SCALE CITY
The Road to Propor tional Reasonin
g:
World Chicken Festival Lesson
TABLE OF CONTENTS
Click on a title to go directly to the page. You also can click on web addresses to
link to external web sites.
Overview of Lesson
Including Kentucky Standards Addressed............................................................2
Instructional Strategies and Activities
• Day One: Hands-On Measurement .................................................................. 3-5
• Day Two: Watching the Video and Investigating Circles .................................. 5-7
• Day Three: Online Interactive and Scaling Recipes........................................... 7
• Day Four: Assessment .........................................................................................7
Support/Connections/Resources .............................................................. 8
Writing for the Lesson ................................................................................... 8-9
Adaptations for Diverse Learners/Lesson Extensions ...................... 9-11
• Predict and Prove Game
• Enrichment: How Gear Ratios Work
Applications Across the Curriculum .........................................................11
Performance Assessment ............................................................................ 12
Open Response Assessment ....................................................................... 13
Multiple Choice Assessment ...................................................................... 14-16
Key to Performance and Multiple Choice Assessments.................... 17
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circle
Grades 6-8
Essential
Question:
WORLD CHICKEN FESTIVAL: SCALING UP
RECIPES AND CIRCLES
Length:
1-4 days
How do you use proportional reasoning to
scale recipes? What
happens to the area of
a circle when its radius
changes?
Technology
computer
computer projector
Internet connection
computer lab for
individual or paired
exploration
overhead projector
calculators
Vocabulary
area
circle
circumference
constant
diameter
direct proportion
equivalent
fraction
pi
radius
ratio and different
methods of expressing ratio (1:4, 1/4;
and 1 to 4)
scale
scale factor
variable
x÷y=k
Concept/Objectives:
Students will learn how
proportional reasoning is used to adjust
recipes. Students will
understand the meaning of specific terminology of circles including
radius, diameter, pi,
area, and circumference.
Activity:
Students will determine
area given the radius of
a circle. Students will
apply understanding of
equivalent ratios and
fractions to solve problems in preparing food
according to recipes.
Resources Used in
This Lesson Plan:
Scale City Video:
Greetings from
the World Chicken
Festival
Online Interactive:
Sunnyside Up!
Assessments
(included in this
lesson)
Classroom Handouts
(PDFs)
All resources are
available at
www.scalecity.org
Instructional Strategies and Activities
NOTE TO TEACHER:
You may want to send an email to parents to let them know about the Scale City
web site and encourage them to have their children access the site at home for
additional practice.
Sample email to parents
Our mathematics class is exploring proportional reasoning as it applies to real-world
problems. This concept is important in algebraic thinking and mathematical reasoning.
Kentucky Educational Television has created online interactive learning activities and
other resources for students to explore this concept.
We will be using this web site during class instruction. I encourage the students to access
the site from home or in a library for additional practice. The web address is
www.scalecity.org.
Sincerely,
Teacher
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 2
DAY ONE: HANDS-ON MEASUREMENT AND
FRACTION REVIEW
The purpose of Day One is to acquaint students with standard cooking
measurements.
The Measurement Challenge
NOTE TO TEACHER:
“The Measurement Challenge” is included in handouts (“Handout 1: The Measurement Challenge”), though it is not intended as a student handout. However, you
may want to post the problems for any students who have hearing impairments.
This game could also be conducted as a completely silent activity with students
relying on nonverbal communication.
Materials for each group
measuring cups (1 cup, 1/2 cup, 1/3 cup, 1/4 cup)
measuring spoons: 1 tablespoon, 1 teaspoon, 1/2 teaspoon, 1/4 teaspoon
2-quart container
1-gallon jug
individual numbers on paper (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
scratch paper for each student
bell or timer
Directions
1. Divide students into groups of three to four. Each group will choose a group name.
Write the group names on the board with space to tally points.
2. Have students write their group name on an 8-inch x 11 ½-inch paper and place it
in the center of the group. This piece of paper is the target. When students are asked a
question, they must place the relevant measurements on the target before the bell rings.
Have students write the digits 0-9 on a piece of paper and cut them out individually.
These numbers will be used in rounds two and three.
3. Explain the rules of “The Measurement Challenge.” You will present a challenge
orally to the students and ring a bell after the recommended time for each challenge in
a round. Teams receive a point for correct displays on the targets. You also may reward
bonus points for creativity or speed.
4. Before beginning “The Measurement Challenge,” make sure students have the
needed materials. (see list above.)
5. Begin Round One. Read the following challenges to the students. Allow five seconds
per challenge.
