Subscribe

6th grade · Math · Unit 20 of 21

Perfect Squares & Cubes

Build squares and cubes

What your child practices

Using unit squares and unit cubes to see why 36 is a perfect square (a 6 by 6 square) and 27 is a perfect cube (a 3 by 3 by 3 cube), and what the exponents 2 and 3 mean.

New York State Learning Standards learning standard: NY-6.G.5 · using area and volume models to explain perfect squares and perfect cubes

How we explain it

Children can open this short lesson before they practice.

  1. A perfect square is a number of unit squares that fills a square: 5 × 5 = 5² = 25.
  2. A perfect cube is a number of unit cubes that fills a cube: 3 × 3 × 3 = 3³ = 27.
  3. That is why the exponent 2 is read “squared” and 3 is read “cubed”.

Example: How many unit cubes build a cube with 4 on each edge? Each layer is 4 × 4 = 16 cubes. There are 4 layers: 16 × 4 = 64. Answer: 64 = 4³

Perfect Squares & Cubes in New York

In the New York State Learning Standards, this is unit 20 of 21 in 6th grade Math, after Long Division and before Center, Spread & Shape.

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 cube is built from unit cubes, 7 on each edge. How many unit cubes does it use?

    • 294
    • 343
    • 49
    • 21

  2. Question 2

    Why is 8 called a perfect cube?

    • 8 = 4 + 4
    • 8 unit cubes make a 2 by 4 rectangle
    • 8 unit cubes make a 2 by 2 by 2 cube
    • 8 is even

  3. Question 3

    A cube made of 512 unit cubes has the same number on each edge. How many on each edge?

    • 10
    • 6
    • 64
    • 8

  4. Question 4

    Which number of unit cubes can make a cube with no pieces left over?

    • 65
    • 60
    • 48
    • 64

  5. Question 5

    A square is built from unit squares, 4 on each side. How many unit squares does it use?

    • 16
    • 20
    • 14
    • 8

  6. Question 6

    What does 6² mean in a model?

    • a cube with 6 on each edge
    • 6 squares in a row
    • a square with 6 unit squares on each side
    • 2 squares with 6 units each

More 6th grade