Wyoming Math 7.G.6

7.G.6 is a cluster heading. These are the individual standards under it.

• 7.G.6a

  Area and surface area of objects composed of triangles and quadrilaterals

• 7.G.6b

  Volume of objects composed only of right prisms having triangular or quadrilateral bases.

01

What Students Need to Do

Students find the area of shapes made from triangles and quadrilaterals. They find the exposed surface area and volume of right prisms, including solids made by joining prisms together.

02

What Mastery Looks Like

Given a diagram with dimensions, students find the area of each exposed face without counting hidden faces. They find each prism’s base area, multiply by its length, and give answers in square or cubic units.

03

Common Misconceptions

Students count faces where two prisms touch as exposed surface area. They use a triangle’s slanted side as its height, or give volume in square units.

04

How to Assess It

A right prism has a right-triangle base with sides 3, 4, and 5 cm and a length of 10 cm. Find its surface area and volume, showing how you found the triangle’s area.

1. 01

   Tape a 2 cm cube to a 4 cm cube; mark the hidden faces, then calculate total volume and exposed surface area.

2. 02

   Draw two joined rectangular prisms and explain why the touching faces are excluded from surface area but their volumes still add.

3. 03

   Give pairs four sketches of joined right prisms with labeled dimensions; have them find each total volume, then trade papers to check.

4. 04

   Measure a cereal box and a triangular mailing tube; estimate cardboard area without flaps and the space each holds.

• 7.RP.3

  Solve multi-step real-world and mathematical problems involving ratios and percentages.

• 8.F.4

  Apply the concepts of linear functions to real-world and mathematical situations.

• 7.SP.1

  Solve real-world and mathematical problems involving: