# Math Building Blocks: Chapter 5Squares, Cubes, and Radicals

5-1     Squares and Square Roots

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Understand connections between block diagrams, exponents, square numbers, and square roots.

5.2     Cubes and Cube Roots

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Understand connections between block diagrams, exponents, cube numbers, and cube roots.

5.3     irrational Square Roots

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Make the connection between square roots and exponents of 1/2. Explore properties of square roots.

5.4     irrational Cube Roots

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Make the connection between cube roots and exponents of 1/3. Explore properties of cube roots.

5.5     Powers of Powers

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Visualize the effects of taking powers of powers. Explore the meaning of rational exponents whose numerator is not 1.

5.6     Multiplication and Division with Fractional Powers

Tasks: Describe the mathematical meaning of each image. Create your own examples.
Learning goals: Represent multiplication and division involving fractional powers visually and numerically with both radicals and exponents.

5.7     Numeric Representations of a Diagram

Tasks: Write as many expressions as you can for each image.
Learning goals: Think flexibly about relationships between exponents and radicals. Explore properties of exponents and radicals.