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.