Frosted Flakes
Real World Performance Tasks
Real World Real Life, Real Data, Real-­‐Time -­‐ These activities put students into real life scenarios where they use real-­‐time, real data to solve problems. In the Seriously Cereal series, we use data from online sources and update our activities regularly. Note -­‐ some data has been rounded or simplified in order to adjust the math to the appropriate level. Engaging Relevant – Students today often eat cereal for breakfast, making these activities very relevant to children’s everyday lives. Authentic Tasks -­‐ Through these activity sheets students learn how the packaging design industry works and are prompted to form opinions and ideas about how they would solve real life problems. A glossary is included to help them with the unfamiliar terms used. Student Choice -­‐ Each set of activity sheets is available in multiple versions where students will do the same activities using data for different breakfast cereals (e.g., Frosted Flakes, Raisin Bran, Lucky Charms etc.) You or your students can pick their favorite breakfast cereal company. Modular Principal Activity -­‐ The activity sheets always start with repeated practice of a core skill matched to a common core standard, as set out in the Teacher Guide. This principal activity (or Level 1 as it is labeled to students) can be used in isolation. Step Up Activity -­‐ For the Level 2 questions, students are required to integrate a different skill or set of skills with increasing complexity. The additional skills used to answer these questions are set out in the Teacher Guide. Challenge -­‐ This is designed to require critical thinking skills and stretch students to reason with math and data to come to conclusions. They are matched up with one of the Common Core Standards for Mathematical Practice. These activities work well with students in pairs or small groups where they can discuss the math. Cross-­‐Curricular Activity -­‐ Every activity sheet also includes a finale that you can use to extend the math lesson into another subject (usually ELA). These could be assigned in a second lesson or for homework. Customizable All of the activity sheets are provided in Word so that they can be differentiated to add remove or edit questions or even add space for students to show their work. Suggested customizations for each activity sheet are given in the Teacher Guide. Community We would love you and your students to tell us about your experience. Join the conversation on Twitter starting your tweet with @nextlesson and using #GloriousFood Updated September 2014 © NextLesson 2014 Geometric Shapes, Volume & Area
Teacher Guide
Sound bite for Students: “In the real world, we need to calculate volume and surface area in packaging and product design.” Skills Practiced: Principal Activity (Level 1): -­‐ Draw and label rectangles and triangles given geometric conditions -­‐ Create geometric drawings using a scale Step Up Activity (Level 2): -­‐ Calculate the volume and surface area of 3-­‐D shapes Common Core Math Standards Addressed: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three 7.G.A.2 measures of angles or sides, noticing when the conditions determine a unique Principal triangle, more than one triangle, or no triangle. Activity: Solve problems involving scale drawings of geometric figures, including 7.G.A.1 computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Step Up Activity: Solve real-­‐world and mathematical problems involving area, volume and surface 7.G.B.6 area of two-­‐ and three-­‐dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Differentiation Tips: You can edit any of the activity sheets to: -­‐ change the numbers or tasks given (e.g. round to nearest whole number to eliminate decimals, only have students work with the rectangular prism, add in other shaped boxes) -­‐ add or remove hints for differentiation purposes (e.g. remove the hint in Q3, remove the two step questions for finding surface area in Level 2, provide formulas for additional assistance) -­‐ remove/add questions (such as adding in other 3-­‐D shaped cereal boxes) -­‐ allow students to use calculators Due to school paper restriction, the spacing provided is only for answers. However, you could modify the spacing to add room for work if desired. Updates: At NextLesson we strive to engage students with data that is real and real-­‐time. This lesson uses data as of September 2014. Please come back for the most recent updates. Updated September 2014 © NextLesson 2014 Frosted Flakes
Name: ________________________________
You are a Product Manager for Kellogg's
Frosted Flakes. You are responsible for
overseeing the production of a new line of
cereal boxes.
Your Challenge: How should you
package and label your cereal?
LEVEL 1
You want to create a scale drawing of your current box to sketch your new packaging designs.
You start by dividing the actual measurements of the box by 3.
1.
Fill in the table to show the dimensions of your scale drawing when dividing by 3.
Round your answers to the nearest hundredth.
Cereal Box Dimensions
Length of Box
Width of Box
Height of Box
Actual Dimensions
10 inches
3 inches
14 inches
Dimensions for Scale Drawing
2.
Based on the dimensions of the scale drawing, draw the dimensions of three rectangles to
represent the views of the front, the side and the top of the box on a separate sheet of
paper. Label the sides of each rectangle with the actual dimensions of the cereal box.
For new special edition packaging, you want to try a triangular prism as a novelty cereal box that
will be the same height as the regular box. You have two possible designs. Below are the sizes of
the triangles that would form the ends of each box.
Type of Triangle
Triangle 1
Isosceles
Triangle 2
Equilateral
Updated September 2014 Details
Two angles of 70 degrees along the bottom edge.
The bottom edge will measure 4 inches.
Another side will measure 5.85 inches.
One side measures 4 inches.
1 © NextLesson 2014 Frosted Flakes
Because the triangles are a little smaller, you use only a 2:1 scale to create a reduced scale
drawing of your triangles.
3.
Fill in the missing actual dimensions for each of the triangles, and then convert all of the
dimensions using your scale. Round your answers to the nearest hundredth.
Triangle 1 Actual
Dimensions
Triangle 1 Dimensions
for Scale Drawing
Triangle 2 Actual
Dimensions
Triangle 2 Dimensions
for Scale Drawing
4.
Side 1
Triangle Dimensions
Side 2
4 inches
5.85 inches
4 inches
Side 3
Height of Box
14 inches
14 inches
On another piece of paper, draw Triangles 1 and 2 according to the scaled dimensions you
found above. Then, draw the other faces of each box. You may draw just one rectangle to
represent identical faces. Make sure to label each triangle or rectangle so that they can be
told apart, and label the angles of the triangle and the sides of all of the faces with the
actual measurements.
Hint: Angle measurements do not change in a scale drawing.
Updated September 2014 2 © NextLesson 2014 Frosted Flakes
LEVEL 2
Now that you have your shapes to represent the faces of the box, you can start completing the
design of your Frosted Flakes cereal box for construction. The boxes are made of cardboard. In
order to make a box, you must know the amount of cardboard that is needed.
Surface Area
5.
a.
b.
Calculate the area of each unique face of the rectangular prism cereal box and
label them on your drawings from Level 1.
Determine the total surface area of the rectangular prism cereal box.
6.
a.
b.
Calculate the area of each unique face of the Triangle 1 (isosceles) triangular
prism cereal box and label them on your drawings from Level 1. Hint: Triangle
1 has a height of 5.5 inches.
Determine the total surface area of the Triangle 1 triangular prism cereal box.
7.
a.
b.
Calculate the area of each unique face of the Triangle 2 (equilateral)
triangular prism cereal box and label them on your drawings from Level 1.
Round answers to the nearest tenth. Hint: Triangle 2 has a height of 3.5 inches.
Determine the total surface area of the Triangle 2 triangular prism cereal box.
8. The cost of cardboard means that the lower the surface area, the cheaper the box will be to
produce. Which design will cost the least for Kellogg's?
Volume
You also need to consider how much cereal each of the boxes will hold.
9.
Calculate the volume of the rectangular prism.
10. Calculate the volume of the Triangle I (isosceles) triangular prism.
11. Calculate the volume of the Triangle 2 (equilateral) triangular prism.
12. Which cereal box will give customers the most cereal?
Updated September 2014 3 © NextLesson 2014 Frosted Flakes
Challenge
1. Kellogg's Frosted Flakes costs $0.20 per ounce. A box with the dimensions in Question 1
holds 27 ounces of cereal. Use these measurements to calculate how much cereal each of
the triangular boxes will hold and how much you should charge for each one. Round your
answers to the nearest hundredth when necessary.
2. Design another special-edition cereal box that isn’t a rectangular prism and show the
dimensions (lengths and angles) in a scale drawing. Identify the surface area and volume of
your box and assess how much cereal it could hold and how much you would charge
customers.
3. In reality, not all cereal boxes will cost the same amount per ounce of cereal. What other
factors might you consider when deciding how much to charge for your cereal?
Updated September 2014 4 © NextLesson 2014 Frosted Flakes
Finale You could give students one of the following ideas or have them choose themselves.
1. Kellogg's is considering improving the look of its cereal box. They are in need of a new label.
Construct a net of your new label design for the cereal box. Complete the design of the label.
2. The company wants to start shipping 48 boxes of cereal in a container. Find the minimum
dimensions needed for a container that will hold 48 cereal boxes. Create a spreadsheet model to
quickly calculate how many boxes of cereal you can ship when an order comes in from a
distributor or store.
3. Frosted Flakes wants to create more environmentally-friendly products. Brainstorm and create
a brochure explaining other materials that the Kellogg's company can use to hold its cereal.
Make sure that the materials are environmentally-friendly.
4. How are cereal boxes designed? Investigate the process of creating cereal boxes: from
drafting the design, to the materials used and the actual manufacturing of the cereal boxes.
Formulate a revision plan that you believe would work best for creating the design that you have.