1. Show me 1/3 cup.
2. Show me 1 tablespoon.
3. Show me 1/4 teaspoon.
4. Show me 1 teaspoon.
5. Show me 1 gallon.
6. Show me 2 quarts.
7. Show me 1/2 cup.
8. Show me 1 tablespoon.
9. Show me 1/2 teaspoon.
10. Show me 1/4 cup.
11. Show me 1 cup.
Materials
string (two colors per
student)
scissors (one pair per
student)
round pans, lids, and
other circular
objects
12-inch diameter
skillet
measuring tape
three 12-inch
squares
Kentucky
Academic
Expectations
2.7
2.8
2.12
Kentucky
Program of
Studies
Grade 6
MA-6-NPO-U-1
MA-6-NPO-U-4
MA-6-NPO-S-NO3
MA-6-NPO-S-RP3
Grade 7
MA-7-NPO-U-4
MA-7-NPO-S-RP2
MA-7-NPO-S-RP3
Grade 8
MA-8-NPO-U-4
MA-8-NPO-S-RP1
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 3
NOTE TO TEACHER:
If several teams earn less than seven points in this round, do a review of the measuring tools and then repeat the round. The second time you may choose to allow three
or four seconds per question.
6. Begin Round Two. Read the following challenges to the students. Allow 30 seconds
Kentucky Core
Content for
Assessment 4.1
Grade 6
MA-06-1.3.1
MA-06-1.4.1
Grade 7
MA-07-1.3.1
MA-07-1.3.2
MA-07-1.4.1
Grade 8
MA-08-1.3.1
MA-08-1.3.2
MA-08-1.4.1
MA-08-3.1.3
MA-08-5.1.5
© KET, 2009
per challenge.
1. Put 2 measuring tools together to make 3/4 cup. (1/2 cup and 1/4 cup)
2. Put 2 measuring tools together to make 5/6 cup. (1/2 cup and 1/3 cup)
3. Put 2 measuring tools together to make 7/12 cup. (1/3 cup and 1/4 cup)
4. Put 2 measuring tools together to make 1 1/2 cups. (1 cup and 1/2 cup)
5. Show me 1 1/4 teaspoons.
6. There are 4 quarts in a gallon. Show me 1 1/2 gallons. (1-gallon and 2-quart
containers)
7. There are 3 teaspoons in a tablespoon. Using the numbers and measuring
spoons, show the equivalent to 2 tablespoons without using the tablespoon.
(6 teaspoons, 12 1/2-teaspoons, 24 1/4-teaspoons)
8. Using the 1/4 cup and the numbers, show how many 1/4 cups make 3 cups. (12)
9. There are 16 tablespoons in a cup. Using the tablespoon and numbers, show how
many tablespoons there are in 1/2 cup. (8)
10. There are 4 cups in a quart and 4 quarts in a gallon. Use the cup and numbers.
Show how many cups are in a gallon. (16)
NOTE TO TEACHER:
Student performance in Round Two may indicate a need for some review of fractions. If necessary, pause the game and review the problems that students missed.
You may also need to review note-taking strategies that help with oral problems.
Discuss how to write pertinent information from the problem as it is read.
7. Begin Round Three. Read the following challenges to the students. Allow 30 seconds
per question, except for question 10. Allow 90 seconds for this question.
1. Flour is the main ingredient in banana bread. If you are making one loaf of
banana bread, what measuring tool would you most likely use to measure the
flour? (1 cup)
2. Show the measuring tool that is less than a 1/4 cup and more than a teaspoon.
(tablespoon)
3. Use numbers and measuring tools to display the answer to this question:
Which measuring cup is smaller: 2/3 cup or 3/4 cup? (2/3 cup)
4. Display the answer to this problem: 1 cup minus 3/4 cup. (1/4 cup)
5. There are 4 cups in a quart. Display the answer to this problem: 2 quarts
minus 6 cups. (2 cups)
6. There are 3 teaspoons in a tablespoon. Using a tablespoon and numbers, show
how many tablespoons are in 24 teaspoons. (8)
7. The recipe calls for 3/4 cup of whole-wheat flour. How much flour is needed to
double the recipe? (1 1/2 cups)
8. 1/4-teaspoon salt is used in the recipe. Show how much salt you need to make
12 batches of the recipe. (3 teaspoons or 1 tablespoon)
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 4
9. Which cup is closer in amount to 1/3 cup: 1/4 cup or 1/2 cup? (1/4 cup is
1/12 less, 1/2 cup is 2/12 more)
10. How could you measure 1/6 of a cup? Show and explain the tools you
would use. One option: 2 (1/3 cups) – 1/2 cup = 4/6 – 3/6 = 1/6; another
option: 1/4 cup – (1 tablespoon + 1 teaspoon) = 3/12 cup – (1/16 cup+
1/48 cup) = 12/48 cup – (3/48+ 1/48) = 12/48-4/48 = 8/48 = 1/6; other
options: 8 teaspoons (1/6 of 48) or 3 tablespoons (9 teaspoons) minus 1
teaspoon or 2 tablepoons (6 teaspoons) + 2 teaspoons.
8. Have students complete “Handout 2: Applied Fractions.”
DAY TWO: WATCHING THE VIDEO AND INVESTIGATING CIRCLES
NOTE TO TEACHER:
Clear a large space in the middle of the room and place chairs in a horseshoe facing the space. You need a square
at least 11 feet by 11 feet for this activity. If you don’t have the space, you can cut the space in half and adjust the
numbers accordingly. Make sure students can see the television and overhead. You will be marking on the floor
of the area. If a dry eraser marker or chalk will damage the floor, then paper the area with bulletin board paper,
freezer paper, or brown paper bags first.
If you do all the suggested discussion and activities, you might need to allow two days to complete this part of
the lesson.
1. Use an Internet projector to watch the “Greetings from the World Chicken Festival” video at www.scalecity.org. Or
download the video to a DVD to show to your class. Guide students to write down significant numbers related to the
skillet as they watch the video.
2. Write “Skillet Stats” on the board. Record and discuss the numbers students collected from the video.
3. Guide students to compare a standard skillet with the world’s largest.
The World Chicken Festival in London, Kentucky features the World’s Largest Stainless Steel Skillet, which can cook 600
quarters of chicken at one time. This skillet is 10 feet, 6 inches in diameter and 8 inches deep. A standard skillet for home
use is 12 inches in diameter and 2 inches deep. Ask the students how much bigger the World’s Largest Skillet is than a
standard skillet? (Convert the inches to feet. It’s simpler to convert 12 inches to one foot and 10 feet 6 inches to 10.5 feet. So the
skillet is 10.5 times the diameter of a standard skillet and 4 times the depth.) . You might ask students to think about how much
oil such a large skillet requires—how would that compare to a standard skillet? How would the area of the small skillet’s bottom
compare to area of the larger skillet? At this point, you’re not asking them to do computations—the lesson is teaching them about
area of circles and, as time permits, volume of cylinders. Instead, the idea is for them to use logical thinking skills to visualize and
predict what the differences might be.)
4. Present the definitions of radius and diameter on the overhead or chalkboard. Differentiate between a chord and the
diameter. Mark 10 feet, 6 inches off in the room so students can see a length the same size as the diameter of the World’s
Largest Skillet.
5. Follow these steps to create a representation of a standard skillet and the World’s Largest Skillet on the classroom floor.
• Determine the radius of a 10-foot, 6-inch diameter. (5 feet 3 inches)
• Cut string to measure 6 feet, 3 inches. The extra foot will allow for 6 inches on
each side to secure to sidewalk chalk or another drawing utensil and a stationery
center point marker.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 5
• Determine where the center of the circle should be and mark it.
• Tie sidewalk chalk or white board marker to one end of the string and a pencil to
the other end to hold in place at the center of the circle. Make sure that the remaining string is 5 feet, 3 inches long.
• Draw a circle with a 5-foot, 3-inch radius by moving the string around the center
points. Using the same method, create a concentric circle with a 6-inch radius
inside the larger circle.
6. Explain that every circle has a number in common, called pi. Distinguish “pi” from “pie.” Tell students that they are
going to discover what pi is. Divide them into pairs and have them measure and record the diameter and circumference of
several different sized circles (pie plates, plastic lids, the 12-inch circle, the 10.5-foot circle, etc.) using rulers and measuring
tape. Then have them divide the circumference of each circle by the diameter. You could tell some students to measure to
the nearest sixteenth of an inch and do the computation in fractions and others to measure in centimeters to the nearest
millimeter and do the computation in decimals.
When the students have finished, they can compare the values of their ratios. Hopefully, everyone will find they are about
3 1/7 or 3.14. Ask students at this point to define pi (the value of the ratio of a circle’s circumference to its diameter). You
might talk with students about the fact that pi is always an approximation and that it is an irrational number—the decimal
representations will never end and never repeat.
