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A Recipe For Success
by Roger C. Henderson
Boise State University

Grade: 6th
Time Allotment: One 45-minute class period
Subject Matter: Mathematics

Overview:
This is an interactive, media enhanced lesson that requires students to examine ratios and proportions. The primary goal is to develop connections between math and real-world situations. Through the use of video, students will explore a relevant application of ratios and proportions. Using the internet, students will apply this concept through guided practice and interactive feedback. Students will then make connections to other real-world examples by applying this knowledge to similar problems in other areas. This lesson incorporates mathematical skills, reading, and writing in an interdisciplinary format.

Learning Objectives:
Students will be able to:

  • Apply equivalent ratios
  • Apply scaling to ratios and proportions
  • Apply ratios and proportions in real-life situations

Standards:
National Standards:
(From National Council of Teachers of Mathematics grades K-12)

Idaho State Standards

I: Numbers and Operations

  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
  • Compute fluently and make reasonable estimates.
  • Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods
  • Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Problem Solving

  • Solve problems that arise in mathematics and in other contexts.
  • Apply and adapt a variety of appropriate strategies to solve problems.

Communication

  • Communicate mathematical thinking.

Connections

  • 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.

Media Components :
Video:
Cyberchase: For Real, "A Battle of Equals"
The trailing segments to Cyberchase called Cyberchase: For Real present real-world applications for mathematics. This segment addresses converting a recipe for popcorn balls.

Web Sites
Allrecepies
www.allrecipes.com
Allrecipes is a community-based recipe and meal planning web site on the internet. The site offers food ideas and resources including recipes, menu ideas, meal preparation tips, special diet content, culinary ware and news. A key aspect of the site is that it has a conversion feature that allows users to convert recipes for different serving sizes. The site has an area for kids that has desert recipes - for example, there is a recipe for a smack mix called "Puppy Chow" that can be found at: http://christmas.allrecipes.com/AZ/PuppyChow.asp

Materials:
Per Class

  • TV
  • VCR
  • Video
  • Overhead projector

Per Group of 3-4 Students

  • Computer with internet connection

Per Student:


Prep For Teachers

  • Bookmark the web site listed in Media Components. Make sure that the link is current and that the recipe conversion feature is still available. Search the kids' recipes and select 2 recipes for examples.
  • Make copies of the worksheet to distribute. One worksheet per 3 students.
  • Review the lesson plan. Pay particular attention to the sections containing Focus for Media Interaction. These sections contain specific tasks for students to complete and/or information to identify during or after viewing of video elements, web sites or other multimedia elements.

Introductory Activities
This "warm-up" activity is used to gain student interest. The activity is a group discussion to review the concepts of ratios and proportions.

Step 1
:
Get the students involved by asking the following questions:

  • "By a show of hands, how many of you enjoy cooking?"
  • If limited response, try "Again by a show of hands, how many of you enjoy eating?"

Step 2:
The teacher then explains, "Cooking commonly uses math." Expand on this idea with the following questions:"

  • Do you know what a recipe is?"
  • State with a bit of humor - "You are all very close. However, to be precise a recipe is a list of materials and directions that describes the proper approach for combining ratios of ingredients in the proper proportions."

Step 3:
Review the concepts of ratios and proportions.

  • "Do you recall what a ratio is?"
  • "A ratio is a comparison of 2 or more numbers."
  • "Do you remember what a proportion is?"
  • "A proportion is an equation formed by the equivalence of two (or more) ratios."

Step 4:
Explain the objective of the lesson. "Through today's lesson, we will apply mathematics to our intuition and experience in a real-world example - recipe conversions."

Learning Activities
Step 1:
.To provide students with a specific task to complete while viewing, give them a Focus for Media Interaction by asking students to watch and listen for the scenario in the video that can be represented mathematically. Tell students to write an equation for the recipe in the video.

Step 2:
START the video at the beginning of the "For Real" segment. You should see 2 girls walking down a sidewalk carrying some groceries.

Step 3:
PAUSE the video after the older girl says "equals 40 popcorn balls." She says this after she writes the recipe down. The teacher now asks the class if they have the recipe written down. The teacher should write (or display) the recipe on the overhead projector or board.

Step 4:
Provide a Focus for Media Interaction by asking students to watch for how the characters decide to modify the recipe. Tell the students to think of other possible ways that the recipe could be modified. Tell the students to think of the recipe in mathematical terms. When the students are ready, RESUME PLAY.

Step 5:
PAUSE the video after the older girl says "we just need to multiply all of the ingredients by 10." The teacher should ask the class "does this seem like a reasonable way to modify the recipe?" Have the students work through converting the recipe to 400 popcorn balls. Once the students have had a chance to work the example, RESUME PLAY and finish the segment. When the older girl says "I hate popcorn," STOP.

Culminating Activity

Note to Teacher: Students will turn in the work from the Culminating Activity as part of their Assessment of this lesson.

Step 1:
Divide students into groups of three based around a computer with internet access.

Step 2:
Pass out a worksheet to each group.

Step 3: Students should complete the first part of the worksheet. When they are finished with the first part of the worksheet, the students should access the bookmarked page.

Step 4: Demonstrate the use of the recipe conversion feature of the site. Have the students compare their answers to the first part of the worksheet with conversions of the recipe for "Puppy Chow."

Step 5: Draw closure to the lesson by reviewing the concepts of ratios and proportions and how they relate to recipes.
"A ratio is a comparison of 2 or more numbers. A recipe is an example of a ratio. The quantities of ingredients in a recipe could be written as a ratio."
"A proportion is an equation formed by the equivalence of two (or more) ratios. A recipe can be increased or decreased by multiplication or division. The proportion of servings and ingredients should remain similar."

Step 6: For the remainder of the lesson the students continue working in groups to finish the worksheet.

Extensions

Social Studies:
Explore demographics throughout the U.S. and the world. Based on historical trends predict how the population will change over the next 10 years. What ratios are expected to increase? What ratios are expected to decrease?

Art:
Scale and proportion can be explored in detail through art. Explore how proportion has been used to mirror an image. Explore how proportion and scale has been used to distort and create images. Create a piece of art that is scaled up or down in only one dimension.

Science:
Apply ratios and proportions to mixing chemicals in a science lab.

COMMUNITY CONNECTIONS:

  • Ask a local artist to come and discuss with the class how he or she uses ratios and proportions in art. For example, mixing of colors or creating objects to scale.
  • Invite an architect or contractor to discuss how scale is used in creating or using building plans.
  • Talk to the professionals in your cafeteria. Have someone explain the process of menu planning. Ask the professionals how they adjust recipes for the school.

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