5. Kellogg's wants to make their cereals more healthy and nutritious. Review the ingredients for
a Kellogg's cereal. Then list some ways that Kellogg's could make the cereal healthier. Be sure to
compare the new and previous ingredients.
Updated September 2014 5 © NextLesson 2014 Frosted Flakes
ANSWER KEY LEVEL 1 1.
Length of Box
10 inches
Actual Dimensions
Dimensions for Scale Drawing
2.
Cereal Box Dimensions
Width of Box
Height of Box
3 inches
14 inches
3.33 inches
1 inch
4.67 inches
Due to school paper restriction, images have been shrunk. The measurements
should be as follows:
L = 10 in
W= 3 in
H = 14 in
3.
Note: Scale dimensions for Sides 2 and 3 of Triangle 1 have been rounded.
Triangle Dimensions
Side 2
Side 1
Triangle 1 Actual
Dimensions
Triangle 1 Dimensions
for Scale Drawing
Triangle 2 Actual
Dimensions
Triangle 2 Dimensions
for Scale Drawing
Side 3
Height of Box
4 inches
5.85 inches
5.85 inches
14 inches
2 inches
2.93 inches
2.93 inches
7 inches
4 inches
4 inches
4 inches
14 inches
2 inches
2 inches
2 inches
7 inches
Updated September 2014 © NextLesson 2014 Frosted Flakes
ANSWER KEY 4.
Due to school paper restriction, images have been shrunk.
For the side views of the prism, the missing measurements are as follows:
H = 14 in
Updated September 2014 © NextLesson 2014 Frosted Flakes
ANSWER KEY LEVEL 2 5.
Students should sketch and label their drawings from Level 1 with the following:
a. Top: 30in2
Front: 140in2
Side: 42in2
b. Total Surface Area: 424 in2
6.
Students should sketch and label their drawings from Level 1 with the following:
a. Triangle 1: 11 in2
Side 1: 56 in2
Sides 2 and 3: 81.9 in2
b. Total Surface Area: 241.8 in2
7.
Students should sketch and label their drawings from Level 1 with the following:
a. Triangle 2 : 7 in2
Sides 1, 2, and 3: 56 in2
b. Total Surface Area: 182 in2
8.
Triangular Prism 2/Equilateral Triangle Prism
9.
420 in3
10. 154 in2
11. 98 in2
12. Rectangular Prism
Updated September 2014 © NextLesson 2014 Frosted Flakes
ANSWER KEY Challenge 1. The Triangle 1 (isosceles) prism box can hold 9.9 ounces and should cost $1.98.
The Triangle 2 (equilateral) prism box can hold 6.3 ounces and should cost $$1.26.
2. Answers will vary. Give credit for answers that design a box that isn’t a rectangular
prism, include a scale drawing with labeled angles and side lengths, correctly
identify surface area and volume, and calculate how much cereal it could hold and
how much customers should be charged.
3. Possible answers include:
-the cost of materials and production of the box
-the cost of ingredients for the cereal
-the demand for that particular cereal/brand
Updated September 2014 © NextLesson 2014 Frosted Flakes
Job Background
Product Managers come within the categpry of “Advertising, Promotions and Marketing Managers” according to the Bureau of Labor Statistics. Quick Facts: Advertising, Promotions, and Marketing Managers 2012 Median Pay
$115,750 per year $55.65 per hour Entry-­‐Level Education
Bachelor’s degree Work Experience in a Related Occupation
On-­‐the-­‐job Training
See How to Become One
None Number of Jobs, 2012
216,000 Job Outlook, 2012-­‐22
12% (As fast as average) Employment Change, 2012-­‐22
25,400 What Advertising, Promotions, and Marketing Managers Do Advertising, promotions, and marketing managers plan programs to generate interest in a product or service. They work with art directors, sales agents, and financial staff members. Work Environment About 24 percent of advertising and promotions managers worked for advertising agencies in 2012. About 16 percent of marketing managers worked in the management of companies and enterprises industry. How to Become an Advertising, Promotions, or Marketing Manager A bachelor’s degree is required for most advertising, promotions, and marketing management positions. These managers typically have work experience in advertising, marketing, promotions, or sales. Pay In May 2012, the median annual wage for advertising and promotions managers was $88,590. The median annual wage for marketing managers was $119,480 in May 2012. Job Outlook Employment of advertising, promotions, and marketing managers is projected to grow 12 percent from 2012 to 2022, about as fast as the average for all occupations. Advertising, promotions, and marketing will continue to be essential for organizations as they seek to maintain and expand their share of the market. Updated September 2014 © NextLesson 2014