Surface Area and Volume + Business

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Essential Questions for students (objectives):  Is there a relationship between the outside of a container and how much it holds?  What are the mathematical reasons behind the packaging chosen by businesses? 

Supplies: You-tube video (4:31 minutes in length), journal 1 handout, project handout with rubrics, access to information on surface area and volume from texts or internet, sticky notes,  Essential Question poster

CCSS:  7G.6, 8G.9, TEKS 7.8 A, B, C, 7.9 A,B,C,D, 8.6 A, B, 8.7 A, B
Instructional Format:  Video, teacher–lead instruction, cooperative groups, self-paced project learning

Time needed: 25-30 minutes if used for introductory purposes or if the project is used it can last the length of the geometry unit.
Vocabulary for a Word Wall:  Surface area, volume, prism, pyramid, sphere, slant height, lateral height, lateral edge
Lesson Description:

1) Show essential question intro to surface area and volume video to students. (This is a you-tube video that takes approximately 4 ½  minutes)

2) Pause the video at the first blue screen with “What do I notice?  What do I wonder?”  and have students generate their own initial answers to those questions.  Share responses with a partner.

3) Play the video through the comparisons of tea-bags submerged in water, then pause the video at the next blue screen.  Ask students to revise/add to their initial notice and wonder questions.  Share out as a class.

4) Pause the video at the blue screen prompting, “What are the reasons for the different packaging?”   Either have students discuss in groups and share out or have students write in their interactive journals.

5) Pause video on blue screen with the question:  “Is there a relationship between the outside of a container and how much it holds?”   Ask students to either generate initial thoughts and record them either individually or as groups and write them on post-its.  Students can also generate “I wonder” post-its (I would choose a different color for these).  Have students place post-its on/around the essential question poster.  These questions/ideas can be re-visited throughout the unit on surface area and volume and could be used as an essay question or group presentation that would be required to use evidence & vocabulary from the unit.

         a. Alternate activity – use journal entries to have students record thoughts on the essential question.

6) The Over-arching Essential Question (hook): What are the mathematical reasons behind the packaging chosen by businesses?  Can be used as a research question that must be answered with evidence provided by the unit on surface area and volume or it could even be used as an essay question on a summative or formative assessment.

Project:  I use a self-paced project that I hand out immediately after the video.  Students use any available resource to research surface area and volume in order to complete the project.  I always have 3-D geometric shapes available (and nets) for students to use in an exploratory fashion.  The only “teaching” I do in this unit are small mini-lessons that show how the surface area or volume formulas are generated.  I have an authentic audience some and judge the presentations (either administration or business leaders from the community).  The project includes a work plan in order to help students build self-regulation skills (for more ideas on self-regulation, see any of Dr. Cash’s books from Free Spirit Press).   In addition, the project stresses collaboration and includes a collaboration rubric. 

Assessment (Acceptable Evidence): Rubrics from the project.
Cautionary notes/ misconceptions/additional connections:  This introductory lesson is a great time to mention the CCSS Mathematical Practice #3 – Constructing Mathematical Arguments.   Click on this link if you want to see lessons or information on The 8 Mathematical Practices - Grades 6-12.


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