Applied+Algebra+Lesson


 * Lesson Outline**

**1. Goals** To gain understanding of the concept of infinite geometric Series in a visual way

**2. Objectives** Students will represent an infinite geometric series by using piece of paper as a form of visual representation

**3. Materials and resources**
 * Blank square piece of paper and scissors
 * Calculator
 * Slides presentation of procedure
 * Videos describing concepts
 * Widgets to calculate results
 * Additional website support

**4. Motivation** Begin by considering a real-life example that generates numbers that form an arithmetic sequence.

Example (from []): > a. Show the amount of pie eaten each day for the first seven days. b. For each of the first seven days, write the total amount of pie eaten so far. > c. If Jack lives forever, how much of the pie will he eat?
 * Jack baked a pie and promptly ate one-half of it. Determined to make the pie last, he decided to eat only one-half of the pie that remained each day.


 * Transition:** Explain to the students that the focus of today’s lesson is to understand the concept of infinite geometric series by representing a series using a piece of paper as visual aid. They will learn represent the series by using a piece of paper and will learn to check their answer using a calculator.

**5. Lesson Procedure**
 * Introduce the subject being presented by showing a real-life example that generates numbers that form an arithmetic sequence.
 * Shortly refresh the concepts of sequence, series, infinite series and geometric series.
 * Shortly refresh the concept of divergence or convergence of series.
 * Ask students to write out a few terms of the geometric series ½+1/4+1/8 +…
 * Ask students to try to guess weather this series diverges or converges.
 * Ask students to calculate the value of the sum of the infinite series by using a calculator.
 * Ask students to reflect on the kind of assumptions that need to be made to calculate the answer to the sum of the geometric series.
 * Ask students to use square piece of paper to make a visual representation of the geometric series sum.
 * Use the square sheet of paper to model ½ + ½ = 1
 * Use the square sheet of paper to model ½ + ¼ + ¼ = 1
 * Use the square sheet of paper to model ½ + ¼ + 1/8 + 1/8 = 1
 * Ask students to think about the number of times the procedure can be continued
 * Ask students to infer about the assumptions that can be made about the result of the sum of ½ + ¼ + 1/8 + 1/16 + …. = ?

**6. Closure** Request that students write about the concepts of divergence and convergence of series, and asked students to describe in their own words what the concept of infinite geometric series means.

**7. Extension** Request the students to investigate a possible application of the concept in a daily situation and have students discuss their findings with other peers.

**8. Assessment** Interactive quiz of main concepts such as understanding of divergence or convergence, ability to identify the concept of sequences, series, infinite series, and geometric series.