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Using Childrens Literature and the TI-73 Jim Rahn T 3 Regional Conference Staten Island, NY November 3, 2006

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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 should be used 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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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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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.

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Thinking about a Table InOut You give me a number and place it under the IN column Ill tell you the number that fits in the OUT column Try this with several numbers Whats happening?

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Build a Table InOut This is an example of a FUNCTION. For each IN (Input) there is exactly one OUT (Output) 3 times the Input + 1= Output

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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 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. What feature(s) of your table tells you that this is a doubling relationship. Explain. What feature(s) of your equation tells you that this is a doubling relationship. 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 5 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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Looking at Other Literature with Functions Connections The Doorbell Rang by Pat Hutchins Mulberry Books, New York 1986 (jrr) Bats on Parade by Kathi Appelt Morrow Junior Books,1999

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One Watermelon Seed by Celia Barker Lottridge, Stoddart Kids, 1997 (jrr) One Hundred Hungry Ants by Elinor J. Pinczes, Houghton Mifflin, 1993

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Counting on Frank by Rod Clement, Gareth Stevens Publishing, 1991 (jrr) Ten Red Apples by Virginia Miller Candlewick Press, 2002

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The Great Divide by Dayle Ann Dodds 1999 Double those Wheels by Nancy Raines Day Dutton Childrens Books, 2002

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Counting Sheep by Julie Glass, Random House, 2000 The 12 Circus Rings by Seymour Chwast, Gulliver Books, 1993

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The Kings Chessboard by David Birch, Dial Books for Young Readers, 1988 Annos Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno, Philomel Books, 1983 (jrr)

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Alice in Pastaland-A Math Adventure by Alexandra Wright, Charlesbridge Publishing, 1997 (jrr) Each Orange Had 8 Slices by Paul Giganiti Jr., Greenwillow Books, 1992

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Annos Counting Book by Mitsumasa Anno, Harper Trophy, 1986 (jrr) The Grapes of Math by Greg Tang, Scholastic Books, 2001 (jrr)

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Amanda Beans Amazing Dream by Cindy Neuschwander, Scholastic Books, 1998 (jrr)

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The Greedy Triangle by Marilyn Burns, Scholastic Books, 1994 (jrr)

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Task Read the childrens book Define the independent and dependent variables Collect a table of data Enter the data into your graphing calculator Obtain a graph of the data Verbally describe the function relationship. Support your reason for the function you have chosen.

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Linear Functions Two of Everything by Lily Toy Hong y = 2x y = number of purses coming out of the pot x = number of times a purse is placed in the pot

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Constant Function Ten Red Apples: A Bartholomew Bear Counting Book by Virginia Miller y =10 y = total number of apples in the tree x = number of red apples in the tree (x is between 0 and 9 and an integer)

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Linear Function Counting Sheep by Julie Glass y = ax y = number of animals counted x = number of times the man counts the animals a changes depending on the number of animals in the group (i.e. a = 2 for kangaroos) a is sometimes negative and sometimes positive

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Linear Function One Watermelon Seed by Celia Barker Lottridge y = 10x y = number of pieces of produce harvested x = number of seeds or plants planted not requested

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Exponential Functions The Kings Chessboard by David Birch y = 2 (x-1) y = number of grains of rice that the wise man received on day x x = number of the day the wise man has been receiving rice from the king

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Exponential Functions The Great Divide by Dayle Ann Dodds y = 80(1/2) (x) y= 80(1/2) (n-1) y = total number of racers in the race x = number of obstacles (or number of splits or the number of divides) through the 5 th obstacle n = number of legs in the race through the 6 th leg

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Exponential Functions Double Those Wheels by Nancy Raines Day y = 2 x y = number of wheels x = number of times the wheels have doubled

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Quadratic Functions Bats on Parade by Kathi Appelt y = x 2 y = number of bats in section x of the marching band x = section number of band (assuming the drum majorette is section 1, the piccolos are section 2, the flutes are section 3, etc.)

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Quadratic Function The 12 Circus Rings by Seymour Chwast y = (1/2)x 2 + (1/2)x or (1/2)(x)(x+1) y = number of circus performers (people and animals) performing in the ring x = number of the circus ring

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Quadratic Function One Watermelon Seed by Celia Barker Lottridge y = (1/2)x 2 + (1/2)x or (1/2)(x)(x+1) y = number of seeds/plants planted. x = number of different type of seeds/plants planted

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Quadratic Function One Watermelon Seed by Celia Barker Lottridge y = 5x(x+1) y = total number of pieces of produce harvested x = number of different type of seeds/plants planted

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Rational Functions The Doorbell Rang by Pat Hutchins y = 12/x y = number of cookies that each child will get when the cookies are shared equally (before Grandma arrives) x = number of children

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Rational Functions The Doorbell Rang by Pat Hutchins y = 1/x y = fraction of a dozen that each child will get when the cookies are shared equally x = number of children

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Rational Functions One Hundred Hungry Ants by Elinor J. Pinczes y = 100/x y = number of ants in a line x = number of lines of ants

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Rational Functions Counting on Frank by Rod Clement y = 745/ax y = number of jelly beans that Frank can eat per day if he eats jelly beans each x = number of days that Frank will eat jelly beans

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Linear Functions Counting on Frank by Rod Clement y = 15x y = number of peas Frank drops on the floor each day x = number of days that Frank will drop peas on the floor

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Linear Functions Counting on Frank by Rod Clement y = 5475x y = number of peas Frank drops on the floor each year x = number of years that Frank will drop peas on the floor

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Factorial Function Annos Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno y = x! y = total number of things x = level of the story

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Various Functions Alice in Pastaland – A Math Adventure by Alexandra Wright Each page presents a different path relationship that can be investigated ways to make 6 multiples of 5 and 20 cents multiples of 12 sums that make 9 doubling magic square where total is 15 constantly subtraction of 5

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Amanda Beans Amazing Dream – A Mathematical Story by Cindy Neuschwander Multiples of various numbers

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Each Orange Had 8 Slices – A Counting Book by Paul Giganti, Jr. Various multiples

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Using Childrens Literature and the TI-73 Jim Rahn T 3 Regional Conference Staten Island, NY November 3, 2006

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