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5th grade · Math · Unit 14 of 15

Volume of Boxes

Cubes, layers and l × w × h

What your child practices

Finding volume by counting unit cubes and layers, using V = l × w × h, finding a missing side, and adding the volumes of two boxes.

New York State Learning Standards learning standard: NY-5.MD.3; NY-5.MD.4; NY-5.MD.5 · understanding volume, measuring it with unit cubes, and relating it to multiplication and addition

How we explain it

Children can open this short lesson before they practice.

  1. Volume counts the unit cubes that fill a solid.
  2. For a box, V = length × width × height.
  3. For two boxes stuck together, add their volumes.

Example: A box is 4 in long, 3 in wide and 2 in high. What is its volume? 4 × 3 = 12 cubes in one layer. 2 layers: 12 × 2 = 24. Answer: 24 cubic inches

Volume of Boxes in New York

In the New York State Learning Standards, this is unit 14 of 15 in 5th grade Math, after Unlike Denominators and before Line Plots with Fractions.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A box is 2 cubes long, 2 cubes wide and 2 cubes high. How many unit cubes fill it?

    • 12
    • 8
    • 6
    • 4

  2. Question 2

    A box has a volume of 240 cubic feet. It is 8 ft long and 6 ft wide. How high is it?

    • 5 ft
    • 10 ft
    • 226 ft
    • 48 ft
    • 2 ft

  3. Question 3

    Which unit tells how much space is inside a fish tank?

    • inches
    • square inches
    • square feet
    • cubic feet

  4. Question 4

    A shape is made of two boxes: 2 × 5 × 2 and 4 × 4 × 2 (in cm). What is its total volume?

    • 52 cm³
    • 62 cm³
    • 640 cm³
    • 50 cm³
    • 12 cm³

  5. Question 5

    A box is 4 ft long, 6 ft wide and 3 ft high. What is its volume?

    • 108 cubic feet
    • 24 cubic feet
    • 13 cubic feet
    • 69 cubic feet
    • 72 cubic feet

  6. Question 6

    Each layer of a box holds 12 unit cubes. There are 3 layers. How many cubes fill the box?

    • 35
    • 48
    • 36
    • 38
    • 15

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