Basketball Hamburger Pig Car $5.87 $6.45 $5.50 $ diameter 7.5 height

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1 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. Basketball Hamburger Pig Car Ingredient $5.87 $6.45 $5.50 $6.20 Cost 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 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 $ $ $ $ 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 Basketball Hamburger Pig Car Box Size 12 x 12 x 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 $ 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.

2 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. 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 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 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? Box Size Box Cost Ingredient Cost Labor Cost Total Cost (box, ingredients, labor) Basketball Hamburger Pig Car 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.

3 Problem Based Learning and Common Core, A Natural Connection SAS Math Day August 7, 2014

4 Fort King Middle School Ocala, Florida

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

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

8 What is PBL? Problem Based Learning

9 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

10 PBL keeps students from asking, Will I ever use this real life?

11 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!

12 What does that mean for math classes? Engaged students who find relevance in what they are doing in math classes!

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

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17 What do you think were some of their answers?

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22 Each group had 1-2 minutes to present their findings to the management of Hansen s Cakes. Post presentation discussions were AWESOME!!! Video

23 Moving with Volume

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27 Developing your own PBL math lessons is as easy as 1,2,3

28 1. Pick 2. Brainstorm 3. Lay it out

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

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

31 3. Lay it out What resources will you need? How will you know if students have mastered the skill?

32 It may several attempts to create the most effective lesson. Don t give up! Change and try again.

33 Let s practice! Work with a partner and follow the 3 steps. 1. Pick 2. Brainstorm 3. Lay it out.

34 Resources Teacher Pages Emergent Math 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 Lori Warren lwarren@wcpss.net Christopher Davis cdavis7@wcpss.net

35 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 Box Width Box Height Number of (inches) (inches) (inches) boxes used Cost per box Small $1.70 Medium $2.35 Large $3.00 What is the total volume of the boxes that need to be moved? Small Boxes Medium Boxes Large Boxes Total Volume of all Boxes: What is the cost for all the boxes? Cost of small boxes Cost of medium boxes Cost of large boxes Total Cost of all Boxes?

36 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 $ 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? Volume of 16 Foot Truck Volume of 24 Foot 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? Volume of Boxes vs. Volume of 16 Foot Truck Volume of Boxes vs. Volume of 24 Foot Truck 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. Cost of Boxes Cost of Truck Cost of Labor Total Cost

37 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 Box Width Box Height Number of (inches) (inches) (inches) boxes used Cost per box Small $1.70 Medium $2.35 Large $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 $ 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)