# 2020 Colorado Academic Standards Online

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.

**Current selections are shown below (maximum of five)**

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*Content Area:* Mathematics
// *Grade Level:* Seventh Grade
// *Standard Category:* 4. Geometry

**Mathematics**

**Seventh Grade, Standard 4. Geometry**

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- MP2. Reason abstractly and quantitatively.
- MP3. Construct viable arguments and critique the reasoning of others.
- MP5. Use appropriate tools strategically.

7.G.A. Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them.

*Students Can:*

- Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (CCSS: 7.G.A.1)
- Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (CCSS: 7.G.A.2)
- Describe the two-dimensional figures that result from slicing three-dimensional figures, as in cross sections of right rectangular prisms and right rectangular pyramids. (CCSS: 7.G.A.3)

Academic Contexts and Connections:

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Colorado Essential Skills and Mathematical Practices:
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- Investigate what side and angle measurements are necessary to determine a unique triangle. (Entrepreneurial Skills: Inquiry/Analysis)
- Reason abstractly by deconstructing three-dimensional shapes into two-dimensional cross-sections. (MP2)
- Describe, analyze, and generalize about the resulting cross-section of a sliced three-dimensional figure and justify their reasoning. (MP3)
- Appropriately use paper, pencil, ruler, compass, protractor, or technology to draw geometric shapes. (MP5)

- How are proportions used to solve problems involving scale drawings?
- What are some examples of cross-sections whose shapes may be identical but are from different three-dimensional figures?

- This expectation is in addition to the major work of the grade.
- In Grade 6, students solve real-world and mathematical problems involving area, surface area, and volume.
- In Grade 7, this expectation connects with analyzing proportional relationships and using them to solve real-world and mathematical problems.
- In Grade 8, students understand the connections between proportional relationships, lines, and linear equations, and understand congruence and similarity using physical models, transparencies, or geometry software. In high school, students use geometric constructions as a basis for geometric proof.

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- MP1. Make sense of problems and persevere in solving them.
- MP4. Model with mathematics.
- MP6. Attend to precision.

7.G.B. Geometry: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

*Students Can:*

- State the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (CCSS: 7.G.B.4)
- Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (CCSS: 7.G.B.5)
- Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (CCSS: 7.G.B.6)

Academic Contexts and Connections:

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Colorado Essential Skills and Mathematical Practices:
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- Solve problems involving angle measure, area, surface area, and volume. (Entrepreneurial Skills: Inquiry/Analysis)
- Persevere with complex shapes by analyzing their component parts and applying geometric properties and measures of area and volume. (MP1)
- Model real-world situations involving area, surface area, and volume. (MP4)
- Reason accurately with measurement units when calculating angles, circumference, area, surface area, and volume. (MP6)

- How can the formula for the area of a circle be derived from the formula for the circumference of the circle?
- What are the angle measure relationships in supplementary, complementary, vertical, and adjacent angles?
- What are some examples of real-world situations where one would need to find (a) area, (b) volume, and (c) surface area?

- This expectation is in addition to the major work of the grade.
- In previous grades, students understand concepts of angle, measure angles, and solve real-world and mathematical problems involving area, surface area, and volume.
- In Grade 8, students understand congruence and similarity using physical models, transparencies, or geometry software, and understand and apply the Pythagorean Theorem. Students also use the formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.

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