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Common Core: Math
CCLS - Math: 8.NS.2
- The Number System
- Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers.
- State Standard:
- 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 (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
- In Topic B, students learn that to get the decimal expansion of a number (8.NS.A.1), they must develop a deeper understanding of the long division algorithm learned in Grades 6 and 7 (6.NS.B.2, 7.NS....
- In Topic A, students learn the notation related to roots (8.EE.A.2). The definition for irrational numbers relies on students’ understanding of rational numbers, that is, students know that rational...
- Student Outcomes Students calculate the decimal expansion of pi using basic properties of area. Students estimate the value of expressions such as pi2.
- Student Outcomes Students use rational approximations of irrational numbers to compare the size of irrational numbers. Students place irrational numbers in their approximate locations on a number...
- Student Outcomes Students apply the method of rational approximation to determine the decimal expansion of a fraction. Students relate the method of rational approximation to the long division...
- Student Outcomes Students use rational approximation to get the approximate decimal expansion of numbers like the square root of 3 and the square root of 28. Students distinguish between rational and...
- Student Outcomes Students know the intuitive reason why every repeating decimal is equal to a fraction. Students convert a decimal expansion that eventually repeats into a fraction. Students know...
- Student Outcomes Students apply knowledge of equivalent fractions, long division, and the distributive property to write the decimal expansion of fractions.
- Student Outcomes Students know that the long division algorithm is the basic skill to get division-with-remainder and the decimal expansion of a number in general. Students know why digits repeat in...
- Student Outcomes Students know the intuitive meaning of an infinite decimal.
- Student Outcomes Students know that every number has a decimal expansion (i.e., is equal to a finite or infinite decimal). Students know that when a fraction has a denominator that is the product of...
- Student Outcomes Students know that for most integers n, n is not a perfect square, and they understand the square root symbol. Students find the square root of small perfect squares. Students...
- Grade 8 Module 7: Introduction to Irrational Numbers Using Geometry Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented...