Virginia SOL 7.MG.1.a
The Standard
Develop the formulas for determining the volume of right cylinders and solve problems, including those in contextual situations, using concrete objects, diagrams, and formulas.
Virginia Standards of Learning for Mathematics · 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.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect a cylinder's volume to the area of its circular base multiplied by its height. They use models, diagrams, and the formula V = πr²h to solve numerical and contextual problems.
What Mastery Looks Like
- Students explain the formula as the area of a circular base multiplied by the cylinder's height. They identify needed measurements, calculate accurately, label answers with cubic units, and interpret the result in context.
Common Misconceptions
- Students often use the diameter as the radius, forget to square the radius, or substitute circumference for base area. They may also report square units instead of cubic units or use the cylinder's slanted side rather than its vertical height.
How to Assess It
- Exit ticket: A can has a diameter of 8 cm and a height of 12 cm. Draw and label it, then find its volume in terms of π and using 3.14.
Lesson moves
Ways to Teach It
Stack identical cardboard circles, measure the stack's height, and connect the base area and number of layers to the cylinder's volume.
Ask students to explain in writing why a cylinder with double the radius has four times the volume when height stays fixed.
Run a card sort matching cylinder diagrams, measurements, expressions, and volumes, including cards that use diameter instead of radius.
Measure a food can, calculate its volume, and compare the result with the capacity printed on its label.
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Printable 7.MG.1.a Worksheet
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Related Standards
- 8.MG.2.b
Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
- 5.MG.2.d
Investigate and develop a formula for determining the volume of rectangular prisms using concrete objects.
- 5.MG.2.e
Solve problems, including those in context, to estimate and determine the volume of a rectangular prism using concrete objects, diagrams, and formulas when the ...
- 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, us...
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