Use the options below to create customized views of the 2020 Colorado Academic Standards. For all standards resources, see the Office of Standards and Instructional Support.

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clear Content Area: Mathematics // Grade Level: Sixth Grade // Standard Category: 4. Geometry

Mathematics Prepared Graduates:

• MP1. Make sense of problems and persevere in solving them.
• MP4. Model with mathematics.
• MP5. Use appropriate tools strategically. Grade Level Expectation:

6.G.A. Geometry: Solve real-world and mathematical problems involving area, surface area, and volume. Evidence Outcomes:

Students Can:

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. (CCSS: 6.G.A.1)
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. (CCSS: 6.G.A.2)
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. (CCSS: 6.G.A.3)
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. (CCSS: 6.G.A.4) Academic Contexts and Connections: Colorado Essential Skills and Mathematical Practices:

1. Recognize that problems can be identified and possible solutions can be created with respect to using area, surface area, and volume. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
2. Make sense of a problem by understanding the context of the problem before applying a formula. (MP1)
3. Model real-world problems involving shape and space. (MP4)
4. Strategically use coordinate planes, nets of three-dimensional figures, and area and volume formulas as tools to solve real-world problems. (MP5) Inquiry Questions:

1. What is the difference between what area measures and what volume measures?
2. How does using decomposition aid in finding the area of composite figures?
3. How are nets of three-dimensional figures used to find surface area? Coherence Connections:

1. This expectation supports the major work of the grade.
2. In Grade 4, students solve problems involving measurement and converting from a larger unit to a smaller unit. In Grade 5, students understand concepts of volume, relate volume to multiplication and to addition, and graph points on the coordinate plane to solve real-world and mathematical problems.
3. In Grade 6, this expectation connects with graphing points in all four quadrants of the coordinate plane and finding distances between points with the same first coordinate or the same second coordinate.
4. In Grade 7, students draw, construct, and describe geometrical figures and describe the relationships between them, and solve real-world and mathematical problems involving angle measure, area, surface area, and volume. In Grade 8, students understand congruence and similarity and understand and apply the Pythagorean Theorem.

Need Help? Submit questions or requests for assistance to bruno_j@cde.state.co.us