NY Next Generation Math NY-6.G.5

Math6th GradeSolve real-world and mathematical problems involving area, surface area, and volume.

The Standard

Use area and volume models to explain perfect squares and perfect cubes.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students use area models to explain perfect squares and volume models to explain perfect cubes. They connect equal side or edge lengths to repeated multiplication and exponent notation.
What Mastery Looks Like: A student arranges 36 unit squares as a 6-by-6 square and explains that 36 is 6 squared. The student builds a 3-by-3-by-3 cube and explains that 27 is 3 cubed.
Common Misconceptions: Students may call any even number a perfect square or confuse multiplying by two with squaring. They may count visible cubes only or use unequal edge lengths for a perfect cube model.
How to Assess It: Ask students to model 49 as a square and 64 as a cube using drawings or manipulatives. Have them write the matching multiplication and power expressions.

Lesson moves

Arrange unit squares into equal-sided arrays and unit cubes into equal-edged solids, recording the matching powers.
Ask students why a 4-by-9 rectangle does not show 36 as a perfect square.
Play perfect-power sort with area models, volume models, multiplication expressions, and numerical values.
Analyze square tile designs and cube-shaped packages to identify perfect squares and cubes.

Free download

$Preview of the NY-6.G.5 printable worksheet$

A ready-to-print activity worksheet aligned to NY-6.G.5, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

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