Active+Learning

= Active Learning Investigation = = Grade 7 - Math = // Overview // Title: Super Foods Inc. - a real world investigation of surface area and volume. Grade 7 - 50 minutes

== Students have recently explored the formulas for the volume and surface area of cylinders and rectangular prisms. Students use these formulas to create new rectangular prism containers with the same volume as a given cylindrical container, while trying to minimize surface area. Real world cylindrical cans will be measured and converted into a rectangular prism to hold the same volume. Students will:
 * use and explore volume formulas for cylinders and rectangular prisms.
 * use and explore surface area formulas for cylinders and rectangular prisms.
 * explore surface areas
 * solve real world problems using surface area and volume formulas.

**Scenario:** Students are hired by a local company, Super Foods Inc., to evaluate new designs for their canned foods. Currently, the company ships cylindrical cans in rectangular prism boxes. The boxes are standard and cannot be changed. The company would like to save money by keeping the surface area of the metal of the can as small as possible. The task is for students to analyze volume and surface area to decide if a change in the can design will help Super Foods Inc. make a greater profit. Students will need to prove the volume of the containers is the same and record their notes and calculations for reporting back to the company.

Students learn to use volume and surface area formulas to solve real world problems. They also learn that working backwards to solve a problem is a viable means for problem solving. In this investigation, students work backwards from a known volume to create various dimensions of rectangular prisms. Students also learn that there are many different rectangular prisms that have the same volume as a cylinder. Students learn of all the possible rectangular prisms, the cube has the smallest surface area. Any prism that is longer on one or both sides will increase the surface area. In addition, students learn that a cylinder with the same volume as a rectangular prism, will always have a smaller surface area and thus be cheaper to manufacture.

**Learning Target 1**: (concept) Students will understand how the surface area of a rectangular prism changes as the dimensions change. EOL: Students will answer the question, how does the surface area of a rectangular prism change as you change the dimensions, and be able to explain which dimensions create the smallest surface area. Assessment: Essay. Students will answer the question how does the surface area of the rectangular prism change as you change the dimensions, and be able to explain that when a rectangular prism is a cube, the surface area is minimized. (Questions 3B and 3C)  **Learning Target 2:** (skill-introduced) <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Students will be able to recognize and apply geometric ideas and relationships to solve real world problems. //<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">CCSS.Math.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. // <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">EOL: Students will recommend a specific shape container for Super Food Inc. supported by mathematical reasoning and calculations. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Assessment: Essay/Personal Communication. Students will present their findings to each other and/or the class stating which container shape they recommend using mathematical calculations and data to support their reasoning. (Question 3E) <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">**Learning Target 3:** (skill-practiced) <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Students will be able to use formulas to determine the volume and surface area of cylinders and rectangular prisms. //CCSS.Math.8.G.9// //<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Know the formulas for the volumes or cones, cylinders and spheres and use them to solve real-world mathematical problems. // <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">EOL: Students will calculate the surface area and volume of an actual cylindrical can, and find the surface area of various prisms with equal volume. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Assessment: Product. Students will correctly use formulas to calculate the surface area and volume of rectangular prisms and cylinders. (Questions 1 and 2)

//<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">Rationale and Relationship to Standards //

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">This investigation looks at the concepts of volume and surface area for cylinders and rectangular prisms. These concepts and skills are important because they provide students with tools that help them make sense of the world and to make informed decisions in their life. This investigation gives students a common, real world business application for why we study volume and surface area.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">This investigation meets the Common Core State Standard Math 7.G.6 which says, "Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms" (CCSS Math, 2012, p. 50). This investigation also meets the Common Core State Standard Math 8.G.9 "Know the formulas for the volumes or cones, cylinders and spheres and use them to solve real-world mathematical problems" (CCSS Math, 2012, p. 56).

//<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 20px;">Description // <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">In this investigation __students will work in pairs__ to try to determine if a fictitious company called Super Foods Inc. should change the shape of their food containers from cylinders to rectangular prisms in order to save money. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Materials needed: Investigation packet ALI - Super Foods Inc., various cylindrical cans, tape measures, rulers, calculators.



<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Students will work in table partner pairs to begin this investigation. Each student is responsible for completing an investigation packet. Students may use their text book and logbook notes during this investigation. Text book pages 9, 22 and 23 are useful for assistance with surface area and volume of rectangular prisms and pages 32-37 are useful for assistance with surface area and volume of cylinders. This activity is based off of Problem 3.4 in their __Filling and Wrapping__ text book (Lappan et al., 2006).

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">1. Class discussion -ask students the following questions.
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Instructional Plan **
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Why do soups and soda pop come in cylindrical containers?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">When food companies ship these items, are the boxes completely filled?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What is the shape of the shipping boxes? Why do you think they are this shape?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">If we ship items in rectangular prism shaped boxes, why do we not make containers that fit this packaging better?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What if we shipped food items in prism containers? Is this a good idea?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What other shapes are there that could be used as food containers?

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">2. **Silent write** (1 minute) Prediction - What do you think is the best shape for the food containers? Why? <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> (ask students to share predictions)

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">**The Investigation** <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">3. Hand out the and read the introduction and scenario with students. (Ask for student volunteers.) Students are to complete the worksheet.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">4. Students are to work in table pairs. Allow students to choose a cylindrical container and get the other necessary supplies.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">5. Let students self direct themselves through discovery. They will need to take measurements and make calculations to find volume and surface area of the cylinder. They will then need to work backwards from the volume to find various rectangular prisms with the same volume.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">6. Remind students that the volumes may to be approximately the same, not necessarily exactly the same. They will need to use decimals or fractions such 6.25 cm for dimensions. They should use metric units for all measurements.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">7. Remind them that objects with less surface area require less material to manufacture and can save companies money.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">8. **Square Up-Share** - Once students have found a variety of rectangular prisms, have then square-pair share with other groups and compare their observations for the various prisms.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">9. **Wrap up - Class discussion**
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">How did you come up with different dimensions for the prisms?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> How did you find surface area for the different shapes?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What strategy did you use to determine which shape would be best for Super Foods Inc.?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What did you notice about the surface area of the rectangular prisms as you changed the dimensions?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What did you notice about the surface area of a cylinder compared to a prism given the same volume?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">What shape and dimension can will you recommend? Why? What data will you show the CEO and CFO of Super Foods Inc. that supports your reasoning? Ask students to come to the board and present their design on the document camera.

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">For Struggling students: Possible questions to help: <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> that are the same will create a cube and three dimensions that differ will create a rectangular prism.
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> What pieces of information will we need from this cylinder to find surface area/ volume?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> If we know the volume of the cylinder, how can we create a prism that has the same or similar volume?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Have you used your notes from yesterdays lesson?
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">To help them work backwards, remind them it takes three dimensions to determine volume of a prism. Three dimensions

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Heitschmidt, C. (2013). Cubed cans. Illuminations: Resources for teaching math. Retrieved April 24, 2013, from <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> http://illuminations.nctm.org/LessonDetail.aspx?id=L791
 * <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">References **

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2006). //Filling and wrapping: Three dimensional measurement//. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;"> Upper Saddle River, NJ: Pearson Prentice Hall.

//<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">Assessment // <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Students will complete the investigation worksheet and be able to present their recommendations for newly designed food containers to Super Foods Inc. justifying their recommendation with specific mathematical data and reasoning. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">**Entrance/Exit Ticket** <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">Use this entrance/exit ticket as a quick assessment for the learning targets in this lesson. <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif;">

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">home <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">About Me <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Additional Resources <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Grow Beast Investigation <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Back to CUIN561 Wikispace