Mathematics 6 (Grade 6)
Unit 4: Geometry (6.G)
Students in Grade 6 build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, student discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
What will my child learn?
Students will:
Solve realworld and mathematical problems involving area, surface area, and volume.
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 realworld 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 realworld and mathematical problems.
6.G.A.4
Represent threedimensional 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 realworld and mathematical problems.
Students will:
Solve realworld and mathematical problems involving area, surface area, and volume.
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 realworld and mathematical problems.
 Check for Understanding: Area of Triangles  Area of Shapes on Grids  Area of Composite Shapes  Area of Parallelograms  Areas of Trapezoids  Area Challenge
 Review/Rewind: Intro. to Perimeter, Area
 Enrichment Tasks: Finding Areas of Polygons  Same Base and Height, Variation 1
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 realworld and mathematical problems.
 Check for Understanding: Volume with Fractions  Volume Word Problems with Fractions
 Review/Rewind: Volume of a Rectangular Prism with Fractional Edges
 Enrichment Tasks: Banana Bread  Computing Volume Progression 1
6.G.A.4
Represent threedimensional 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 realworld and mathematical problems.
 Check for Understanding: Nets of 3D Figures  Surface Area Using Nets  Surface Area
 Review/Rewind: Surface Area: Nets of Polyhedra
 Enrichment Tasks: Christo's Building  Painting Barn
What are some signs of student mastery?

Tools & Technology
NCTM's Isometric Drawing Tool (requires Java) can be used to create dynamic drawings on digital isometric dot paper. Draw net figures using edges, faces, or cubes. You can shift, rotate, color, break into parts, and view in 2‑ or 3‑dimensions. 
More 4 U
Watch a video about "Finding the Areas of Triangles, Parallelograms, and Trapezoids." 