HOMECOMING CHILI

TEACHER EDITION

List of Activities for this Unit:

ACTIVITY / STRAND / DESCRIPTION
1 – Alicia’s Chili / AS / Solving problems with recipes and justifying calculations
2 – Calculating Surface Area / AS/ME / Simplifying expressions using order of operations and surface area formulas
3 – Reasoning with Formulas / AS / Simplifying expressions using order of operations and a variety of formulas
4 – Beasley’s Chili Classic / AS / Extracting important information from a problems situations, using a formula and applying order of operations to solve a problem
*See teacher note
5 – Multiple Choice Practice Problems / AS / Practice problems
COE Connections / Illuminance #2
MATERIALS
Warm-Ups
(in Segmented Extras Folder)

Vocabulary: Mathematics and ELL

double
profit
quadruple
ratio
silo
triple

Essential Questions:

  • How does a person sift through all the information provided in a situation and extract only the critical information needed to solve a problem?
  • How is an algebraic equation written based on the information provided?
  • How is an algebraic equation solved?
  • How are other values of a problem determined after solving an equation?

Lesson Overview:

  • *Teacher Note: Use the two related articles on Chili contests to provide students with more background knowledge.
  • Before allowing the students the opportunity to start the activity: assess their prior knowledge with regards to the students’ experiences eating spicy chili or other spicy foods.
  • A warm-up could be done regarding solving equations and what implies.
  • How can the students make their thinking visible?
  • How can students organize a solution?
  • Include the potential for group work/discussion.
  • You might want to carefully scaffold this with ELL students. Including identifying important information and breaking down (decoding) a problem.
  • Use resources from your building.
  • Depending on the abilities of the students, you might want to use Homecoming as a warm-up and Beasley’s Chili Classic as an activity.

Performance Expectations:

4.5.BIdentify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem.

4.5.ESelect and use one or more appropriate strategies to solve a problem and explain why that strategy was chosen.

5.6.ESelect and use one or more appropriate strategies to solve a problem, and explain the choice of strategy.

6.2.DApply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.

6.6.CAnalyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

7.6.CAnalyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

8.5.CAnalyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.

Performance Expectations and Aligned Problems

Chapter 2“Homecoming Chili” Subsections: / 1-Alicia’s Chili / 2- Calculating Surface Area / 3- Reasoning with Formulas / 4- Beasley’s Chili Classic / 5- Multiple Choice Practice Problems
Problems Supporting:
PE 4.5.B / 4, 5 / 3 / 1, 2, 3 / 1, 2, 4
Problems Supporting:
PE 4.5.E≈ 5.6.E ≈ 6.6.C ≈ 8.5.C / 4, 5 / 1, 2, 3 / 1, 2, 3
Problems Supporting:
PE 6.2.D / 2, 3, 4, 5 / 1, 2, 3 / 1, 2, 3 / 1, 2, 3 / 2, 3, 4

Assessment: Use the multiple choice and short answer items from Algebraic Sense and Number Sense that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.

1 – Alicia’s Chili

1.Alicia’s favorite chili recipe calls for 3 pounds of ground beef. The recipe serves 8 people.

  1. How many people will a double (two times as big) recipe serve? 16 people
  1. How many people will a triple (three times as big) recipe serve? 24 people
  1. How many people will a quadruple (four times as big) recipe serve? 32 people

2.How can you determine the amount of ground beef needed for a double recipe?

2 • 8 = 16

3.How can you determine the amount of ground beef needed for a quadruple recipe?

4 • 8 = 32

4.How many pounds of ground beef are in each serving when the recipe requires 3 pounds of ground beef to serve 8 people?

Show your work using words, numbers and/or diagrams.

()() = () = ()

5.Alicia bought a package of ground beef that weighs 11.5 pounds to make a large batch of chili for the annual Homecoming Chili Dinner at the local high school.

How many people could Alicia expect to serve if 3 pounds serves 8 people? 30 people or by skimping a little 31.

Show your work using words, numbers and/or diagrams.

11.5 ÷ 3 = 3.83 three pound groupings, 3.83 • 8 = 30.67 ≈ 30 or 31

2 -Calculating Surface Area

  1. The formula for the surface area of a right cylinder is SA = 2 r ² + 2rh

What is the surface area of this cylinder? ≈835.66cm2

Show your work using words, numbers and/or diagrams.

  1. Mr. Borden built a silo (storage building) in the shape of a cylinder. The radius is 8 meters and the height is 18 meters.

What is the surface area of the silo? ≈ 1,306.90m2

Show your work using words, numbers and/or diagrams.

SA = 2(8m)2 + 2(8m)(18m)

= 128m2 + 288m2

= 416m2 (This is the exact surface area!)

≈ 1,306.90m2

  1. The formula for determining the surface area of a sphere is SA = 4r². Mrs. Fernandez wanted to wrap a ball with a radius of 5 cm.

What is the surface area of the ball? ≈ 314.16cm2

Show your work using words, numbers and/or diagrams.

SA= 4r²

= 4(5cm)2

= 100cm2 (This is the exact surface area!)

≈314.16cm2

3 -Reasoning With Formulas

  1. The height of a thrown ball is modeled by the equation h = -6t² + 17t + 6, where h represents the height of the ball in feet and t represents the time (in seconds) after the ball was thrown.
    How high is the ball after 3 seconds? =3 feet

Show your work using words, numbers and/or diagrams.

h= -6t² + 17t + 6

= -6(3)² + 17(3) + 6

= -6(9) + 17(3) + 6

= -54 + 51 + 6

= 3

2.Marshall realized that he could determine the total cost, c, of buying tickets to the movies for him and his six friends was c = $8.50n where n is the number of tickets.
What was the cost for the 7 of them to attend the movie? = $59.50

Show your work using words, numbers and/or diagrams.

c = $8.50n

= $8.50(7)

= $59.50

3.Tony earns $75.00 per hour plus a fee of $35.00 for coming to someone’s house to work on a computer. The equation that can be used to determine how much money Tony can earn given any known number of hours he works on a computer is E= 75h + 35, where E represents his earnings and h represents the number of hours worked.
How much money would Tony earn by working for 7hours on a computer at
someone’s home? = $578.75

Show your work using words, numbers and/or diagrams.

E= $75h + $35

= $75(7.25) + $35

= $578.75

4 - Beasley’s Chili Classic

Each fall, Beasley Root Beer sponsors the annual Chili Chowdown Classic for Burpsburg’s chili cooks and chili consumers. Several booths are set around the parking lot. The cooks stir up huge pots of steamy, spicy chili. The customers line up with bowls for chili and mugs for Beasley’s tasty, thirst-quenching root beer. A glorious, gastronomical gathering!

Toots Beasley brews a big, bubbly batch of root beer for the event. Toots charges $1.35 for a quart of root beer. He has learned from experience that a customer drinks a quart of root beer for each two tablespoons of chili powder consumed. Further, Toots knows that the number of bowls (B) of chili sold by a cook is related to the number of tablespoons (T) of chili powder used per bowl by the equation: B = -T² + 7T + 22. Cooks may use additional spices in their chili, of course, but chili powder is the vital variable as far as Toots is concerned.

  • Alicia uses 3 tablespoons of chili powder per bowl in her Alicia Atomic Chili.
  • Connie Carney throws in 5 tablespoons per bowl of her Chili Connie Carney.
  • Prudence Pennywhistle uses no chili powder at all in the Prudent Potfull.
  • David Chung tosses 4 tablespoons per bowl in his David’s Dragon-Breath Chili.
  • Voratia Vesuvius stirs 7 tablespoons per bowl into her Volcano chili.
  1. How many quarts of root beer will Toots sell? = 276

Show your work using words, numbers and/or diagrams.

Using B = -T² + 7T + 22 to calculate the number of bowls of chili made yields:

Alicia uses 3 tablespoons of chili powder per bowl in her Alicia Atomic Chili. (34 bowls)(3tbl/bowl) = 102 tbs

Connie Carney throws in 5 tablespoons per bowl of her Chili Connie Carney.(32 bowls)(5tbl/bowl) = 160 tbs

Prudence Pennywhistle uses no chili powder at all in the Prudent Potfull.( 0 bowls)(0tbl/bowl) = 0 tbs

David Chung tosses 4 tablespoons per bowl in his David’s Dragon-Breath Chili.(34 bowls)(4tbl/bowl) = 136 tbs

Voratia Vesuvius stirs 7 tablespoons per bowl into her Volcano chili.(22 bowls)(7tbl/bowl) = 154 tbs

Total tbs = 552

-OR-

Total tablespoons of chili powder used: 34(3) + 32(5) + 0(0) + 34(4) + 22(7) = 552

Number of quarts of root beer sold: 552 ÷ 2 = 276

2.How much money will Toots take in by selling root beer at the Chili Classic? = $234.60

Show your work using words, numbers and/or diagrams.

276 • $0.85 = $234.60

3.It costs Toot $0.40 to make each quart of root beer.

How much profit (total sales minus cost) will Toots make at the Chili Classic? = $124.20

Show your work using words, numbers and/or diagrams.

276 • ($0.85 - $0.40) = $124.20

5 - Multiple Choice Practice

1.Eddie’s Towing Company charges $40 to secure a car for towing and $1.70 for each mile the car is towed.

Which equation represents the relationship between the number of miles towed, m, and the total charges, c?

A.c = $40 + $1.70

B.c = $40 + $1.70m

C.c = $40m + $1.70m

D.c = $40m + $1.70

Show your work using words, numbers and/or diagrams.

This is a linear relationship; it has the form y = mx + b.

The rate in this scenario is the $1.70 per mile and the flat fee of $40.00 is the y-intercept.

The equation is therefore: c = $1.70m + $40

2.Kim needs a certain shade of pink paint. This shade is made by mixing white and red paint in a ratio (a comparison of two numbers) of 1 to 3.

Which is the number of fluid ounces of red paint that would be needed to make 12 fluid ounces of this pink paint?

A.4 fluid ounces

B.6 fluid ounces

C.8 fluid ounces

D.9 fluid ounces

Show your work using words, numbers and/or diagrams.

1:3  1oz of white for every 3oz of red which  4oz of paint so 1 of the 4oz is white and 3oz of the 4oz are red. Thus of the 12 oz must be red or 9oz of red.

3.Mario uses 5 tomatoes to make half a liter of tomato sauce.

Which is the amount of sauce he can make from 15 tomatoes?

A.One and a half liters

B.Two liters

C.Two and a half liters

D.Three liters

Show your work using words, numbers and/or diagrams.

5 tomatoes  0.5 liters

3(5 tomatoes  0.5 liters) = 15 tomatoes  1.5 liters

4.The dance committee had $240.00 to spend on supplies for the dance.
They spent of the money.

Which is the amount of money they had remaining after spending of the original amount?

A.$85.00

B.$90.00

C.$120.00

D.$150.00

Show your work using words, numbers and/or diagrams.

• $240.00 = 5 • $30.00 = $150.00 was spent. $240 - $150 = $90.00 remaining.

Teacher: Ch. 2 “Homecoming Chili”Segmented Revision 2008Page 1 of 11