About This Chapter
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n greater than or equal to 1. (CCSS.Math.Content.HSF-IF.A.3)
Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (CCSS.Math.Content.HSF-BF.A.2)
Standard: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)
About This Chapter
Once students fully understand sequences, they'll understand the various ways of writing sequences and will be able to use them as examples for different circumstances. Your students will also be able to create different kinds of functions and read them from a table. These lessons help students understand and do the following:
- Identify a mathematical sequence
- Understand sequences as mathematical functions
- Classify arithmetic sequences
- Use writing rules to describe sequences
- Find and classify geometric sequences
You'll recognize when your students have a thorough knowledge of the standard when they're able to understand and use the rules for writing geometric and arithmetic sequences and recognize recursive sequences. The lessons combined with the standard could prove useful to students should they choose to apply for college, and it they could also be useful for such careers as finance, marketing, biochemistry and city planning.
How to Use These Lessons in Your Classroom
Following are a few suggestions that you could include in your regular curriculum to help you meet the standards for the Common Core.
Let Students Create Quizzes
Watch the lessons that identify, classify and teach the writing rules for arithmetic and geometric sequences. Allow your students to help themselves and each other by creating quizzes for the class. Each student would write out a short quiz. Collect the quizzes and pass them out randomly. After the students have completed the quizzes, discuss the answers in an open forum.
Design a Stadium Game
Have the class watch the How to Find and Classify and Arithmetic Sequence lesson. Have them graph stadiums in the shape of a trapezoid, pentagram and circle. Black out the sections inside the shapes where the games will be played. Using the lines on the graph as 'rows', have them write equations to figure out how many people will fit in each row around the playing field for each shape.
Preview Lessons and use Quizzes as Homework
In addition to regular homework, assign the video lessons for students to watch as a refresher. Use the corresponding quizzes the next day in class to go over the basic principles of sequences. Identify areas where students could use more help, and review the video lessons together.
1. What is a Mathematical Sequence?
Math is often the most fun when it acts like a puzzle to be solved. The branch of math where this is the most true involves sequences. Get an introduction to the basics and important vocabulary, as well as learn where sequences appear in nature!
2. How to Find and Classify an Arithmetic Sequence
Arithmetic sequences are everywhere, and with a few tricks you learn here, you could end up looking like a psychic the next time you go to a movie or a football game!
3. Finding and Classifying Geometric Sequences
Want your YouTube video to get a lot of hits? Besides including a cute baby or an adorable cat, getting your video to have a big common ratio is the key. Learn what I'm talking about here!
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Common Core Math - Functions: High School Standards course
- Common Core HS Functions - Basics
- Common Core HS Functions - Graphing
- Common Core HS Functions - Linear Functions
- Common Core HS Functions - Quadratic Functions
- Common Core HS Functions - Common Functions & Transformations
- Common Core HS Functions - Polynomial Functions
- Common Core HS Functions - Rational Functions
- Common Core HS Functions - Exponential & Logarithmic Functions
- Common Core HS Functions - Trigonometric Functions