7. Distribute “Handout 3: Circles” and pieces of string. Students can now test the ratio of pi on questions 1-3 on the handout by seeing if they need a little over three times as much string for the circumferences of the circles as they do for their
diameters.
8. Use an overhead calculator to show how pi is represented on calculators and the value you get from pi. Discuss intriguing information about pi. Scientists are still looking for more numbers or some kind of pattern in the numbers they have
found. (Additional background information is available at The Story of Pi, www.geocities.com/capecanaveral/lab/3550/
pi.htm, and at Ask Dr. Math: About Pi, mathforum.org/dr.math/faq/faq.pi.html.)
Questions:
• What ratio does pi represent? Circumference ÷ diameter
• If you had a calculator with pi and knew the circumference, could you find the
diameter?
9. Have students do questions 4 and 5 on “Handout 3: Circles.”
10. Show students how to use the radius to calculate the area of a circle. Ask what they predict will happen to the area of
the circle when they double or triple the radius. They might even draw a few circles on cm grid paper, measuring the
radius in cm and counting the squares to find area. Ask them to compare the effect of doubling or tripling the radius or
diameter of a circle with doubling or tripling the sides of a square or rectangle. In each case, what happens to the area?
Have students look at question 6 on “Handout 3: Circles” and compare the numbers to see how much larger the area of
the 10.5-foot circle is than the 1-foot circle.
1-Foot Diameter
Area = pr2
Area = p (0.5)2
A = 0.79 ft2
10.5 Foot Diameter
Area = pr2
Area = p (5.25)2
A = 86.55 ft2
The area of the larger circle is more than 100 times larger than the 12-inch skillet. Consider with students why area does
not grow proportionally to diameter.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 6
11. Have students do the practice problems on “Handout 4: Circle Practice”
examining pi, exploring radius, and calculating the area of circles.
12. As time allows, offer students a challenge. If you know that the bottom side
of rectangular box (a prism) has an area of 100 square inches and that the height
of the box is 12 inches, how can you use that information to determine its volume?
(The area of the bottom or top of a rectangular prism times its height equals its
volume, so the volume of the box is 1200 in3.)
Then ask what information do you need to determine the volume of a can of Pringles (a cylinder)? (You would need its
radius and its height. Its volume equals the area of its top or bottom— pr2—times its height.) Ask students to consider the 1-ft
and 10.5-ft skillets. What would they need to know to compare how much oil each would use?
TEACHING TIP:
An extension of this discussion of the volume of cylinders would be to have groups
of students measure the radius of a jar’s circular base in centimeters, measure its
height in centimeters, use the formula they came up with in the discussion to find
the volume, and then fill the jar with rice or water measured in milliliters to compare with their calculations. The metric system works well because a milliliter is the
same as a cubic centimeter.
13. The Open Response (see page 13 ) or “Writing for the Lesson” (see page 8) could be used as homework.
DAY THREE: ONLINE INTERACTIVE AND SCALING
RECIPES
1. Complete any activities remaining from Day 2.
2. Ask students, “What is the greatest number of people you have cooked for?” Share your own experiences. Talk about
how you have to change your recipe to cook for so many people.
3. Using an Internet projector, go to the online interactive, “Sunnyside Up,” at www.scalecity.org. Work together to scale
up a recipe for 108 people at a family reunion.
4. Use “Handout 5: Sunnyside Up Biscuits” when you get to the biscuit calculations on the interactive. This will help
students try their own calculations. Allow time for work and have students submit their answers to check responses.
5. Complete the interactive with the concept of radius and area at the end as a review of yesterday’s material.
6. As guided practice, have students calculate leftovers from the biscuit ingredients.
7. Students complete “Handout 6: Scale City Recipes” as class work or homework. “Handout 7: Scaling Down Recipes” is
provided for additional practice.
8. Students also might do the Performance Assessment (see page 12) as homework.
DAY FOUR: ASSESSMENT
If students do the Performance Assessment, they could present their findings to the class. You also could have them do the
Multiple Choice Assessment (see page 14) as a final activity.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 7
Support/Connections/Resources
The Story of Pi
www.geocities.com/capecanaveral/lab/3550/pi.htm
For many millennia, scholars have been searching for the value of pi. This web site
highlights the discoveries from the beginning more than 4,000 years ago.
Geometry: Area of a Circle
math.about.com/library/weekly/aa111002a.htm
This step-by-step activity helps you understand the area of a circle and lets you practice using the formula.
