Strand: EXPRESSIONS AND EQUATIONS (8.EE)

Work with radical and integer exponents (Standards 8.EE.1-4). Understand the connections between proportional relationships, lines, and linear relationships (Standards 8.EE.5-6). Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations (Standards 8.EE.7-8).

Standard 8.EE.2

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

• "Ponzi" Pyramid Schemes
The student's task is to find the fatal catch in this sure-fire money making scheme.
• 100 People
In the 1990s researchers calculated that if there were just 100 people in the world, there would be 20 children, 25 people would not have food and shelter, 17 people would speak Chinese, and 8 would speak English. In this task, students are asked to estimate the real numbers, given that there are approximately seven billion people in the world.
• A Million Dollars
In this task, students will figure out questions such as: How much does a million Dollars in Dollar bills weigh? How many burgers can you buy for a million Dollars?
• Chapter 7 - Mathematical Foundation (UMSMP)
This is Chapter 7 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Rational and Irrational Numbers.
• Chapter 7 - Student Workbook (UMSMP)
This is Chapter 7 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Rational and Irrational Numbers.
• Chapter 8 - Mathematical Foundation (UMSMP)
This is Chapter 8 of the Utah Middle School Math Grade 8 textbook. It provides a Mathematical Foundation for Integer Exponents, Scientific Notation and Volume.
• Chapter 8 - Student Workbook (UMSMP)
This is Chapter 8 of the Utah Middle School Math Grade 8 student workbook. It focuses on Integer Exponents, Scientific Notation and Volume.
• Estimating Length Using Scientific Notation
This lesson unit is intended to help you assess how well students are able to estimate lengths of everyday objects, convert between decimal and scientific notation, and make comparisons of the size of numbers expressed in both decimal and scientific notation.
• Giantburgers
Every day 7% of Americans eat at Giantburger restaurants! The student's task is to decide whether this newspaper headline can be true.
• Grade 8 Math Module 7: Introduction to Irrational Numbers Using Geometry (EngageNY)
Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2: Lessons 15 and 16, M3: Lessons 13 and 14). In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle. In cases where the side length was an integer, students computed the length. When the side length was not an integer, students left the answer in the form ofx2=c, where c was not a perfect square number. Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.
• Grade 8 Unit 2: Exponents and Equations (Georgia Standards)
In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system; recognize that every rational number has a decimal representation that either terminates or repeats; recognize that irrational numbers must have decimal representations that neither terminate nor repeat; understand that the value of a square root can be approximated between integers and that nonperfect square roots are irrational; locate rational and irrational numbers on a number line diagram; use the properties of exponents to extend the meaning beyond counting-number exponents; recognize perfect squares and cubes, and understanding that non-perfect squares and non- perfect cubes are irrational.
• Grade 8 Unit 3: Geometric Applications of Exponents (Georgia Standards)
In this unit students will distinguish between rational and irrational numbers; find or estimate the square and cubed root of non-negative numbers, including 0; interpret square and cubed roots as both points of a line segment and lengths on a number line; use the properties of real numbers (commutative, associative, distributive, inverse, and identity) and the order of operations to simplify and evaluate numeric and algebraic expressions involving integer exponents, square and cubed roots; work with radical expressions and approximate them as rational numbers; solve problems involving the volume of a cylinder, cone, and sphere; determine the relationship between the hypotenuse and legs of a right triangle; use deductive reasoning to prove the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in right triangles; determine if a triangle is a right triangle, Pythagorean triple; apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and solve problems involving the Pythagorean Theorem.
• How old are they?
In this task, students will use equations to solve a number puzzle about three people's ages
• Writing Expressions and Equations video
How to write an equation using what we know to solve a problem we don't know.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.