Curriculum / Math / 8th Grade / Unit 7: Pythagorean Theorem and Volume / Lesson 4
Math
Unit 7
8th Grade
Lesson 4 of 16
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Represent rational numbers as decimal expansions.
The core standards covered in this lesson
8.NS.A.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.
The foundational standards covered in this lesson
7.NS.A.2.D — Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
All rational numbers have a decimal expansion. Write the decimal expansion of the rational numbers below.
a. $${{2\over5}}$$
b. $${{9\over8}}$$
c. $${-{7\over25}}$$
d. $${{108\over125}}$$
e. $${-{492\over10,000}}$$
f. $${\sqrt{16}}$$
g. $${\sqrt{0.16}}$$
h. $${\sqrt{1\over16}}$$
Follow the directions to approximate the location of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$on the number lines below.
Grade 8 Unit 8 Lesson 14 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 30, 2018, 6:55 p.m..
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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Which of the rational numbers have a terminating decimal expansion? Select all that apply.
What is the decimal expansion of $$\frac{167}{6}$$?
An example response to the Target Task at the level of detail expected of the students.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 3
Lesson 5
Topic A: Irrational Numbers and Square Roots
Define, evaluate, and estimate square roots.
8.EE.A.2
Understand that some numbers, including $${\sqrt{2}}$$, are irrational. Approximate the value of irrational numbers.
8.NS.A.1 8.NS.A.2
Locate irrational values approximately on a number line. Compare values of irrational numbers.
8.NS.A.2
8.NS.A.1
Represent decimal expansions as rational numbers in fraction form.
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Topic B: Understanding and Applying the Pythagorean Theorem
Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.
8.G.B.6
Understand a proof of the Pythagorean Theorem.
Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Find missing side lengths involving right triangles and apply to area and perimeter problems.
8.G.B.7
Solve real-world and mathematical problems using the Pythagorean Theorem (Part I).
Solve real-world and mathematical problems using the Pythagorean Theorem (Part II).
Find the distance between points in the coordinate plane using the Pythagorean Theorem.
8.G.B.8
Topic C: Volume and Cube Roots
Define and evaluate cube roots. Solve equations in the form $${x^2=p}$$ and $${x^3=p}$$.
8.EE.A.2 8.NS.A.2
Solve real-world and mathematical problems involving the volume of cylinders and cones.
8.G.C.9
Solve real-world and mathematical problems involving the volume of spheres.
Solve real-world problems involving multiple three-dimensional shapes, in particular, cylinders, cones, and spheres.
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