Maryland Math 7.GR.B.4

7.GR.B.4 is a cluster heading. These are the individual standards under it.

• 7.GR.B.4.a

  Solve problems involving area, surface area, and volume of polygonal figures and polyhedral solids, including triangles, quadrilaterals, other polygons, cubes, ...

• 7.GR.B.4.b

  Solve problems involving volume of curved-surface solids, including cones, cylinders, and spheres—figures without edges.

• 7.GR.B.4.c

  Interpret and justify solutions in context by comparing different geometric representations, estimating or checking for reasonableness, and explaining how the r...

01

What Students Need to Do

Students find polygon areas by splitting shapes into familiar parts. They calculate surface area of cubes, prisms, and pyramids, and volume of those solids plus cylinders, cones, and spheres. They choose units and check whether answers fit the situation.

02

What Mastery Looks Like

A student can find the area of an L-shaped floor by two methods and get the same result. They can add face areas on a prism or pyramid net and find the volume of a cone, cylinder, or sphere. They label square and cubic units correctly and check their answers against the object's size.

03

Common Misconceptions

Students sometimes add side lengths when asked for area or leave out faces hidden in a drawing when finding surface area. They may use the diameter as the radius in a volume formula. They may also use square units for volume or assume a cone holds as much as a cylinder with the same base and height.

04

How to Assess It

Exit ticket: A closed box measures 4 cm by 3 cm by 2 cm. Sketch its faces, find its surface area and volume, then explain why the answers use different units.

1. 01

   Cut and fold paper nets of a cube and a square pyramid, then measure the faces and calculate each total surface area.

2. 02

   Compare an L-shaped floor split into rectangles with one found by subtracting a cutout; write why both area methods match.

3. 03

   Give pairs dimension cards for prisms, pyramids, cylinders, cones, and spheres; have them match each with its volume formula and calculate.

4. 04

   Measure a cylindrical storage jar and calculate its volume; pour in water from a marked measuring cup to check your estimate.

• 4.GR.A.2

  Use the four operations to solve problems in context involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems in...

• 5.GR.C.5

  Relate volume to the operations of multiplication and addition and solve problems in context.