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STANDARDS

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US-VA

Math

Virginia Math

Grade 7: Measurement and Geometry

7.MG.1

The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context.

7.MG.1.a

Develop the formulas for determining the volume of right cylinders and solve problems, including those in contextual situations, using concrete objects, diagrams, and formulas.
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7.MG.1.b

Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, including those in contextual situations, using concrete objects, two-dimensional diagrams, nets, and formulas.
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7.MG.1.c

Determine if a problem in context, involving a rectangular prism or right cylinder, represents the application of volume or surface area.

7.MG.1.d

Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a factor of 1/4, 1/3, 1/2, 2, 3, or 4, including those in contextual situations.
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7.MG.1.e

Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a factor of 1/2 or 2, including those in contextual situations.
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7.MG.2

The student will solve problems and justify relationships of similarity using proportional reasoning.

7.MG.2.a

Identify corresponding congruent angles of similar quadrilaterals and triangles, through the use of geometric markings.
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7.MG.2.b

Identify corresponding sides of similar quadrilaterals and triangles.
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7.MG.2.c

Given two similar quadrilaterals or triangles, write similarity statements using symbols.
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7.MG.2.d

Write proportions to express the relationships between the lengths of corresponding sides of similar quadrilaterals and triangles.
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7.MG.2.e

Recognize and justify if two quadrilaterals or triangles are similar using the ratios of corresponding side lengths.
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7.MG.2.f

Solve a proportion to determine a missing side length of similar quadrilaterals or triangles.
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7.MG.2.g

Given angle measures in a quadrilateral or triangle, determine unknown angle measures in a similar quadrilateral or triangle.
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7.MG.2.h

Apply proportional reasoning to solve problems in context including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths.
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7.MG.3

The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals.

7.MG.3.a

Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid:

7.MG.3.a.i

parallel/perpendicular sides and diagonals;
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7.MG.3.a.ii

congruence of angle measures, side, and diagonal lengths; and
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7.MG.3.a.iii

lines of symmetry.
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7.MG.3.b

Sort and classify quadrilaterals as parallelograms, rectangles, trapezoids, rhombi, and/or squares based on their properties:

7.MG.3.b.i

parallel/perpendicular sides and diagonals;
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7.MG.3.b.ii

congruence of angle measures, side, and diagonal lengths; and
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7.MG.3.b.iii

lines of symmetry.
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7.MG.3.c

Given a diagram, determine an unknown angle measure in a quadrilateral, using properties of quadrilaterals.
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7.MG.3.d

Given a diagram, determine an unknown side length in a quadrilateral using properties of quadrilaterals.
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7.MG.4

The student will apply dilations of polygons in the coordinate plane.

7.MG.4.a

Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been dilated. Scale factors are limited to 1/4, 1/2, 2, 3, or 4. The center of the dilation will be the origin.
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7.MG.4.b

Sketch the image of a dilation of a polygon limited to a scale factor of 1/4, 1/2, 2, 3, or 4. The center of the dilation will be the origin.
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7.MG.4.c

Identify and describe dilations in context including, but not limited to, scale drawings and graphic design.
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