6.G.A.2 6th Grade Geometry

Volume with Fractional Edge Lengths

Find the volume of a right rectangular prism with fractional edge lengths, and apply the volume formulas in real-world problems.

How to explain it

At this standard, students find the volume of right rectangular prisms with fractional edge lengths by applying V = l x w x h and V = B x h, converting mixed numbers to improper fractions, and solving real-world problems.

The anchor students hold onto: To find the volume of a rectangular prism, multiply all three edge lengths: V = l x w x h. Always convert mixed numbers to improper fractions first.

Where this leads next: Nets & Surface Area (6.G.A.4, Sheet #101) — unfold 3D prisms to compute total surface area.

Worked examples

Example 1 V = l x w x h

Find V: l=5/2, w=3/2, h=4 (ft).

Step 1V = l x w x h

Step 2l = 2 1/2 = 5/2; w = 1 1/2 = 3/2

Step 3V = 5/2 x 3/2 x 4 = 15/4 x 4

Step 4V = 15 ft³

Answer15 ft³

Example 2 V = B x h

V=Bh. B=4 1/2 sq in, h=2 in.

Step 1V = B x h

Step 2B = 4 1/2 = 9/2 sq in

Step 3V = 9/2 x 2 = 18/2

Step 4V = 9 in³

Answer9 in³

Common mistakes

What students write Student multiplies mixed numbers digit by digit: 2 1/2 x 3 computed as "2 x 3 = 6, then add 1/2 = 6.5" instead of converting to 5/2 first and getting 7.5.

The fix Convert ALL mixed numbers to improper fractions FIRST: 2 1/2 = 5/2. Then multiply as a single fraction: 5/2 x 3 = 15/2 = 7.5. Never split a mixed number mid-computation.

What students write Student uses only B (one edge length) instead of B = l x w (base AREA) in V = B x h, multiplying just one dimension by h.

The fix In V = B x h, B is BASE AREA — a two-factor product for rectangular prisms: B = l x w. Always compute B = l x w first, then multiply by h.

Teacher tip

Head off the two predictable errors before they happen. First: Convert ALL mixed numbers to improper fractions FIRST: 2 1/2 = 5/2. Then multiply as a single fraction: 5/2 x 3 = 15/2 = 7.5. Never split a mixed number mid-computation. Second: In V = B x h, B is BASE AREA — a two-factor product for rectangular prisms: B = l x w. Always compute B = l x w first, then multiply by h.