Content Area Learning Activity:

Alternative for Mobile LearningAlternative for Mobile Learning

**Background**

**Content Area:**Algebra I

**Title**: Mobile Lesson on Graphing Equations

**Grade Level:**9th/10th Grade Algebra I

**Pre-Planning**

This lesson will require a device that runs the Apple iOS platform. It would be suited well for a classroom that had iPads, iTouchs, or a group that has enough iPhone. Only free apps will be selected for this lesson.

**Big Idea(s):**

Formulas and graphs are part of everyone's lives. Whether driving a car and needing to calculate the distance or mapping out the route. If a person wants to compare which cell phone company or plan to select, they might review charts or graphs. Algebraic formulas and graphs are used almost every day without most people realizing they are using math. When it comes to analyzing anything, whether the cost, price or profit of a business, a person will need to be able to do algebra. Entering data to balance a person's check book or pay a credit card will use algebraic expressions and equations. Decisions such as which cell phone provider gives the best contracts to deciding what type of vehicle to buy, you will use algebra to decide which one is the best one. By drawing up a graph and weighing the best option you are more likely to get the best value for your money. Finding the area of a shape is a fundamental skill that will help in many life skills. Most everyone lives in houses with painted walls. If you are going to paint the walls yourself, you need to know how much paint to plan to buy. If someone else is painting it, checking their math on the amount of space to be painted so you can compare estimates is also important. I have also used it in landscaping. Examples include, buying fertilizer, buying landscaping rock, buying stain for a fence, and the list could continue. The determination of area also uses formulas which help general algebraic skills that will be used later in physics and chemistry classes (to name only a few).

**Essential Questions:**

Which cell phone company has the "best" plan?

Define parameters of at least 2 different cell phone plans.

Create graphs using apps to compare the two plans.

**Objective:**

Students compare cell phone plans by analyzing tables, graphs, and equations in this sample lesson. A variety of graphing calculator apps will be useful to students during their analysis and provide opportunities to make sense of the different rate plans. Students will analyze the data they generate from the various phone plans, plot that data on a graph, and make recommendations for the "best" phone plan, based on their analysis. Students are also encouraged to share their thinking with their classmates, and report their findings to the class.

**Summative Assessment:**Students will use a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent the two cell phone plans they chose to evaluate. Students should represent functions, patterns, and relationships effectively. Students will complete an initial worksheet with partners and then evaluate two additional plans by themselves for assessment.

**Standards Addressed:**

These standards and benchmarks are from McREL's online database, Content Knowledge: A Compendium of Standards and Benchmarks for K-12 education (4th edition, 2004) (http://www.mcrel.org/standards-benchmarks/.) The mathematics portion of the database was developed using National Council of Teachers of Mathematics (NCTM) standards in addition to other nationally recognized standards documents.

**Standard 1:**Uses a variety of strategies in the problem-solving process

**Benchmark 1: Uses a variety of strategies (e.g., identify a pattern, use equivalent representations) to understand new mathematical content and to develop more efficient solution methods or problem extensions**

Benchmark 2: Constructs algorithms for multi-step and non-routine problems

Benchmark 5: Uses formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations

Benchmark 7: Understands connections between equivalent representations and corresponding procedures of the same problem situation or mathematical concept (e.g., a zero of a function corresponds to an x-intercept of the graph of the function, the correspondence of binary multiplication to a series electrical circuit and the logical operation "and")

**Standard 4:**Understands and applies basic and advanced properties of the concepts of measurement

**Benchmark 1: Solves problems involving rate as a measure (e.g., speed, density)**

**Standard 8:**Understands and applies basic and advanced properties of functions and algebra

**Benchmark 2: Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations**

Benchmark 4: Understands properties of graphs and the relationship between a graph and its corresponding expression (e.g., maximum and minimum points)

Benchmark 7: Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships

Benchmark 11: Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities

**Standard 9:**Understands the general nature and uses of mathematics

**Benchmark 7: Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments**

**Lesson Opening**

*(the hook)*:Instruct students to take out their cell phones or use one of the class iPads and download the app: Algebra Champ. Students then select a "fighter" and a fighter name (students should make up a name). The volume should definitely be ON! This app has great audio. It will be fun for the students to hear the sounds of all the other players around them. Students should select Difficulty Level 1. Each student should play round one, when they get to the results page, they should then take a screen shot of their results and send to the teacher. The teacher will then project the results (which is why the names should be anonymous). Level 1 should take the students less than 30 seconds to complete. The students should then move on to Level 2. A small prize (candy, eraser, etc) should be given to the first student to complete each of the levels with 100% average. Total time: 15 minutes.

