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Module 7: Introduction to irrational numbers using geometry

Topic A: Square and cube roots

Learn
Intro to square rootsSquare roots of perfect squaresIntro to cube rootsWorked example: Cube root of a negative numberSquare root of decimalDimensions of a cube from its volumeSquare roots reviewCube roots reviewIntro to rational & irrational numbersClassifying numbers: rational & irrationalClassifying numbersClassifying numbers reviewApproximating square rootsApproximating square roots walk throughApproximating square roots to hundredths
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

Learn
Converting a fraction to a repeating decimalConverting repeating decimals to fractions (part 1 of 2)Converting repeating decimals to fractions (part 2 of 2)Comparing irrational numbers with radicalsComparing values with calculatorWriting repeating decimals as fractions reviewWriting fractions as repeating decimals review
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

Learn
Finding distance with Pythagorean theoremDistance formulaUse Pythagorean theorem to find area of an isosceles trianglePythagorean theorem word problem: carpetPythagorean theorem word problem: fishing boatPythagorean theorem in 3D
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

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