Maryland Math 7.GR.A.2
The Standard
Describe the two-dimensional figures that result from slicing three-dimensional figures (e.g., right rectangular prisms, right cylinders) with a plane. Use the resulting shapes to explain how the structure of the solid connects to volume and surface area.
Maryland College and Career Ready Standards for Mathematics (2025) · USE STRUCTURE AND REPRESENTATION TO ANALYZE GEOMETRIC FIGURES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students picture a flat cut through a rectangular prism or cylinder, then name and sketch the shape it makes. They use repeated slices to explain volume and identify which outside surfaces count toward surface area.
What Mastery Looks Like
- Students sketch rectangular cuts through a prism, plus circular and rectangular cuts through a cylinder, with each cut labeled. They explain volume using equal base slices stacked to the solid's height, and surface area using its outside faces or surfaces.
Common Misconceptions
- Some students draw the solid's outline instead of the flat face made by the cut. Others expect every cut through a cylinder to be a circle or count an internal cut face as part of the original solid's surface area.
How to Assess It
- Exit ticket: Draw a horizontal cut and a centered vertical cut through a cylinder. Name both shapes, explain how the horizontal slice helps find volume, and list the surfaces that make up the original cylinder's surface area.
Lesson moves
Ways to Teach It
Shape two clay prisms and two clay cylinders, cut one of each horizontally and the others vertically, then trace the exposed faces.
Sketch a cylinder cut halfway up and ask: Why does its circle help find volume, but not the curved side's area?
Give pairs cards showing cuts parallel to prism faces and horizontal or vertical cylinder cuts; match each to a rectangle or circle.
Show a soup can, sketch a horizontal cut, then use the circle and can height for capacity and the curved side for label area.
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