Transcript Graphing Calculator Skills to Prepare Students for the HSPA

Using Children’s
Literature and the
TI-73
Jim Rahn
www.jamesrahn.com
[email protected]
T 3 Regional Conference Staten
Island, NY
November 3, 2006
With the TI-73 Graphing
Calculator

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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
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through a table
through a graph
through an equation
and verbally describe patterns they observe

Students using this grade-appropriate
calculator will be developing skills
they will need in high school and the
workplace after high school
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.
•
•
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).
To clear all memory
Press 2nd
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.

When you have
reset all the
memory you will
get a screen that
says that.
scientific
calculator
Shift Key
Using the 2nd
Key places an 
on the screen
and activates
all commands
in YELLOW.
variable key
Mode Key
Window/Table
Keys
Y=
Window Zoom
Format
Table
Trace
Table Set
Graph
Cursor Keys
Find the ON key to turn the calculator
on.
To turn it off you press 2nd ON.
Some Basic Graphing
Calculator Skills

Keys to check before you begin any type
of work on your graphing calculator
Working on the Homescreen

To get back to the Homescreen from any
other screen press 2nd Quit.
Thinking about a Table
•
You give me a
number and place it
under the IN column
•
I’ll tell you the
number that fits in the
OUT column
•
Try this with several
numbers
•
What’s happening?
In
Out
Build a Table
•
•
This is an example of
a FUNCTION.
For each IN (Input)
there is exactly one
OUT (Output)
In
Out
5
16
8
25
12
37
20
61
50
151
3 times the Input + 1= Output
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
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•
•
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•
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•
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•
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•
humble
clever
grateful
village
identical
enough
ancient
knelt
peer
exactly
magical
naturally
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.
Incorporating Literature with
the TI-73

Two of Everything by Lily Toy Hong
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
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 2nd (Y=) PLOT and select
choice 1. Plot 1

Stat Plot Window
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?

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.

Press Y= and enter this relationship in
the Y1 slot.
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?

Questions to think about
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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?
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.

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.

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.

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.

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.
Additional Activity 1

Suppose you had a choice between
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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.
Activity 2
Use the premise of the magic pot to
inspire narrative writing
 give a prompt such as:
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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.
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

One Watermelon Seed by
Celia Barker Lottridge,
Stoddart Kids, 1997
(jrr)

One Hundred Hungry Ants
by Elinor J. Pinczes,
Houghton Mifflin, 1993

Counting on Frank by Rod
Clement,
Gareth Stevens Publishing,
1991
(jrr)

Ten Red Apples by Virginia
Miller
Candlewick Press, 2002

The Great Divide by
Dayle Ann Dodds
1999

Double those Wheels
by Nancy Raines Day
Dutton Children’s
Books, 2002

Counting Sheep by Julie Glass,
Random House, 2000

The 12 Circus Rings by
Seymour Chwast, Gulliver
Books, 1993

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)
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Alice in Pastaland-A Math
Adventure by Alexandra
Wright, Charlesbridge
Publishing, 1997 (jrr)
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Each Orange Had 8 Slices by
Paul Giganiti Jr., Greenwillow
Books, 1992

Amanda Bean’s Amazing
Dream by Cindy
Neuschwander, Scholastic
Books, 1998 (jrr)

The Greedy Triangle
by Marilyn Burns,
Scholastic Books, 1994
(jrr)
Task
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Read the children’s 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.
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

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
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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
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
Exponential Functions
The King’s 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
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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 5th
obstacle
n = number of legs in the race
through the 6th leg
Exponential Functions
Double Those Wheels by Nancy
Raines Day
 y = 2x
 y = number of wheels
 x = number of times the wheels have
doubled

Quadratic Functions
Bats on Parade by Kathi
Appelt
 y = x2
 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.)

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 ring
 x = number of the circus ring

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

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

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
Anno’s 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
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Alice in Pastaland – A Math Adventure by
Alexandra Wright
Each page presents a different path relationship
that can be investigated
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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
Amanda Bean’s Amazing Dream – A
Mathematical Story by Cindy
Neuschwander
 Multiples of various numbers

Each Orange Had 8 Slices – A
Counting Book by Paul Giganti, Jr.
 Various multiples

Using Children’s
Literature and the
TI-73
Jim Rahn
www.jamesrahn.com
[email protected]
T 3 Regional Conference Staten
Island, NY
November 3, 2006