Chapter 5: The Real Number System
Overview: Students are introduced to irrational numbers and are able to differentiate between rational and irrational numbers, as well as estimate the approximate value of irrational numbers.
Common Core Learning Standards:
- 8.N.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers, show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
- 8.N.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. For example, by truncating the decimal expansion of , show that it is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
LESSON LEARNING GOALS:
BIG IDEAS/ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
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Documents & Files
Chapter 5 Practice Test & Answer Key
m8_ch5_examview_-_rational_and_irrational_numbers.pdf |
Extra Resources
VIDEOS:
Lesson 5.0
Square roots – https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers- operations/cc-8th-roots/v/introduction-to-square-roots
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for- college/v/understanding-square-roots
Cube roots – https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc- 8th-roots/v/introduction-to-cube-roots
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/cube-root-tutorial/v/simplifying- radical-expressions1
Rational & irrational numbers – https://www.khanacademy.org/math/pre-algebra/order-of- operations/rational-irrational-numbers/v/introduction-to-rational-and-irrational-numbers
Lesson 5.1
Rational numbers – https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core- algebra-foundations-negative-numbers/e/fractions_on_the_number_line_3
Lesson 5.2
Repeating decimals – https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/decimals- fractions-pre-alg/v/converting-a-fraction-to-a-repeating-decimal
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th- repeating-decimals/v/coverting-repeating-decimals-to-fractions-1
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th- repeating-decimals/v/coverting-repeating-decimals-to-fractions-2
Lesson 5.3:
Real numbers: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre- alg/v/number-sets
Closure – http://mathbitsnotebook.com/Algebra1/RealNumbers/RNClosure.html
Additive & Multiplicative identity properties – http://www.virtualnerd.com/pre-algebra/algebra- tools/identity-definition.php
Additive & Multiplicative inverse properties – http://www.virtualnerd.com/algebra-1/algebra- foundations/inverse-properties-of-addition-and-multiplication.php
Commutative properties – http://www.virtualnerd.com/pre-algebra/algebra-tools/commutative-property- definition.php
Associative properties – http://www.virtualnerd.com/pre-algebra/algebra-tools/associative-property- definition.php
Reflexive property of equality – http://study.com/academy/lesson/reflexive-property-of-equality- definition-examples.html
Transitive property of equality – http://study.com/academy/lesson/transitive-property-of-equality- definition-example.html
Symmetric property of equality – http://study.com/academy/lesson/symmetric-property-of-equality- definition-examples.html
Lesson 5.0
Square roots – https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers- operations/cc-8th-roots/v/introduction-to-square-roots
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for- college/v/understanding-square-roots
Cube roots – https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc- 8th-roots/v/introduction-to-cube-roots
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/cube-root-tutorial/v/simplifying- radical-expressions1
Rational & irrational numbers – https://www.khanacademy.org/math/pre-algebra/order-of- operations/rational-irrational-numbers/v/introduction-to-rational-and-irrational-numbers
Lesson 5.1
Rational numbers – https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core- algebra-foundations-negative-numbers/e/fractions_on_the_number_line_3
Lesson 5.2
Repeating decimals – https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/decimals- fractions-pre-alg/v/converting-a-fraction-to-a-repeating-decimal
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th- repeating-decimals/v/coverting-repeating-decimals-to-fractions-1
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th- repeating-decimals/v/coverting-repeating-decimals-to-fractions-2
Lesson 5.3:
Real numbers: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre- alg/v/number-sets
Closure – http://mathbitsnotebook.com/Algebra1/RealNumbers/RNClosure.html
Additive & Multiplicative identity properties – http://www.virtualnerd.com/pre-algebra/algebra- tools/identity-definition.php
Additive & Multiplicative inverse properties – http://www.virtualnerd.com/algebra-1/algebra- foundations/inverse-properties-of-addition-and-multiplication.php
Commutative properties – http://www.virtualnerd.com/pre-algebra/algebra-tools/commutative-property- definition.php
Associative properties – http://www.virtualnerd.com/pre-algebra/algebra-tools/associative-property- definition.php
Reflexive property of equality – http://study.com/academy/lesson/reflexive-property-of-equality- definition-examples.html
Transitive property of equality – http://study.com/academy/lesson/transitive-property-of-equality- definition-example.html
Symmetric property of equality – http://study.com/academy/lesson/symmetric-property-of-equality- definition-examples.html