Lesson plan

# 3. The meaning of volume does not change when we work with new types of 3D figures (C)

teaches Common Core State Standards CCSS.Math.Content.7.G.A.3 http://corestandards.org/Math/Content/7/G/A/3
teaches Common Core State Standards CCSS.Math.Content.7.G.B.6 http://corestandards.org/Math/Content/7/G/B/6
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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Lesson objective: Extend the concept of volume of rectangular prisms to non-rectangular prisms.

Students bring prior understanding of volume and knowledge of using the formulas V = B * h and V = l * w * h to find the volume of rectangular prisms from CCSS.5.MD.5.B and using these formulas given fractional measurements from CCSS.6.G.A.2.  This prior knowledge is extended to non-rectangular prisms as students find and compare the volume of both rectangular and triangular prisms. A conceptual challenge students may encounter is understanding the relationship between the area of the base and the volume of the prism.

The concept is developed through comparing the volume rectangular and triangular pencil cases with similar measurements, which demonstrates the need to find the area of the base in order to find the volume of the figure.

This work helps students deepen their understanding of equivalence because the volume of all prisms is always dependent on the the area of the base.

Students engage in Mathematical Practice 7: Look for and make use of structure as they learn the importance of the area of the base of a prism when finding the volume.

Key vocabulary:

• base
• face
• height
• prism
• volume