look at the underside of their bottles and see if their calculations were correct. (How close are you?) 2. Students will notice that their answers are not consistent with the numbers stated on the bottle.**

**Activity 2: Conversion using Proportions****TEACHING INTERJECTION:**Explain to students that their volume calculations need to be converted into either ounces or milliliters. This can be done using proportions (previously covered material). Provide students with conversion information. 3. Students convert their findings to milliliters and ounces. 4. If wrong, students discuss the reasons their answers still do not equal the measurements on the underside of their bottles.

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