Math for the week of March 23,2020
Volume and the Operations of Multiplication and Addition
Concrete understanding of volume and multiplicative reasoning (5.MD.C.3) come together in Topic B as the systematic counting from Topic A leads naturally to formulas for finding the volume of a right rectangular prism (5.MD.C.5). Students come to see that multiplying the edge lengths or multiplying the height by the area of the base yields an equivalent volume to that found by packing and counting unit cubes.
Next, students solidify the connection of volume as packing with volume as filling by comparing the amount of liquid that fills a container to the number of cubes that can be packed into it. This connection is formalized as students see that 1 cubic centimeter is equal to 1 milliliter. Complexity increases as students use their knowledge that volume is additive to partition and calculate the total volume of solid figures composed of non-overlapping rectangular prisms.
Word problems involving the volume of rectangular prisms with whole number edge lengths solidify understanding and give students the opportunity to reason about scaling in the context of volume. This topic concludes with a design project that allows students to apply the concepts and formulas they have learned throughout Topics A and B to create a sculpture of a specified volume composed of varied rectangular prisms with parameters stipulated in the project description.
Lessons in this Topic
- Standards 5.MD.C.5 | 5.MD.C.5.a | 5.MD.C.5.b | 5.MD.C.5.c
- Lesson 4: Use multiplication to calculate volume.
- Lesson 5: Use multiplication to connect volume as packing with volume as filling.
- Lesson 6: Find the total volume of solid figures composed of two non-overlapping rectangular prisms.
- Lesson 7: Solve word problems involving the volume of rectangular prisms with whole number edge lengths.
- Lesson 8: Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.
- Lesson 9: Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.