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Understanding Rational Exponents Through the Game "Two Truths and a Lie"

This lesson introduces rational exponents and their properties through an interactive game called "Two Truths and a Lie." Students will explore the rules of even and odd roots, evaluate expressions using calculators, and simplify exponential expressions with variables. By engaging with the material through critical thinking and problem-solving, learners will deepen their understanding of exponents in both theoretical and real-world applications. Assignments will further reinforce these concepts through practice problems.

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Understanding Rational Exponents Through the Game "Two Truths and a Lie"

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  1. 9.1 Rational Exponents

  2. Recall  Properties of Integer Exponents Also recall  if n is even & a ≥ 0 nonnegative nth root of a if n is even & a < 0 not a real number if n is odd nth root of a If m is an integer, n is a positive integer, and

  3. Throughout this lesson we are going to play “Two Truths and a Lie.” It is based on the ice breaker game where you tell 3 things about yourself – 2 are true, 1 is not. We are doing it “Math Style” today! You will be asked to find a “lie” and fix it to make it a truth. Ex 1) Express in radical form & evaluate a) Two Truths & a Lie 1 2 3 What went wrong?

  4. If you are asked to use your calculator & evaluate, be thoughtful about the parentheses needed. Get an error message? Maybe you need to augment how you enter it. Ex 2) Evaluate using a calculator. a) two ways to enter = –1.48 (–7) ^ (1 / 5) b) Two Truths & a Lie 1 2 3 What went wrong?

  5. Properties of Exponents are also used in simplifying exponential expressions with variables in them. Note: The order the problem is done can vary from person to person – Do what you are comfortable with! Ex 3) Simplify each expression a) b) Two Truths & a Lie 1 2 3 What went wrong?

  6. Formulas in real world situations often are rational expressions. Ex 4) T = time in seconds to complete 1 pendulum swing L = length of pedulum g = acceleration due to gravity ≈ 9.80 m/s2 Determine period of pendulum on a clock that is 99.5 cm long 99.5 cm  0.995 m ≈ 2.0 sec

  7. Homework #901 Pg 443 #1–53 odd (omit 17, 31)

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