 Mathematics Grade 8

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.1

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

• "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?
• Ants versus humans
This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.
• 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.
• Extending the Definitions of Exponents, Variation 1
This is an instructional task meant to generate a conversation around the meaning of negative integer exponents.
• 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 1: Integer Exponents and Scientific Notation (EngageNY)
In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent. Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other. This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form.
• 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.
• How old are they?
In this task, students will use equations to solve a number puzzle about three people's ages
• Raising to the zero and negative powers
The goal of this task is to use the quotient rule of exponents to help explain how to define the expressions ck for c>0 and k is greater than or equal to 0. This important definition is motivated and explained by the law of exponents: adopting the definitions for the expressions c0 and c-n given in the task allows us to maintain the intuitive product and quotient rules known for all positive exponents (which this task assumes students are familiar with).
• 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.

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