NOTE TO TEACHER:
If you have software like Geometer’s Sketchpad or GeoGebra, you can ask students to draw circles with diameters
or radii of different lengths and then use the computer to measure areas and perimeters. If students put these data
in a chart, or graph the length of the radius or diameter on the x-axis and circumference (or area) on the y-axis, it
would give them a good look at whether the relationship is linear, proportional, and/or direct.
Writing for the Lesson
Scale City Pizza has just introduced a 20-inch pizza, the biggest pizza available in town. Write a 30-second commercial
with math facts promoting this pizza. Consider the following information and do calculations to add details. Round your
answers to the nearest whole number.
A. A pepperoni pizza has one pepperoni for every two square inches. Compare the number of pepperonis on the
14-inch and 20-inch pizzas.
B. Describe how many times bigger the 20-inch pizza is than a 14-inch. Finding the area of each pizza will allow you to
set up a ratio of the area of the larger pizza to the area of the smaller pizza. The answer to this division problem will tell
you how many times larger the 20-inch pizza is compared to a 14-inch.
C. If the 14-inch pizza costs $9.99, what’s a fair price for the 20-inch pizza? Why? Determine the price for the pizza and
include that information in your commercial.
D. Describe how many middle school students a 20-inch pizza will feed. Four middle school students can share a
14-inch pizza.
E. Broadcasters are firm on the amount of time for an advertisement. A general rule is three seconds per line, but
reading pace varies. Use your creativity and your math skills to write a 30-second commercial advertising the new 20inch pizzas.
KEY to Math Calculations for “Writing for the Lesson”
A = pr2
14-inch pizza:
Radius = 7 inches, Area = 154 square inches (rounded)
20-inch pizza
Radius = 10 inches, Area = 314 square inches (rounded)
TEACHING TIP:
Students are asked to round the figures in these calculations to the nearest whole number due to rules governing
significant digits and measurement. See the Vocabulary list at the Teacher’s Diner for more information about
this concept.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 8
A. A pepperoni pizza has one pepperoni for every two square inches. Compare the
number of pepperonis on the 14-inch and 20-inch pizzas.
The 20-inch pepperoni pizza would have 157 pepperonis.
The 14-inch pepperoni pizza would have 77 pepperonis.
The 20-inch pepperoni pizza would have 80 more pepperonis than the 14-inch.
B. Describe how many times bigger the 20-inch pizza is than a 14-inch. Finding the area of each pizza will allow you to
set up a ratio of the area of the larger pizza to the area of the smaller pizza. The answer to this division problem will tell
you how many times larger the 20-inch pizza is compared to a 14-inch.
(area of 20-inch pizza) ÷ (area of 14-inch pizza) = 2.0408 = 2 (rounded to the nearest whole number)
The 20-inch pizza has twice as much space for toppings as the 14-inch.
C. If the 14-inch pizza costs $9.99, what’s a fair price for the 20-inch pizza? Why? Determine the price for the pizza and
include that information in your commercial.
When students realize that the 20-inch pizza is really more than twice as big as the 14-inch pizza, they may decide it should
cost twice as much. However, some students will also realize that people probably don’t expect to pay twice as much for the
pizza, so they may decide on a compromise price that is less than double the $9.99 price for the 14-inch pizza.
D. Describe how many middle school students a 20-inch pizza will feed. Four middle school students can share a 14inch pizza.
4 ÷ 154 = x ÷ 314
x = (4 × 314) ÷ 154
x = 8.16 or 8 students
Instead of calculating, some students may use the information about area to infer that since the area of the 20-inch is double
that of the 14-inch, it will feed twice as many students or eight.
TEACHING TIP:
This writing activity gives you an opportunity to talk about multiplicative relationships rather than additive ones.
The 20-inch pizza is about double the size of the 14-inch pizza, so it has about twice as many pepperonis or 80
more. What if you had two other pizzas with diameters that varied by six inches? Would the larger one still hold 80
more pepperonis? Would it have double the area of the smaller one? What would the difference be between two
pizzas whose areas were in a ratio of 7:10?
Adaptations for Diverse Learners/Lesson Extensions
Predict and Prove Game
Materials needed per group:
• measuring cups (2 cup measure, 1 cup, 1/2 cup, 1/3 cup, 1/4 cup)
• measuring spoons: 1 tablespoon, 1 teaspoon, 1/2 teaspoon, 1/4 teaspoon
• 2-quart container
• 1-gallon jug
• individual numbers on paper (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
• scratch paper for each student
• water or solid material to practice measuring cups, gallons, and quarts, such as beans
or Styrofoam packing
• salt or some similar substance to practice measuring teaspoons and tablespoons
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 9
1. Divide students into pairs or small groups. Each team makes a tally sheet with two columns labeled “Predict” and “Prove.”