**Lesson Body:**

**Explanation:**Briefly introduce the problem. Students should find choosing a cell phone plan interesting and relevant. Ask how much students (or their parents) pay for their cell phone plans each month. Ask how students would decide which cell phone plan to purchase and if there are any tools that might be helpful to them in making a decision? Provide students with the two different cell phone plans (see Worksheet 1), and before they do any analysis, ask them which they would choose, and why.

Next, have students begin working on the analysis of the cell phone plans. Students should work with partners, one with the iPad app and the other with the cell phone app.

At this point, students should download the free graphing calculator app: Scientific Graphing Calculator By William Jockusch. Students will complete worksheet 1 with their partner. This should take 10 -15 minutes.

**Check for Understanding:**

Next students should download Quick Graph: Your Scientific Graphing Calculator By Colombiamug to their personal device. This app is free and should be on all the classroom devices. Provide students with Worksheet 2. At this point, students should work independently to analyze the two additional cell phone plans. This worksheet should be turned in for a grade. This should take approximately 10 - 15 minutes.

**Extended Practice:**

Students should repeat the previous worksheet #2 using a third graphing calculator app, Good Grapher - scientific graphing calculator By Iurii Mozharovsky. Students should work with a partner or a small group. The students should then compare all three graphing calculator apps and answer the following questions:

1. Which app did you like best and why?

2. Which app was the easiest to use?

3. Which app was the most like your regular graphing calculator?

**Fun Extended Practice:**

Let the students choose their favorite app and challenge them to create the most interesting picture they can. First demonstrate an example (below). Students should select polar mode.

Then you will get the r1= and can do cool stuff like

r1 = sin(4*t)

r2 = 1-cos(t)

r3 = t^2

r4 = log(t)

Have the students experiment and share their designs. Ask students to send their favorite design to the teacher. This should take 10 minutes.

**Closing:**

A combination of a screencasting app and a computer control tool, Doceri allows the math teacher to be mobile in their classroom while still projecting content to the front of the room. Doceri supports AirPlay mirroring through AppleTV, Reflector or AirServer. In addition, PPT and Keynote files can be imported into Doceri, allowing the teacher to annotate directly over their presentations on an iPad. Both teachers and students can also use the screencasting tool to created problem solving screencasts on an iPad.

To generate a project, record the math lesson (above) live in class as the teacher presents with Doceri connected to the classroom projector. Afterwards, post a screencast of all the equations, graphs, and pictures students worked out step by step or sent to the teacher during the lesson. The teacher will even be able to work backwards through the equations and graphs and add annotations to demonstrate where any errors were made. In addition, the teacher can write out the appropriate steps to utilizing the graphing calculator apps.

**Materials:**

Classroom set of iPads or iTouchs

Personal cell phones

Graph Paper

Worksheet 1

Worksheet 2

**Sources:**

This lesson is an adaptation of the lesson plan "Algebra: Cell Phone Plans" created by The SEDL National Center for Quality Afterschool

McREL's online database, Content Knowledge: A Compendium of Standards and Benchmarks for K-12 education (4th edition, 2004) (http://www.mcrel.org/standards-benchmarks/.)

EdTech Teacher:

http://edtechteacher.org/index.php/teaching-technology/mobile-technology-apps/309-ipads-math

http://edtechteacher.org/index.php/teaching-technology/tmwt

http://coolcatteacher.blogspot.com/2012/08/89-lesson-plans-and-ideas-for-teaching.html