IM 6.1.17 Lesson: Squares and Cubes

[img]data:image/png;base64,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[/img][br]The number 9 is a perfect [b]square[/b]. Find four numbers that are perfect squares and two numbers that are not perfect squares.
A square has side length 7 in. What is its area?
The area of a square is 64 sq cm. What is its side length?
Use the 32 snap cubes in the applet’s hidden stack to build the largest single cube you can. Each small cube has side length of 1 unit.
How many snap cubes did you use?
What is the side length of the cube you built?
What is the area of each face of the built cube? Show your reasoning.
What is the volume of the built cube? Show your reasoning.
This applet has a total of 64 snap cubes. Build the largest single cube you can.
How many snap cubes did you use?
What is the edge length of the new cube you built?
What is the area of each face of the built cube? Show your reasoning.
What is the volume of the built cube? Show your reasoning.
The number 27 is a perfect [b]cube[/b]. Find four other numbers that are perfect cubes and two numbers that are [i]not[/i] perfect cubes.[br][img]data:image/png;base64,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[/img]
A cube has side length 4 cm. What is its volume?
A cube has side length 10 inches. What is its volume?
A cube has side length s units. What is its volume?
Make sure to include correct units of measure as part of each answer.
A square has side length 10 cm. Use an [b]exponent[/b] to express its area.
The area of a square is [math]7^2[/math] sq in. What is its side length?
The area of a square is 81 m[math]^2[/math]. Use an exponent to express this area.
A cube has edge length 5 in. Use an exponent to express its volume.
The volume of a cube is 63 cm[math]^3[/math]. What is its edge length?
A cube has edge length [math]s[/math] units. Use an exponent to write an expression for its volume.
The number 15,625 is both a perfect square and a perfect cube. It is a perfect square because it equals [math]125^2[/math]. It is also a perfect cube because it equals [math]25^3[/math]. Find another number that is both a perfect square and a perfect cube. How many of these can you find?
Close

Information: IM 6.1.17 Lesson: Squares and Cubes