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**Part A:** The Concept of Area

**Part B:** Reasoning About Measurement

**Part C:** Problems That Illustrate Measurement Reasoning

**Homework**

This is the final session of the *Measurement* course! In this session, we will examine how measurement concepts from the previous nine sessions might look when applied to situations in your own classroom. This session is customized for three grade levels. Select the grade level most relevant to your teaching.

In the previous sessions, we explored many different topics related to measurement. You put yourself in the position of a mathematics learner, both to analyze your individual approach to solving problems and to get some insights into your own understanding of measurement topics. It may have been difficult to separate your thinking as a mathematics learner from your thinking as a mathematics teacher. Not surprisingly, this is often the case! In this session, however, we will shift the focus to your own classroom and to the approaches your students might take with mathematical tasks involving measurement. **Note 1**

For the list of materials that are required and/or optional in this session, see **Note 2**.

In this session, you will do the following:

- Explore the development of the concept of area in the middle school grades
- Examine students’ understanding of surface area and volume relationships
- Investigate instructional tasks on surface area and volume that are developmentally appropriate for middle school students
- Explore how you might teach related measurement topics

**Previously Introduced**

**Area: **Area is a measure of how much surface is covered by a figure.

**Surface Area: **Surface area is the area enclosing a three-dimensional or solid object. You can find it by taking the sum of the areas of all of the surfaces of a three-dimensional object.

**Volume: **Volume is the three-dimensional space taken up by an object.

**Note 1**

This session uses classroom case studies to examine how children in grades 6-8 think about and work with measurement concepts. If you are taking this course on your own, you may want to share your observations on Channel Talk or ask some of your colleagues for their input. Using the classrooms of fellow teachers as well as your own as case studies will allow you to make additional observations.

**Note 2**

**Materials Needed:**

- Unit cubes (optional)
- Protractor (optional)