Hansen’s Cakes is a popular bakery in Los Angeles, California. They have created 4 new

cakes and need to decide which ones to sell in their bakery. Your job is to determine

which cake would be the least expensive to create, package and sell in their bakery.

The table below contains some information for each cake.

When a customer purchases a cake, Hansen’s will pack the cake in a box. The table below contains the cost and dimensions of the boxes that are

available for Hansen’s to use in their bakery.

Length (inches) Width (inches) Height (inches) Cost/box

12 12 12 $ 0.78

14 10 4.25 $ 0.40

14 14 8 $ 0.68

16 10 7 $ 0.70

Questions:

1. What size box should Hansen’s choose for each cake? Fill in table below.

2. What is the total cost of each cake (ingredients, labor, box)? Fill in table below.

3. What cake do you recommend Hansen’s sell in their bakery? Basketball Cake

4. Hansen’s wants to wrap each of these cakes in special wrapping paper. How much wrapping paper is needed to wrap 1 cake?

5. Hansen’s wants to build a new display to showcase the cake that you think they should sell. They want to have at least 5 of these cakes in the

display case at all times. What size display case do you think they should build? Create a sketch of the case in the space below. Label the

dimensions of the display case.

Basketball Hamburger Pig Car

Ingredient Cost

$5.87 $6.45 $5.50 $6.20

Labor Cost $12.25 $13.50 $12.75 $12.80

Dimensions 12” diameter 10 “ height

13” diameter 7.5 “ height

16” x 8” x 6” 15” x 10” x 5.5 “

Basketball Hamburger Pig Car

Box Size 12 x 12 x 12 14 x14 x8 16 x 10 x 7 16 x 10 x7

Box Cost $ 0.78 $0.68 $ 0.70 $0.70

Cake Cost $18.12 $19.95 $18.25 $19.00

Total Cost $18.90 $20.63 $18.95 19.70

Hansen’s Cakes is a popular bakery in Los Angeles, California. They have created 4 new

cakes and need to decide which ones to sell in their bakery. Your job is to determine

which cake would be the least expensive to create, package and sell in their bakery.

The table below contains some information for each cake.

When a customer purchases a cake, Hansen’s will pack the cake in a box. The table below contains the cost and dimensions of the boxes that are

available for Hansen’s to use in their bakery.

Length (inches) Width (inches) Height (inches) Cost/box

12 12 12 0.78

14 10 4.25 0.40

14 14 8 0.68

16 10 7 0.70

Questions:

1. What size box should Hansen’s choose for each cake? Fill in table below.

2. What is the total cost of each cake (ingredients, labor, box)? Fill in table below.

3. What cake do you recommend Hansen’s sell in their bakery?

4. Hansen’s wants to wrap each of these cakes in special wrapping paper. How much wrapping paper is needed to wrap 1 cake?

5. Hansen’s wants to build a new display to showcase the cake that you think they should sell. They want to have at least 5 of these cakes in the

display case at all times. What size display case do you think they should build? Create a sketch of the case in the space below. Label the

dimensions of the display case.

Basketball Hamburger Pig Car

Ingredient Cost $5.87 $6.45 $5.50 $6.20

Labor Cost $12.25 $13.50 $12.75 $12.80

Dimensions 12” diameter 10 “ height

13” diameter 7.5 “ height

16” x 8” x 6” 15” x 10” x 5.5 “

Basketball Hamburger Pig Car

Box Size

Box Cost

Ingredient Cost

Labor Cost

Total Cost (box, ingredients, labor)

Problem Based Learning and Common Core, A Natural Connection

SAS Math DayAugust 7, 2014

Fort King Middle School Ocala, Florida

“The Apollo program was designed to land humans on the Moon and bring them safely back to Earth.”

http://www.nasa.gov

Look at the astronaut and the “hose”. What math objectives could be addressed by this picture?

What is PBL?Problem Based Learning

“A form of inquiry-based education , originally invented for medical school, where learning is initiated with an ill structured problem and students learn to direct their own course of study.” Dr. Shelagh Gallagher

PBL keeps students from asking, “Will I ever use this

real life?”

Difference in Problem Based and Project Based?

Project Based Learning

• Multi Disciplinary

• Tend to be lengthy

Problem Based Learning

• Mainly single subject

• Less amount of time

Really, they are very much alike and you can use what works best

for you!

What does that mean for math classes?

Engaged students who find relevance in what they are doing in math classes!

Mr. Christopher Davis, 6th grade math teacher, Rolesville Middle School

What do you think were some of their answers?

Video

Each group had 1-2 minutes to present their findings to the

management of Hansen’s Cakes.

Post presentation discussions were AWESOME!!!

Video

Moving with Volume

Developing your own PBL math lessons is as easy as

1,2,3

1. Pick2. Brainstorm3. Lay it out

1. Pick

•Pick your objectives or skills.•Which skills do you want your students to apply and demonstrate mastery.

2. Brainstorm

•Brainstorm real world ideas and scenarios.•Bring objectives and real world ideas together.•Let your imagination guide you!

3. Lay it out

•What resources will you need?•How will you know if students have mastered the skill?

