Exponents

Students will understand that…

• A fraction in simplest form is a perfect square if it can be written as a product of two equal fractions.
• A decimal is a perfect square if it can be written as a fraction that is a perfect square.
• The square root of a non-perfect square can be approximated using the roots of perfect squares as benchmarks.
• Powers are used to represent repeated multiplication.
• Exponents are included in the order of operations.
• Exponent laws are applied to simplify and evaluate expressions with powers.
• Patterns in powers can be used to explain and validate exponent laws.

Essential Questions:

What does square, perfect square, square root and non-perfect square mean?

What are powers? What is a square and a cube number? What is an exponent?

What are integers? What is the Zero Exponent Law? What are the Order of Operations?

• What is a base? What is a product? What is a quotient?

General Outcomes

• Students will develop number sense.
  • Students will determine the square root of positive rational numbers that are perfect squares.
  • Students will determine an approximate square root of positive rational numbers that are non-perfect squares.
  • Students will demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by:
    • representing repeated multiplication using powers.
    • using patterns to show that a power with an exponent of zero is equal to one.
    • solving problems involving powers.
  • Explain and apply the order of operations, including exponents, with and without technology.
  • Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents.
  • Explain and apply the order of operations, including exponents, with and without technology.