2. Post a conversion chart for use during the game:
3 teaspoons = 1 tablespoon
4 cups = 1 quart
4 quarts = 1 gallon
16 tablespoons = 1 cup
3. Distribute or display the following five questions.
A. How many 1/2 cups are in 2 cups? 4 half-cups
B. How many teaspoons are in a tablespoon? 3 teaspoons
C. How many 1/4 cups are in a cup? 4 half-cups
D. How many tablespoons are in a 1/4 cup? 4 tablespoons
E. How many cups are in 2 quarts? 8 cups
4. Have students work as a team to make predictions without using their measuring devices. One student records the
predictions for the group with permanent ink in the “Predict” column. Teams have five minutes to predict measurements
for the five questions. (Adjust the time as needed.) Award points for accurate predictions.
5. Allow students five minutes to test their predictions. One student records each group’s findings in the “Prove” column
of the paper.
6. Teams with a correct prediction and accurate measurement earn two points per question. Teams who complete one part
of the activity successfully earn one point per question.
7. Repeat the “Predict and Prove” routine as often as desired to reinforce measurements concepts.
Additional Questions
How many 1/3 cups are in 3 cups? 9
How many 1/4 cups are in 1 1/2 cups? 6
How many cups in a half-gallon? 8
How many tablespoons are in 6 teaspoons? 2
How many quarts are in a gallon? 4
How many 1/2 cups are in 1 cup? 2
How many 1/3 cups are in 2 cups? 6
How many 1/4 cups are in a half-cup? 2
How many groups of 2 cups are in 2 quarts? 4
How many 1/2 teaspoons are in a tablespoon? 6
Enrichment: How Gear Ratios Work
Explore how information about circles is necessary to understanding the mechanics of gears. Research the terms revolutions per minute (rpm), diametral pitch, gear ratio, and base radius to demonstrate how understanding of circles is applied.
Students may complete the work independently in “Handout 8: Gears Are Circles.”
How Gear Ratios Work
www.howstuffworks.com/gear-ratio.htm/printable
Gears are everywhere where there are engines and motors producing rotational motion. In this edition of “How Stuff
Works,” you will learn about gear ratios and gear trains so you’ll understand what all these different gears are doing. You
might also want to read “How Gears Work” to find out more about different kinds of gears and their uses.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 10
Gear Terminology
www.gearshub.com/gear-terminology.html
A comprehensive glossary of gear terminology
Ring Gear-Pinion Gear Ratio Calculator
www.csgnetwork.com/rnggrpinioncalc.html
This utility calculates the rear end gear (or front end in the case of a front wheel drive)
ratio of the ring gear and pinion, for automotive applications.
Cycling Cadence and Bicycle Gearing
www.kenkifer.com/bikepages/touring/gears.htm
This article explores the reason for talking about gearing and cycling, why bicycles have gears, the definitions of gear and
cadence, low-gear requirements, gear-planning strategies, and charts of high and low gears.
Macauley, D. (1988). The Way Things Work. Dorling Kindersley Unlimited. London. ISBN: 0-590-42989-2
Applications Across the Curriculum
Social Studies
Discuss food as an element of culture. Examine family and community traditions and the role specific food has in these
celebrations. What cultural celebrations often include large gatherings of people and food?
Practical Living
Interview the school cafeteria manager about the mathematics involved in her job. Ask about the nutrition guidelines that
school cafeterias follow and how that dictates the quantity of certain foods.
Economics
Visit a local bakery or food factory to learn about how food is produced in large quantities.
Research how two fast food chains, Lee’s Famous Recipe and KFC have roots around London, Kentucky. Discuss economic
principles that led to the success of each franchise.
Consumer Studies
Collaborate with another teacher or the County Home Extension Agent to discuss challenges in multiplying the quantity
of ingredients in recipes.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 11
SMENT
S
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A
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PERFO
SCALE CITY
Prompt
Choose your favorite family recipe and convert the recipe to feed a large party of 108.
Directions
1. Select a favorite recipe in your family.
2. Do the calculations to increase the recipe to feed 108 people.
3. Make a grocery list. Investigate how much all of the ingredients would cost.
4. Present to the class what you’ve learned.
PERFORMANCE SCORING GUIDE
4
•The student applies proportional reasoning to this task with no errors.
•The student’s presentation indicates excellent under
standing of mathematics.
•The presentation indicates an outstanding effort overall.
•The student successfully completes all four steps of the performance assessment.
3
•The student applies proportional reasoning to this task with few errors.
