 Unit 1

Integer Exponents and Scientific Notation

Unit Description:

The year begins with students extending their understanding of whole number exponents learned in previous grades to integer exponents in Unit 1. Students develop the properties of exponents. The unit progresses to include work with scientific notation which supports student understanding of positive and negative exponents.

Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

Louisiana Student Standards for Mathematics (LSSM)

 EE – Expressions and Equations A. Work with radicals and integer exponents. 8.EE.A.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. *I can explain why a zero exponent produces a value of one. *I can explain how a number raised to an exponent of -1 is the reciprocal of that number. *I can explain the properties of integer exponents to generate equivalent numerical expressions. 1. Multiplying exponents of the same base. For Example: 32 x 3-5 = 1/33 = 1/27 2. Dividing exponents of the same base.  For example: 3²/ 3-1 = 33 = 27 3. Expand an exponent by another exponent. For example: (2²)³ = 64 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.  For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. -I can express numbers as a single digit times an integer power of 10 (scientific notation). -I can use scientific notation to estimate very large and/or very small quantities. -I can multiply and divide numbers in scientific notation in order to compare growth or decay. -I can compare quantities to express how much larger one is compared to the other. 8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notations are used.  Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading).  Interpret scientific notation that has been generated by technology. -I can perform operations using numbers expressed in scientific notation. -I can use scientific notation to express very large and very small quantities. -I can interpret scientific notation that has been generated by technology. -I can choose appropriate units of measure when using scientific notation.

Enduring Understandings:

·         The properties of integer exponents are used to simplify expressions containing integer exponents.

·         Numbers can be expressed in scientific notation to compare very large and very small quantities and to perform computations with those numbers.

·         Expressions are powerful tools for exploring, reasoning about, and representing situations.

Essential Questions:

·         Why is it helpful to write numbers in different ways?

·         How can you evaluate positive exponents?

·         How can you evaluate negative exponents?

·         How can you develop and use the properties of integer exponents?

·         How can you use scientific notation to express very large and very small quantities?

·         Why are quantities represented in multiple ways?