The number 9 is a "perfect square." 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?
17.2
Activity
Standards Alignment
Building On
5.MD.5.a
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Your teacher will give you 32 snap cubes. Use them to build the largest single cube you can. Each small cube has an edge length of 1 unit.
How many snap cubes did you use?
What is the edge length of the cube you built?
What is the area of each face of the built cube? Be prepared to explain your reasoning.
What is the volume of the built cube? Be prepared to explain your reasoning.
17.3
Activity
Standards Alignment
Building On
5.MD.5.a
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
Make sure to include correct units of measure as part of each answer.
A square has side length 10 cm. Use an exponent to express its area.
The area of a square is sq in. What is its side length?
The area of a square is 81 m2. 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 cm3. What is its edge length?
A cube has edge length units. Use an exponent to write an expression for its volume.
Student Lesson Summary
When we multiply two of the same numbers together, such as , we say that we are squaring the number. We can write it like this:
The raised 2 in is called an exponent.
Because , we write and we say, “5 squared is 25.”
When we multiply three of the same numbers together, such as , we say that we are cubing the number. We can write it like this:
Because , we write and we say, “4 cubed is 64.”
We also use an exponent for square units and cubic units.
A square with a side length of 5 inches has an area of 25 in2.
A cube with an edge length of 4 cm has a volume of 64 cm3.
To read 25 in2, we say “25 square inches,” just like before.
The area of a square with a side length of 7 kilometers is km2. The volume of a cube with an edge length of 2 millimeters is mm3.
In general, the area of a square with a side length of is , and the volume of a cube with an edge length of is .
The word cubed means “to the third power.” This is because a cube with side length has a volume of , or .
In expressions like and , the numbers 3 and the 2 are called exponents. They tell how many times a number is used as a factor.
For example, = , and .
The word squared means “to the second power.” This is because a square with side length has an area of , or .
Standards Alignment
Building On
4.MD.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
