Presentation on theme: "Using Children’s Literature and the TI-73"— Presentation transcript:
1 Using Children’s Literature and the TI-73 Jim RahnT 3 Regional Conference Staten Island, NYNovember 3, 2006
2 With the TI-73 Graphing Calculator Students can collect data in Lists L1 – L6Students can analyze dataStudents can view data in more than one waythrough a tablethrough a graphthrough an equationand verbally describe patterns they observe
3 Students using this grade-appropriate calculator will be developing skills they will need in high school and the workplace after high school
4 Standards stateStudents 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.
5 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).
7 To clear all memoryPress 2nd MEM (0 key)Select choice 7. Reset
8 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.
9 When you have reset all the memory you will get a screen that says that.
16 Find the ON key to turn the calculator on. To turn it off you press 2nd ON.
17 Some Basic Graphing Calculator Skills Keys to check before you begin any type of work on your graphing calculator
18 Working on the Homescreen To get back to the Homescreen from any other screen press 2nd Quit.
19 Thinking about a Table In Out You give me a number and place it under the IN columnI’ll tell you the number that fits in the OUT columnTry this with several numbersWhat’s happening?InOut
20 Build a TableThis is an example of a FUNCTION.For each IN (Input) there is exactly one OUT (Output)InOut51682512372061501513 times the Input + 1= Output
21 Incorporating Literature with the TI-73 Two of Everything by Lily Toy HongAlbert Whitman & Company , 1993A story about a magic pot that changes numbers in a special way
22 Word List humble clever grateful village identical enough ancient kneltpeerexactlymagicalnaturally
23 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.
24 Incorporating Literature with the TI-73 Two of Everything by Lily Toy Hong
25 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
26 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 L2Press 2nd (Y=) PLOT and select choice 1. Plot 1
28 To view a graphPress GRAPH to view a graph of the data you entered in L1 and L2.What is your observation about the graph?
29 Press TRACE and use the cursor arrows to move along the graph. What is your observation about what you are seeing?
30 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.
31 Press Y= and enter this relationship in the Y1 slot.
32 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?
33 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?
34 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.
35 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.
36 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.
37 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.
38 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.
39 What other relationship(s) can be explored through this story 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.
40 Additional Activity 1 Suppose you had a choice between 1000 coins5 coins and a magic pot that works ten timesWhich one would you choose and why?Use your calculator to collect data and support why you have made your selection.
41 Activity 2Use the premise of the magic pot to inspire narrative writinggive 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.
42 Looking at Other Literature with Functions Connections The Doorbell Rang by Pat Hutchins Mulberry Books, New York (jrr)Bats on Parade by Kathi Appelt Morrow Junior Books,1999
43 One Watermelon Seed by Celia Barker Lottridge, Stoddart Kids, 1997 (jrr) One Hundred Hungry Ants by Elinor J. Pinczes, Houghton Mifflin, 1993
44 Counting on Frank by Rod Clement, Gareth Stevens Publishing, 1991 (jrr) Ten Red Apples by Virginia Miller Candlewick Press, 2002
45 The Great Divide by Dayle Ann Dodds 1999 Double those Wheels by Nancy Raines Day Dutton Children’s Books, 2002
46 Counting Sheep by Julie Glass, Random House, 2000 The 12 Circus Rings by Seymour Chwast, Gulliver Books, 1993
47 The King’s Chessboard by David Birch, Dial Books for Young Readers, 1988 Anno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno, Philomel Books, 1983 (jrr)
48 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
49 Anno’s Counting Book by Mitsumasa Anno, Harper Trophy, 1986 (jrr) The Grapes of Math by Greg Tang, Scholastic Books, (jrr)
51 The Greedy Triangle by Marilyn Burns, Scholastic Books, 1994 (jrr)
52 Task Read the children’s book Define the independent and dependent variablesCollect a table of dataEnter the data into your graphing calculatorObtain a graph of the dataVerbally describe the function relationship.Support your reason for the function you have chosen.
53 Linear Functions Two of Everything by Lily Toy Hong y = 2x y = number of purses coming out of the potx = number of times a purse is placed in the pot
54 Constant FunctionTen Red Apples: A Bartholomew Bear Counting Book by Virginia Millery =10y = total number of apples in the treex = number of red apples in the tree (x is between 0 and 9 and an integer)
55 Linear Function Counting Sheep by Julie Glass y = ax y = number of animals countedx = number of times the man counts the animalsa changes depending on the number of animals in the group (i.e. a = 2 for kangaroos)a is sometimes negative and sometimes positive
56 Linear Function One Watermelon Seed by Celia Barker Lottridge y = 10x y = number of pieces of produce harvestedx = number of seeds or plants plantednot requested
57 Exponential Functions The King’s Chessboard by David Birchy = 2(x-1)y = number of grains of rice that the wise man received on day xx = number of the day the wise man has been receiving rice from the king
58 Exponential Functions The Great Divide by Dayle Ann Doddsy = 80(1/2)(x)y= 80(1/2)(n-1)y = total number of racers in the racex = number of obstacles (or number of splits or the number of divides) through the 5th obstaclen = number of legs in the race through the 6th leg
59 Exponential Functions Double Those Wheels by Nancy Raines Dayy = 2xy = number of wheelsx = number of times the wheels have doubled
60 Quadratic Functions Bats on Parade by Kathi Appelt y = x2 y = number of bats in section x of the marching bandx = section number of band (assuming the drum majorette is section 1, the piccolos are section 2, the flutes are section 3, etc.)
61 Quadratic Function The 12 Circus Rings by Seymour Chwast y = (1/2)x2 + (1/2)x or (1/2)(x)(x+1)y = number of circus performers (people and animals) performing in the ringx = number of the circus ring
62 Quadratic Function One Watermelon Seed by Celia Barker Lottridge y = (1/2)x2 + (1/2)x or (1/2)(x)(x+1)y = number of seeds/plants planted.x = number of different type of seeds/plants planted
63 Quadratic Function One Watermelon Seed by Celia Barker Lottridge y = 5x(x+1)y = total number of pieces of produce harvestedx = number of different type of seeds/plants planted
64 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
65 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 equallyx = number of children
66 Rational Functions One Hundred Hungry Ants by Elinor J. Pinczes y = 100/xy = number of ants in a linex = number of lines of ants
67 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 eachx = number of days that Frank will eat jelly beans
68 Linear Functions Counting on Frank by Rod Clement y = 15x y = number of peas Frank drops on the floor each dayx = number of days that Frank will drop peas on the floor
69 Linear Functions Counting on Frank by Rod Clement y = 5475x y = number of peas Frank drops on the floor each yearx = number of years that Frank will drop peas on the floor
70 Factorial FunctionAnno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Annoy = x!y = total number of thingsx = level of the story
71 Various FunctionsAlice in Pastaland – A Math Adventure by Alexandra WrightEach page presents a different path relationship that can be investigatedways to make 6multiples of 5 and 20 centsmultiples of 12sums that make 9doublingmagic square where total is 15constantly subtraction of 5
72 Amanda Bean’s Amazing Dream – A Mathematical Story by Cindy Neuschwander Multiples of various numbers
73 Each Orange Had 8 Slices – A Counting Book by Paul Giganti, Jr. Various multiples
74 Using Children’s Literature and the TI-73 Jim RahnT 3 Regional Conference Staten Island, NYNovember 3, 2006
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