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Making Connections in Mathematics with Graphing Calculators and Childrens Literature Jim Rahn www.jamesrahn.com james.rahn@verizon.net Baltimore NCTM Regional Conference October 18, 2013

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Students can collect data in Lists L1 – L6 Students can analyze data Students can view data in more than one way through a table through a graph through an equation and verbally describe patterns they observe With the TI-73 Graphing Calculator

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Students using this grade-appropriate calculator will be developing skills they will need in high school and the workplace after high school

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Standards state Students should be using technology to gather, analyze, and communicate mathematical information. Students should be using graphing utilities to organize and display quantitative information.

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Students should be using graphing calculators to investigate properties of functions and their graphs. Students should be using calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

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Becoming Familiar with the TI73- Explorer

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To clear all memory Press 2 nd MEM (0 key) Select choice 7. Reset

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Select 1. ALL RAM to erase all information that may have been added to the calculator. This restores the calculator to the condition of being a new calculator straight out of a package. (Programs will also be erased.) You will be given one warning screen to make sure you do want to erase all the memory.

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When you have reset all the memory you will get a screen that says that.

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scientific calculator

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Shift Key Using the 2 nd Key places an on the screen and activates all commands in YELLOW.

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variable key

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Mode Key

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Window/Table Keys Y= Window Zoom Format Table Trace Table Set Graph

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Cursor Keys

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Constant Keys Press 2 nd CONST to se C1 to +3. On the home screen start with any number and press the CONST key. f Repeat by pressing the CONST key

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Find the ON key to turn the calculator on. To turn it off you press 2 nd ON.

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Some Basic Graphing Calculator Skills Keys to check before you begin any type of work on your graphing calculator

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Working on the Homescreen To get back to the Homescreen from any other screen press 2 nd Quit. This is the location where you can perform arithmetic operations.

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Lets Teach Aunt Sally a Few Things Enter each of the problems in the calculator and record the answer 12 ÷ 6 x 2 = 12 x 6 ÷ 2 = 18 x 3 ÷ 9 = 18 ÷ 3 x 9 = In what order did the calculator seem to execute the operations in each of the problems above? o 24 ÷ 6 x 3 ÷ 2 = o 24 x 6 ÷ 3 x 2 = o 45 ÷ 3 ÷ 9 x 2 = o 45 x 3 x 9 ÷ 2 =

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Thinking about a Table InputOutput You give me a number and Ill place it under the INPUT column The calculator will reveal the number in the OUTPUT column Try this with several numbers Whats happening? Can you predict what the calculator is doing with the INPUT? TI73

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Build a Table InputOutput 516 825 1237 2061 50151 This is an example of a FUNCTION. For each INPUT there is exactly one OUTPUT. What would happen if you entered a duplicate INPUT? Can you predict what is happening to the input number? 3 times the Input + 1= Output

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Set up the Calculator for studying Input-Output Charts Press Y= and enter a linear function in y1. Press 2 nd TblSet and set up for Independent to be ASK. Press 2 nd Table and begin enter INPUT numbers. Team up with a partner to see if you can predict their equation.

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Incorporating Literature with the TI-73 Two of Everything by Lily Toy Hong Albert Whitman & Company, 1993 A story about a magic pot that changes numbers in a special way

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Word List humble clever grateful village identical enough ancient knelt peer exactly magical naturally

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Vocabulary humble: not fancy in any way. identical: the very same. clever: having a bright mind; very smart. exactly: without any difference. plentiful: more than enough; abundant.

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Incorporating Literature with the TI-73 Two of Everything by Lily Toy Hong Two of Everything by Lily Toy Hong

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Reading the Story Model the story using the bowls and cubes. Record the numbers from the story in your chart and add some other numbers

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Using the Calculator Turn on the calculator Press LIST and enter the IN numbers in L1 and the OUT numbers in L2. Press WINDOW and set up an appropriate window for the numbers used in L1 and L2 Press 2 nd (Y=) PLOT and select choice 1. Plot 1

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Stat Plot Window

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To view a graph Set up a Window that is appropriate for the numbers in the lists. Press GRAPH to view a graph of the data you entered in L1 and L2. What is your observation about the graph?

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Press TRACE and use the cursor arrows to move along the graph. What is your observation about what you are seeing?

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Karen looked at the table and noticed: The number of coins coming out of the pot is always more than the number going into the pot. Find two other patterns. Describe a relationship that would allow the Haktaks to predict the number of coins they would get out of the pot if they knew the number of coins being placed in the pot.

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Press Y= and enter this relationship in the Y1 slot.