•The student’s presentation indicates good under-
standing of mathematics.
•The presentation indicates a respectable effort overall.
•The student successfully completes at least three steps of the performance assessment.
2
•The student applies proportional reasoning to this task with good general understanding.
•The student’s presentation indicates basic mathe- matical precision with possible gaps in understanding or errors in
computation.
•The presentation indicates
some effort overall.
•The student successfully completes at least two steps of the performance assessment.
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•The student applies proportional reasoning to this task with limited understanding.
•The presentation indicates minimal effort overall.
•The student completes at least one step of the performance assessment.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 12
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•No response.
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The math club is creating a circle-shaped poster of a basketball for the state tournament.
A. The poster board measures 17 inches by 22 inches. What is the largest the circle could be in
diameter?
B. What is the radius? How could you use it to construct the circle?
C. What is the area of the circle in square inches?
D. How do the diameter, circumference, radius, and area of this circle compare to those measurements
for the largest circle that can be drawn on a piece of 8 ½-inch by 11-inch paper?
OPEN RESPONSE SCORING GUIDE
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•The student’s answer reflects thorough under-
standing of the concept of pi, diameter, radius, and area as studied in class.
•The answers are complete and accurate with minimal errors.
•The writing and com-
putation indicate sound mathematical reasoning and attention to detail.
•The student communi-
cates mathematical ideas in a focused, logical manner.
3
•The student’s answer
reflects adequate under-
standing of the concept of pi, diameter, radius, and area as studied in class
•The answers are mostly complete and accurate with few errors.
•The student communicates mathematical ideas with an obvious organized approach.
2
•The student’s answer reflects general under-
standing of concepts related to a circle such as pi, diameter, radius, and area as studied in class.
•The response may be incomplete or inaccurate.
•The writing may indicate lack of understanding and/or effort.
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•The student’s answer reflects limited under-
standing of concepts related to a circle such as pi, diameter, radius, and area as studied in class.
•The answers indicate a lack of effort and/or understanding.
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 13
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1. Rudy and his sister are making pumpkin bread for their mother’s birthday. They decide to halve the recipe.
The original recipe calls for 3 1/3 cups flour. They will need
A. 2 1/2 cups flour
B. 1 2/3 cups flour
C. 1 1/2 cups flour
D. 2/3 cups flour
2. Maria’s grandmother’s recipe for gyros has 1 1/2 teaspoons cumin and 1/4 teaspoon nutmeg. This recipe
feeds four. To feed a dozen people, they will need
A. 3 teaspoons cumin and 1/12 teaspoons nutmeg
B. 3 teaspoons cumin and 3/4 teaspoons nutmeg
C. 4 1/2 teaspoons cumin and 3/4 teaspoons nutmeg
D. 12 teaspoons cumin and 3 teaspoons nutmeg
3. The family says Grandma’s pickles are the most important ingredient in making her special potato salad.
She has 1/2 cup of pickles left. Her original potato salad recipe makes 20 servings and calls for 2/3 cup pickles.
Grandma scales down the recipe. If she makes enough potato salad to use all the pickles, the family should
have enough for
A. 18 servings
B. 15 servings
C. 12 servings
D. 10 servings
4. Half of 1/4 is
A. 1/2
B. 1/4
C. 1/8
D. 1/16
5. There are 8 hot dogs in a pack and 12 hot dog buns in a bag. Chip needs to buy enough for 96 hot dogs. He
should buy
A. 12 packs of hot dogs and 8 bags of hot dog buns
B. 10 packs of hot dogs and 8 bags of hot dog buns
C. 12 packs of hot dogs and 6 bags of hot dog buns
D. 8 packs of hot dogs and 8 bags of hot dog buns
6. 1/3 tsp. • 18 is
A. 54 tsp
B. 12 tsp
C. 9 tsp
D. 6 tsp
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 14
Multiple Choice Assessment
7. A recipe requires 1/2 tsp. Worcestershire sauce. The recipe will be scaled up for a party, with each ingredient multiplied by six. (Three teaspoons make a tablespoon.) The amount of Worcestershire sauce
needed is
A. 6 teaspoons
B. 1 tablespoon
C. 2 tablespoons
D. 3 tablespoons
8. The world’s largest frying skillet is 10 feet, 6 inches in diameter and 8 inches deep. A standard skillet for
home use is 12 inches in diameter and 2 inches deep. The larger skillet is
A. 10.5 times wider than a standard skillet and 4 times as deep
B. 8.6 times wider than a standard skillet and 4 times as deep
C. 6.5 times wider than a standard skillet and 4 times as deep
D. 5.8 times wider than a standard skillet and 4 times as deep
9. Oyster stew is a holiday tradition at Dan’s house. One pint of oysters is needed for a recipe for four
people. If 24 people are coming for dinner, the family should buy
A. 1 gallon of oysters, since there are eight pints in a gallon
B. 3/4 of a gallon of oysters, since there are eight pints in a gallon
C. 1/2 of a gallon of oysters, since there are eight pints in a gallon
D. 1/4 of a gallon of oysters, since there are eight pints in a gallon
10. The average ketchup serving size is one tablespoon. There are 60 servings in a 36 oz. bottle. If the
baseball concession organizers plan to have enough ketchup for 150 hotdogs, the organizers should buy at
least
A. 42 oz. of ketchup
B. 64 oz. of ketchup
C. 78 oz. of ketchup
D. 90 oz. of ketchup
11. Pi is
A. a ratio of the area to the circumference
B. a ratio of the radius to the diameter
C. a ratio of the diameter to the area
D. a ratio of the circumference to the diameter
12. If you know the circumference of a circle, you could find the diameter by
A. dividing the circumference by the value of pi
B. multiplying the diameter by the pi
C. multiplying the circumference by the value of pi
D. adding the circumference and the value of pi
13. If the diameter of a circle is 5.3 feet, the circumference of the circle is
A. 10.6 feet
B. 14.3 feet
C. 16.7 feet
D. 21.4 feet
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 15
Multiple Choice Assessment
14. If the circumference of a circle is 13.2 inches, the diameter is
A. 0.24 inches
B. 4.20 inches
C. 26.4 inches
D. 41.5 inches
15. In thinking about the diameter and circumference of a circle, mathematicians have known for thousands of
years that
A. the circumference is always smaller than the diameter
B. the circumference is not related mathematically to the diameter
C. the circumference is about 3 times the diameter
D. the diameter is about 3 times the circumference
16. If you know the radius of a circle, you can find the diameter by
A. multiplying the radius by 2
B. adding three to the radius
C. dividing the radius by 2
D. dividing the radius by pi
17. If you know the radius of a circle, you could use a formula to determine the area. The area of a circle equals
A. p • radius
B. length • width
C. circumference/diameter
D. p • radius2
18. There is a large circle painted on the gymnasium floor. The basketball team does a drill dribbling the balls as
they walk around the line of circle. The path of one complete turn around the circle is equal to the
A. radius of the circle
B. diameter of the circle
C. circumference of the circle
D. pi of the circle
19. When comparing the area of a circle with a one-foot radius with that of a circle with a ten-foot radius, the
area of the smaller circle is
A. 1/10 the area of the larger circle
B. 1/2 the area of the larger circle
C. 1/20 the area of the larger circle
D. 1/100 the area of the larger circle
20. Ken is painting circles on a wall at a day care. He needs to calculate the right amount of paint to buy. He
should probably measure
A. the radius of each circle, determine their areas, and add the areas together
B. the circumferences and find the value of the diameters
C. the circumference and the diameter to determine pi
D. the total number of degrees in each circle and multiply it by the number of circles
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 16
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Open Response Assessment
The math club is creating a circle-shaped poster of a basketball for the state tournament.
A. The poster board measures 17 by 22 inches. What is the largest the circle could be in diameter? 17 inches
B. What is the radius? How could you use it to construct the circle? 8.5 or 8 ½ inches. Students might describe using the radius, string, and a measuring device to create a handmade compass. They would have to describe how they
would determine the center point of the circle and how they would tie the string to a pencil so as to measure exactly
8.5 inches. Alternately, they might imagine a large compass that could be set to 8.5 inches.
C. What is the area of the circle in square inches? 226 [p(8.5)2]
D. How do the diameter, radius, and area of this circle compare to those measurements for the largest circle that
can be drawn on a piece of 8 ½-inch by 11-inch paper?
The diameter of the smaller circle would be 8 ½ inches, so its radius would be 4 ¼ inches—both half the size of the
larger circle’s dimensions. The area of the smaller circle would be 57 square inches (rounded), which is ¼ the area of
the larger circle.
Multiple-Choice Assessment
1. B, 2. C, 3. B, 4. C, 5. A, 6. D, 7. B, 8. A, 9. B, 10. D, 11. D, 12. A, 13. C , 14. B, 15. C, 16. A,
17. D, 18. C, 19. D, 20. A
WORLD CHICKEN FESTIVAL: Scaling Up Recipes and Circles 17