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Algebra 2 6-4 Complete Lesson: Rational Exponents

Last updated over 4 years ago

37 Nsɛmmisa

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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Solve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.

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Solve It! Reasoning: Explain why you cannot cut them into congruent pieces, each with size 4/5.

You cannot cut the three 1-squares into congruent 4/5-pieces because 3 ÷ 4/5 is not a whole number.

You cannot cut the three 1-squares into congruent 4/5-pieces because 3 is an odd number.

You cannot cut the three 1-squares into congruent 4/5-pieces because 3 × 4/5 is not a whole number.

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 2 Got It? What is the expression in radical form?

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Problem 2 Got It? What is the expression in radical form?

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Problem 2 Got It? What is the expression in exponential form?

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Problem 2 Got It? What is the expression in exponential form?

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Problem 2 Got It? Reasoning: Refer to the definition of rational exponent. Explain the need for the restriction that a ≠ 0 if m is negative.

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Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?

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Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 5 Got It?

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Problem 5 Got It?

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Problem 5 Got It?

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Problem 6 Got It?

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Problem 6 Got It?

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Error Analysis: Explain why this simplification is incorrect.

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Review Lesson 6-3: Match each radical expression on the left with its simplified form on the right.

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Review Lesson 4-4: Factor the expression completely.

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Review Lesson 4-4: Factor the expression completely.

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Review Lesson 4-4: Factor the expression completely.

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Review Lesson 4-5: Solve by factoring. Match the solutions on the left with the equation(s) they solve on the right.

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Vocabulary [Real Numbers] Review: Use the terms in the box to complete the diagram. Then give an example of each type of number.

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Use Your Vocabulary: Complete each sentence with the correct form of the word convert.

convert
converted
convertible
conversion

NOUN: Travelers to Europe calculate the __?__ of dollars to euros.
ADJECTIVE: A __?__ sofa is a couch by day and a bed by night.
VERB: To __?__ fractions to decimals, divide the numerator by the denominator.

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

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Reflection: Math Success