In this unit, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons. Extending skills from previous units where they used coordinates and absolute value to find distances between points on a coordinate plane, students determine distance, perimeter, and area on the coordinate plane in real-world contexts. Next in the unit comes real-life application of the volume formula where students extend the notion that volume is additive and find the volume of composite solid figures. They apply volume formulas and use their previous experience with solving equations to find missing volumes and missing dimensions. The final topic includes deconstructing the faces of solid figures to determine surface area. To wrap up the unit, students apply the surface area formula to real-life contexts and distinguish between the need to find surface area or volume within contextual situations.
6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)
Lesson 1: The Area of Parallelograms Through Rectangle Facts
Lesson 2: The Area of Right Triangles
Lessons 3–4: The Area of All Triangles Using Height and Base
Lesson 5: The Area of Polygons Through Composition and Decomposition
Lesson 6: Area in the Real World
Topic B: Polygons on the Coordinate Plane (6.G.A.3)
Lesson 7: Distance on the Coordinate Plane
Lesson 8: Drawing Polygons in the Coordinate Plane
Lesson 9: Determining Perimeter and Area of Polygons on the Coordinate Plane
Lesson 10: Distance, Perimeter, and Area in the Real World
Topic C: Volume of Right Rectangular Prisms (6.G.A.2)
Lesson 11: Volume with Fractional Edge Lengths and Unit Cubes
Lesson 12: From Unit Cubes to the Formulas for Volume
Lesson 13: The Formulas for Volume
Lesson 14: Volume in the Real World
Topic D: Nets and Surface Area (6.G.A.2, 6.G.A.4
Lesson 15: Representing Three-Dimensional Figures Using Nets
Lesson 16: Constructing Nets
Lesson 17: From Nets to Surface Area
Lesson 18: Determining Surface Area of Three-Dimensional Figures
Lesson 19: Surface Area and Volume in the Real World
Lesson 19a: Addendum Lesson for Modeling―Applying Surface Area and Volume to Aquariums