Geometry
Unit description: In this unit students will solve for the area and volume of a variety of polygons in real-world problems. The students will learn to create nets to represent three dimensional polygons.
Essential Outcomes of the Unit
Geometry: Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.1 Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.2 Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Other Standards Addressed in the Unit
Geometry: Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.3 . Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.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.
6.G.5 Use area and volume models to explain perfect squares and perfect cubes.
Essential Questions and Big Ideas
How can I create and interpret geometric shapes on the coordinate plane?
- Lengths on a coordinate plane can be measured by counting spaces between points.
- When two coordinates have an x or y coordinate in common, their distance is represented by the difference between the unique coordinates.
How do I find the areas of geometric shapes using what I know about rectangles?
- Perfect squares are numbers that can represent the areas of squares, as they represent an amount times itself.
- Right triangles can be thought of as halves of rectangles, so the area of a triangle can be found from ½ (l * w) or ½ (b * h).
- Trapezoids can be decomposed into rectangles and triangles to find area.
How do I find the volume of rectangular prisms with whole number and fractional edge lengths?
- Volumes of rectangular prisms can be found by multiplying l * w * h.
- Perfect cubes are numbers that can represent the volume of a cube, as they represent an amount times itself times itself.
- Volumes of rectangular prisms with fractional edge lengths can be found in the same way as if they were whole number edge lengths.
How do I represent 3-D figures using nets?
- A net is a pattern obtained when a three-dimensional figure is laid out flat showing each face of the figure.
- 3 – D figures can have more than one net depending on how it is laid out.
- Nets can be used to determine surface area.
Download the complete Grade 6 Math Unit 5 framework to customize for your own planning.