Mathematics 6 (Grade 6)
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 should my child know and be able to do?
Students will:
Solve real-world 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 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.
Students will:
Solve real-world 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 real-world 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 real-world 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 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.
- 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?
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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." |