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Press GRAPH and what do you observe? Trace along this graph to see what other information is available. Does it make sense in this problem to connect the points with a line? Why or why not?

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Questions to think about If Mrs. Haktak continues her method of putting coins into the purse and placing the purse in the pot, how many coins would she get out of the pot if she were to put 20 coins in the pot?

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What type of function do we call this? Gabe looked at the table and said, The dependent variable appears to be growing exponentially, so I think this relationship must be exponential. Do you agree or disagree. Explain.

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What feature(s) of a graph helps you see the doubling relationship of the pot? Explain.

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Suppose that every time the Haktaks put 1 coin into the pot, 3 identical coins came out. How would your equation, table, and graph change? Explain.

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In the story, Mrs. Haktak combines her coins into one purse, returns the purse to the pot, and pulls out 2 identical purses (and doubles the number of coins). Can Mrs. Haktak continue this method of combining coins into one purse and placing the purse in the pot as many times as she wishes? Explain.

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If we assume that Mrs. Haktak continues to combine coins into one purse before placing it in the pot, what is the relationship between the number of times Mrs. Haktak puts a purse in the pot and the total number of purses Mrs. Haktak has? Represent this relationship symbolically, and define your variables.

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What other relationship(s) can be explored through this story? Explain what the relationship is and how your could represent it symbolically. Be sure to define your variables.

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Additional Activity 1 Suppose you had a choice between 1000 coins 50 coins and a magic pot that works ten times Which one would you choose and why? Use your calculator to collect data and support why you have made your selection.

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Activity 2 Use the premise of the magic pot to inspire narrative writing give a prompt such as: Mr. and Mrs. Haktak had a magic pot that doubled everything that went into it. Think about what you might want a magic pot to do. Write a short story about your magic pot.

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Exploration Task On you table is a copy of a childrens book. Read the story out loud. As the person is reading the story think and define the variables you can monitor as the story progresses. Complete an input-output table. Create a paper graph. Make some observations about the data as it collected

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Exploration with the Graphing Calculator Recreate the data on the homescreen Enter the data in L1 and L2 Create a graph of L1 vs. L2 Create an equation that represents the data. Graph the equation with the data. From the story, should the graph be considered to be a line or just a set of points?

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The Kings Chessboard by David Birch, Dial Books for Young Readers, 1988 (jrr)

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Exploration Task On you table is a copy of a second childrens book. Read the story out loud. As the person is reading the story think and define the variables you can monitor as the story progresses. Complete an input-output table. Create a paper graph. Make some observations about the data as it collected

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Exploration with the Graphing Calculator Recreate the data on the homescreen Enter the data in L1 and L2 Create a graph of L1 vs. L2 Create an equation that represents the data. Graph the equation with the data. From the story, should the graph be considered to be a line or just a set of points?

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The Doorbell Rang by Pat Hutchens One Hundred Hungry Ants by Elinor J. Pinczes,

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The Doorbell Rang by Pat Hutchens One Hundred Hungry Ants by Elinor J. Pinczes,

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What Other Books Could be Use Similarly?

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Quadratic Function The 12 Circus Rings by Seymour Chwast

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Quadratic Functions Bats on Parade by Kathi Appelt

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Exponential Functions Double Those Wheels by Nancy Raines Day

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Linear Function One Watermelon Seed by Celia Barker Lottridge

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Linear Function Ten Red Apples by Virginia Miller

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Exponential Functions The Great Divide by Dayle Ann Dodds

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Exponential Functions The Great Divide by Dayle Ann Dodds

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Linear Functions Counting Sheep by Julie Glass

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Linear Functions Each Orange Had 8 Slices A Counting Book by Paul Giganti, Jr.

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Counting on Frank by Rod Clement, Gareth Stevens Publishing, 1991 (jrr) Alice in Pastaland-A Math Adventure by Alexandra Wright, Charlesbridge Publishing, 1997 (jrr) Looking at Other Literature with Functions Connections

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Amanda Beans Amazing Dream by Cindy Neuschwander, Scholastic Books, 1998 (jrr) The Greedy Triangle by Marilyn Burns, Scholastic Books, 1994 (jrr)

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Annos Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno, Philomel Books, 1983 (jrr) Counting on Frank by Rod Clement Gareth Stevens Publishing 1991 (jrr)

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Various Functions Alice in Pastaland – A Math Adventure by Alexandra Wright Charlesbridge Publisher, 1997 (jrr) Amanda Beans Amazing Dream – A Mathematical Story by Cindy Neuschwander

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Using Childrens Literature and the TI-73 Jim Rahn www.jamesrahn.com james.rahn@verizon.net Baltimore NCTM Regional October 18, 2013

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