It may several attempts to create the most effective lesson. Don’t give up! Change and try again.

Let’s practice!Work with a partner and

follow the 3 steps. 1. Pick

2. Brainstorm3. Lay it out.

Resources

Teacher Pages http://www.cotf.edu/ete/teacher/teacherout.html

Emergent Math http://emergentmath.com/2011/06/27/things-that-are-good-a-problem-based-learning-approach-in-mathematics/

How-to Use Problem-Based Learning in the Classroom by Robert Delisle

The Power of Problem-Based Learning by Barbara J. Duch

Problem-Based Learning in Middle and High School Classrooms: A Teacher's Guide to Implementation by Ann Lambros

http://learnpbl.weebly.com/pbl-ideas.html

http://pblacademy.org/

Lori Warren – lwarren@wcpss.netChristopher Davis – cdavis7@wcpss.net

Name:

Mr. and Mrs. Davis are retiring and have purchased a cabin in the

mountains that sits beside a peaceful stream. He has hired the “You

Call, We Haul” moving company to pack all of his things into boxes,

load them into a moving truck, and deliver the boxes to his cabin in

the mountains.

The owner of the moving

company, Mr. Smith, showed up

Saturday morning to begin

packing all of the Davis’ things into cardboard boxes. Ten hours later, Mr. Smith

packed the last of their things into boxes and breathed a huge sigh of relief. Before

Mr. Smith left Davis’ house, he counted all of the boxes that had been packed

because he needed to determine what size moving truck to use to move the Davis’

to the mountains. The table below contains his data.

Box Size Box Length

(inches) Box Width

(inches) Box Height

(inches) Number of boxes used

Cost per box

Small 16 12 12 101 $1.70

Medium 18 18 16 97 $2.35

Large 18 18 24 70 $3.00

What is the total volume of the boxes that need to be moved?

Total Volume of all Boxes:

What is the cost for all the boxes?

Total Cost of all Boxes?

Small Boxes Medium Boxes Large Boxes

Cost of small boxes Cost of medium boxes Cost of large boxes

Mr. Smith has the choice of two trucks that he could use to move Mr. Davis. The information for each truck is in the

table below. The table also shows the Labor Cost (the amount of money Mr. Smith will charge for his labor).

Truck Size Truck length Truck width Truck Height Cost to use truck Labor Cost

16 Foot 15 feet 7 inches 7 feet 5 inches 6 feet 5 inches $175 $650

24 Foot 24 feet 7 feet 5 inches 7 feet 5 inches $225 $900

Hint: Convert all dimensions to inches. Remember, there are 12 inches in each foot.

What is the volume of each truck?

Questions that need to be answered:

1. What size truck should Mr. Smith use to move the Davis’ things to his cabin in the mountains?

Hint: Compare the total volume of the boxes to the volume of each truck. Which truck is the best choice?

2. How much will it cost Mr. Davis to use the Mr. Smith’s “You Call, We Haul” moving company to move to the

mountains?

Hint: Add up the cost of all boxes, cost of truck, and labor cost.

Volume of 16 Foot Truck Volume of 24 Foot Truck

Volume of Boxes vs. Volume of 16 Foot Truck Volume of Boxes vs. Volume of 24 Foot Truck

Cost of Boxes

Cost of Truck

Cost of Labor

Total Cost

Name:

Moving Company Scenario

Mr. Davis is retiring and Mrs. Davis have purchased a cabin in the

mountains that sits beside a peaceful stream. He has hired the “You

Call, We Haul” moving company to pack all of his things into boxes,

load them into a moving truck,

and deliver the boxes to his

cabin in the mountains.

The owner of the moving company, Mr. Smith, showed up Saturday morning to

begin packing all of the Davis’ things into cardboard boxes. Ten hours later, Mr.

Smith packed the last of their things into boxes and breathed a huge sigh of relief.

Before Mr. Smith left Davis’ house, he counted all of the boxes that had been

packed because he needed to determine what size moving truck to use to move the

Davis’ to the mountains. The table below contains his data.

Box Data Table

Box Size Box Length

(inches) Box Width

(inches) Box Height

(inches) Number of boxes used

Cost per box

Small 16 12 12 101 $1.70

Medium 18 18 16 97 $2.35

Large 18 18 24 70 $3.00

Mr. Smith has the choice of two trucks that he could use to move Mr. Davis. The information for each truck is in the

table below. The table also shows the Labor Cost (the amount of money Mr. Smith will charge for his labor to pack, load,

delivery, and unload the truck).

Truck Data Table

Truck Size Truck length Truck width Truck Height Cost to use truck Labor Cost

16 Foot 15 feet 7 inches 7 feet 5 inches 6 feet 5 inches $175 $650

24 Foot 24 feet 7 feet 5 inches 7 feet 5 inches $225 $900

Hint: Convert all dimensions(length, width, height) to inches.

Questions that need to be answered:

1. What size truck should Mr. Smith use to move Mr. Davis’ things to his cabin in the mountains?

2. Why did you choose this truck?

3. How much will it cost Mr. Davis to use the Mr. Smith’s “You Call, We Haul” moving company to move to the

mountains? (Don’t forget to include the Labor Cost)