Relationships exist between twodimensional and threedimensional shapes and their measures. Students have already learned to find area and volume, but have not explored them together. In this unit, students will find volumes of rectangular prisms filled with fractional edgelength cubes and surface area of rectangular and triangular prisms and pyramids from their nets. Students will learn to identify and draw nets of prisms and pyramids. Students will apply the concept of additive area to find the surface area of geometric solids; this may introduce some confusion between 2 and 3dimensional applications. Finding volume using unit cubes with fractional edge lengths may also challenge students since they are accustomed to unit cubes representing whole units.
Key Concepts:
 Area is a measure of twodimensional space and volume is a measure of threedimensional space.
 The formula for volume of a rectangular prism is connected to filling the prism with unit cubes.
 "Nets" of three dimensional figures allow us to see the faces of the figure and how the sum of the area of the faces results in the surface area.
Prior Knowledge Needed:
 Apply area formulas; (Grade 4, Unit 2; 4.MD.A.3)
 Understand Volume; (Grade 5, Unit 1; 5.MD.C.35)
 Understand the Concept of Multiplying Fractions by Fractions; (Grade 5, Unit 5; 5.NF.B.4)
 Interpret Multiplying Fractions as Scaling: (Grade 5, Unit 7: 5.NF.B.6)
 Solving Problems Involving Geometry; (Grade 5, Unit 9; 5.MD.C.35)
 ProblemSolving in Area of 2D Shapes; (Grade 6, Unit 10; 6.G.A.1)
Units on the Horizon:
 2D Figures; (Grade 7, Unit 11; 7.G.B.4, 6)
 3D Figures; (Grade 7, Unit 12; 7.G.B.6)
 Volume of cones, spheres, and cylinders; (Grade 8, Unit 14; 8.G.C.9)
Lessons

Lesson objective: Differentiate among linear, area, and volume measurements and the units required for each. Students bring prior knowledge of measuring area and volume from CCSS 4.MD.A.3 and 5.MD.C5. This prior knowledge is extended to include length, ...

Lesson objective: Recognize that rectangular prisms can be built with unit cubes with fractional edge lengths which then can be used to determine the prisms' dimensions and volume. Students bring prior knowledge of packing prisms with unit cubes to find...

Lesson objective: Find the dimensions and volumes of all unique prisms possible built with a given number of halfunit cubes. This lesson helps to build the procedural skill of finding the dimensions and volumes of rectangular prisms built with fraction...

Lesson objective: Determine the volume and dimensions of rectangular prisms built with fractional edgelength cubes with fluency. This lesson helps to build fluency with volume of prisms built with fractional edgelength cubes. Prisms are presented with...

Lesson objective: Determine how many fractionalunit cubes it takes to fill a rectangular prism of a given volume. This lesson provides an opportunity for students to apply their knowledge and understanding of volume to a reallife situation. Students a...

Lesson objective: Identify three dimensional figures by their two dimensional nets and then use nets to distinguish between prisms and pyramids. Students bring prior knowledge of classifying twodimensional shapes from CCSS 5.G.B3 and B.4. This prior kn...

Lesson objective: Draw nets of pyramids and prisms. This lesson helps to build the procedural skill of drawing nets of three dimensional figures. Transparent threedimensional figures are used here because they help students see all of the faces of the ...

Lesson objective: Define surface area and determine a strategy for finding the surface area of three dimensional figures from their nets. Students bring prior knowledge of area of composite figures from CCSS 6.G.A.1. This prior knowledge is extended to ...

Lesson objective: Find the surface area of three dimensional figures from their nets. This lesson helps to build the procedural skill of decomposing a net into shapes that have area formulas. Highlighting the shapes within nets is used here because it s...

Lesson objective: Solve a problem involving surface area. This lesson provides an opportunity for students to apply their knowledge and understanding of surface area to a reallife situation. Students are asked to determine how much poster board a teach...