## The Calculus Whiz Who Loved Candy

### Linda Knowles

#### Description

Students develop an equation for finding the volume of a commonly known piece of candy (M&M, Hershey's Kiss, Tootsie Roll Pop, Life Saver, etc.) by using calculus.

#### Objectives

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

Uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two- and three- dimensional shapes including rectangular solids, cylinders, cones and pyramids.

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

#### Materials

-Pencil
-Paper
-Graphing Calculator
-Ruler
-Graph paper
-Candy
-Calculus Candy worksheet (associated file)
-The Calculus of a Kiss worksheet (associated file)

#### Preparations

1. Locate a ruler, graphing calculator, a piece of candy and graph paper for each group or instruct the students to do this.
2. Find an example for review of each way to find the volume of a solid of revolution using calculus techniques (disk, washer and shell method) and prepare a transparency if you use an overhead.
3. Duplicate the worksheets found in the associated file. Have extra copies available for students.

#### Procedures

This lesson is part of a series of lessons entitled “The Calculus Whiz Who …”

Prior knowledge required: Students must be able to find the volume of a solid of revolution using calculus techniques. This must be done by integrating a function or functions and includes the method of disks, washers or shells.

1. Gain students' attention by telling them about the calculus whiz who was quite a math nerd (and proud of it). In fact, he wouldn’t do anything unless he could first apply his calculus knowledge to the situation, even eating a Hershey’s Kiss.

2. Review how to find the volume of a solid of revolution using the disk, washer or shell method.

3. Pass out to each student the Hershey’s Kiss example worksheet entitled “The Calculus of a Kiss”. (See associated file)

4. Go over the process used to find the volume of the Hershey’s Kiss outlined on the worksheet.

5. Place students in groups of three or four.

6. Pass out to each group a different piece of candy, a graphing calculator, a group worksheet entitled “Calculus Candy” (See associated file) and a piece of graph paper.

7. Tell them to follow the steps on the group worksheet using the Hershey’s Kiss worksheet as a guide.

8. Circulate around the room to help each group as needed. Pay attention to students who seem to be having difficulty and provide additional help as needed.

9. After groups have finished have them report to the class as a whole from their worksheets. Discuss and provide feedback especially for groups who are having difficulty. Take up and assess the group worksheet.

#### Assessments

Observe the group activity and assess the papers turned in from each group for accuracy (File Document #2). Since this is a group activity, observe carefully to see which individual students are having difficulty. During the class reporting, make sure that all members of the group participate in the discussion of answers. Note those who seem shaky in their explanations or unsure. Students who do not show mastery will need individual feedback and additional practice time.

When the teacher feels that students understand the concept and processes demonstrated in this lesson, students can do this assignment again individually on a different piece of candy.

#### Extensions

Suggest to the students that they can do this assignment again individually on a different piece of candy for additional practice. This would be a great practice for students who are having difficulty. Be sure to offer a time to review their work.

#### Attached Files

2 worksheets.     File Extension: pdf