NY Next Generation Math NY-5.MD.5.b

Math5th GradeRelate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

The Standard

Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students apply V = l times w times h and V = B times h to right rectangular prisms with whole-number edge lengths. They interpret each measurement and the volume in context.

What Mastery Looks Like

A student finds an 8-by-5-by-3 storage bin's volume as 120 cubic feet. The student identifies the 40-square-foot base and shows that 40 times 3 gives the same volume.

Common Misconceptions

Students may use only two dimensions, add dimensions, or confuse base area with a base edge. They may label volume with linear or square units.

How to Assess It

Give students a right rectangular prism with length 9 centimeters, width 4 centimeters, and height 6 centimeters. Ask them to use both formulas and explain why the results agree.

Lesson moves

Ways to Teach It

  1. Measure whole-number edges on prism models, calculate the base area, and find volume with both equivalent formulas.

  2. Ask students what B represents in V = B times h and how it differs from one base edge.

  3. Play formula label match with prism diagrams, edge measures, base areas, heights, and cubic-unit answers.

  4. Calculate the capacity of rectangular storage bins or garden boxes from whole-number dimensions.

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