Grade 8 Mathematics Module 7, Topic A: Square and Cube Roots

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Title:

Grade 8 Mathematics Module 7, Topic A: Square and Cube Roots

URL:

https://www.engageny.org/resource/grade-8-mathematics-module-7-topic-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 7, 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 numbers are points on a number line (6.NS.C.6) and that every quotient of integers (with a non-zero divisor) is a rational number (7.NS.A.2). Then irrational numbers are numbers that can be placed in their approximate positions on a number line and not expressed as a quotient of integers. Though the term “irrational” is not introduced until Topic B, students learn that irrational numbers exist and are different from rational numbers. Students learn to find positive square roots and cube roots of expressions and know that there is only one such number (8.EE.A.2). Topic A includes some extension work on simplifying perfect square factors of radicals in preparation for Algebra I.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
1. Define the real number system as composed of rational and irrational numbers.

a. Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.

b. Convert a decimal expansion that repeats into a rational number.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.1 Add and subtract fractions with like denominators (e.g. halves, thirds, fourths, tenths).
M.AAS.8.1a Add and subtract decimals to the hundredths place.
M.AAS.8.1b Convert a fraction with a denominator of 100 to a decimal.


Mathematics
MA2019 (2019)
Grade: 8
2. Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.2 Compare quantities represented as decimals in real-world examples to the hundredths place.


Mathematics
MA2019 (2019)
Grade: 8
4. Use square root and cube root symbols to represent solutions to equations.

a. Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

b. Explain that the square root of a non-perfect square is irrational.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.4 Calculate the square of numbers 1 through 10.


Tags: cube root, decimal, expressions, irrational, number line, rational, square root
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Comments

There are five lessons in this topic.

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Author: Hannah Bradley