Students learn to simplify expressions involving exponents. They work with scientific notation and then move on to exponential growth and decay and finally geometric sequences.
Exponent Properties Involving Products -
Exponent Properties Involving Quotients -
Zero, Negative, and Fractional Exponents -
Scientific Notation -
Exponential Growth Functions -
Exponential Decay Functions -
Geometric Sequences and Exponential Functions -
reprise Make a Table; Look for a Pattern -
Problem-Solving Strand for Mathematics
This chapter, Exponential Functions, begins with the essentials of exponential notation and builds sequentially through fairly sophisticated uses of exponents to solve real-world problems. The patterns related to exponential notation provide an opportunity to demonstrate the power of definitions. Looking for a pattern and using a table for projecting compound interest, for example, allows the repeated factor to be discovered and affirms that an exponent is used appropriately in the formula.
Alignment with the NCTM Process Standards
NCTM Process Standards from every strand can be seen in the lesson Problem-Solving Strategies. Students will both analyze and evaluate their own mathematical thinking and the strategies of others (COM.3) and use the language of mathematics to express mathematical ideas precisely (COM.4). In tackling business and scientific real world problems, they will make connections, recognize and apply mathematics in contexts outside of mathematics (CON.3). From a problem-solving perspective students will apply and adapt a variety of appropriate strategies to solve problems that arise in mathematics and in other contexts (PS.2, PS.3), and they will recognize reasoning and proof—specifically in applying the use of defining terms—as fundamental aspects of mathematics (RP.1). In developing tables to help them formulate their conclusions, students will create and use representations to organize, record and communicate mathematical ideas (R.1) and use these representations to model and interpret physical, social, and mathematical phenomena (R.3). This is a rich problem-solving lesson indeed!
- COM.3 - Analyze and evaluate the mathematical thinking and strategies of others.
- COM.4 - Use the language of mathematics to express mathematical ideas precisely.
- CON.3 - Recognize and apply mathematics in contexts outside of mathematics.
- PS.2 - Solve problems that arise in mathematics and in other contexts.
- PS.3 - Apply and adapt a variety of appropriate strategies to solve problems.
- RP.1 - Recognize reasoning and proof as fundamental aspects of mathematics.
- R.1 - Create and use representations to organize, record, and communicate mathematical ideas.
- R.3 - Use representations to model and interpret physical, social, and mathematical phenomena.