Module 7: Introduction to irrational numbers using geometry

Topic A: Square and cube roots

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Intro to square roots
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Square roots of perfect squares
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Intro to cube roots
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Worked example: Cube root of a negative number
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Square root of decimal
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Dimensions of a cube from its volume
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Square roots review
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Cube roots review
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Intro to rational & irrational numbers
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Classifying numbers: rational & irrational
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Classifying numbers
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Classifying numbers review
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Approximating square roots
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Approximating square roots walk through
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Approximating square roots to hundredths
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Practice

Square rootsGet 5 of 7 questions to level up!
Cube rootsGet 5 of 7 questions to level up!
Equations with square roots & cube rootsGet 3 of 4 questions to level up!
Roots of decimals & fractionsGet 3 of 4 questions to level up!
Equations with square roots: decimals & fractionsGet 3 of 4 questions to level up!
Square and cube challengeGet 3 of 4 questions to level up!
Classify numbers: rational & irrationalGet 5 of 7 questions to level up!
Classify numbersGet 5 of 7 questions to level up!
Approximating square rootsGet 3 of 4 questions to level up!

Topic B: Decimal expansions of numbers

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Converting a fraction to a repeating decimal
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Converting repeating decimals to fractions (part 1 of 2)
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Converting repeating decimals to fractions (part 2 of 2)
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Comparing irrational numbers with radicals
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Comparing values with calculator
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Writing repeating decimals as fractions review
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Writing fractions as repeating decimals review
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Practice

Writing fractions as repeating decimalsGet 5 of 7 questions to level up!
Converting repeating decimals to fractionsGet 5 of 7 questions to level up!
Converting multi-digit repeating decimals to fractionsGet 3 of 4 questions to level up!
Comparing irrational numbersGet 5 of 7 questions to level up!
Comparing irrational numbers with a calculatorGet 5 of 7 questions to level up!

Topic C: The Pythagorean theorem

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Finding distance with Pythagorean theorem
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Distance formula
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Use Pythagorean theorem to find area of an isosceles triangle
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Pythagorean theorem word problem: carpet
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Pythagorean theorem word problem: fishing boat
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Pythagorean theorem in 3D
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Practice

Distance between two pointsGet 5 of 7 questions to level up!
Use Pythagorean theorem to find perimeterGet 3 of 4 questions to level up!
Pythagorean theorem word problemsGet 3 of 4 questions to level up!
Pythagorean theorem in 3DGet 3 of 4 questions to level up!

Topic D: Applications of radicals and roots

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Module 7, Topic D: No content yet
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About this unit

"By Module 7 students have been using the Pythagorean Theorem for several months. They are sufficiently prepared to learn and explain a proof of the theorem on their own. The Pythagorean Theorem is also used to motivate a discussion of irrational square roots (irrational cube roots are introduced via volume of a sphere). Thus, as the year began with looking at the number system, so it concludes with students understanding irrational numbers and ways to represent them (radicals, non-repeating decimal expansions) on the real number line. " Eureka Math/EngageNY (c) 2015 GreatMinds.org