Title: |
Grade 8 Mathematics Module 7, Topic B: Decimal Expansion of Numbers |
URL: |
https://www.engageny.org/resource/grade-8-mathematics-module-7-topic-b-overview |
Content Source: |
EngageNY
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Type: |
Lesson/Unit Plan
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Overview: |
In Module 7, 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.A.2d). Students show that the decimal expansion for rational numbers repeats eventually, in some cases with zeros, and they can convert the decimal form of a number into a fraction (8.NS.A.2). Students learn a procedure to get the approximate decimal expansion of numbers like the square root of 2 and the square root of 5 and compare the size of these irrational numbers using their rational approximations. At this point, students learn that the definition of an irrational number is a number that is not equal to a rational number (8.NS.A.1). In the past, irrational numbers may have been described as numbers that are infinite decimals that cannot be expressed as a fraction, like the number pi. This may have led to confusion about irrational numbers because until now, students did not know how to write repeating decimals as fractions and further, students frequently approximated pi using 22/7 leading to more confusion about the definition of irrational numbers. Defining irrational numbers as those that are not equal to rational numbers provides an important guidepost for students’ knowledge of numbers. Students learn that an irrational number is something quite different than other numbers they have studied before. They are infinite decimals that can only be expressed by a decimal approximation. Now that students know that irrational numbers can be approximated, they extend their knowledge of the number line gained in Grade 6 (6.NS.C.6) to include being able to position irrational numbers on a line diagram in their approximate locations (8.NS.A.2). |
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. Unpacked Content
Alabama Alternate Achievement Standards
| 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. Unpacked Content
Alabama Alternate Achievement Standards
| 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. Unpacked Content
Alabama Alternate Achievement Standards
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Tags:
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cube root, decimal, expressions, irrational, number line, rational, square root |
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Accessibility | Text Resources: Content is organized under headings and subheadings |
Comments | There are nine lessons in this topic.
This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. |