Plans and Worksheets for Grade 8
Plans and Worksheets for all Grades
Lessons for Grade 8
Common Core For Grade 8
Examples, solutions, and videos to help Grade 8 students learn how to use rational approximation to get the approximate decimal expansion of numbers and distinguish between rational and irrational numbers based on decimal expansions.
New York State Common Core Math Grade 8, Module 7, Lesson 11
Download Worksheets for Grade 8, Module 7, Lesson 11
Lesson 11 Student Outcomes
• Students use rational approximation to get the approximate decimal expansion of numbers like √3 and √28
• Students distinguish between rational and irrational numbers based on decimal expansions.
Lesson 11 Summary
• We know that any number that cannot be expressed as a rational number is an irrational number.
• We know that to determine the approximate value of an irrational number we must determine between which
two rational numbers it would lie.
• We know that the method of rational approximation uses a sequence of rational numbers, in increments of 100
, and so on, to get closer and closer to a given number.
• We have a method for determining the approximate decimal expansion of the square root of an imperfect
square, which is an irrational number.
Lesson 11 Classwork
Place √28 on a number line. What decimal do you think √28is equal to? Explain your reasoning.
Recall the Basic Inequality:
Let c and d be two positive numbers, and let n be a fixed positive integer. Then c < d if and only if cn
Write the decimal expansion of √3.
Write the decimal expansion of √28.
Between which interval of hundredths would √14 be located? Show your work.
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