HIGH SCHOOL
ACTIVITIES for the
Casio FX-300ES
Number Sense
Problem Solving
Trigonometric Ratios
Combinations and Permutations
Two-Variable Statistics
Tables and Graphing
Probability and Statistics
Polar and Rectangular Coordinates
π (Area and Circumference)
Area and Perimeter
Surface Area and Volume
Exponential Functions
Activities for the Classroom
HIGH SCHOOL
ACTIVITIES
for the
Casio FX-300ES
John Neral
® 2005 by CASIO, Inc.
570 Mt. Pleasant Avenue
Dover, NJ 07801
www.casio.com
300ES-HIGH
The contents of this book can be used by the classroom teacher to make reproductions for
student use. All rights reserved. No part of this publication may be reproduced or utilized
in any form by any means, electronic or mechanical, including photocopying, recording,
or by any information storage or retrieval system without permission in writing from CASIO.
Printed in the United States of America.
Design, production, and editorial by Pencil Point Studio
Contents
Activity 1: Spanning the World and the Universe . . . . . . . . . . . . . . . . . . . . . . . . . 1
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 2: Trigonometric Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 3: Order in the Court! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 4: Exploring Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 5: So, You Want To Be The Apprentice? . . . . . . . . . . . . . . . . . . . . . . . . . 32
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 6: Leaving It All To Chance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
High School Activities for the Casio fx-300ES
iii
Activity 7: Polar and Rectangular Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 8: Exploring π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 9: Measuring Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 10: It’s Uncanny! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
Activity 11: Small Town, U.S.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Teaching Notes
Calculator Notes
Student Activity
Solutions and Answers
iv
HIgh School Activities for the Casio fx-300ES
Activity 1
Spanning the World and
the Universe
Teaching Notes
Topic Area: Number Sense & Problem Solving
NCTM Standards: Number and Operations, Algebra, Measurement, Problem Solving,
Connecting, and Communications
Objective
Students will demonstrate the ability to express a number in standard form and in
scientific notation. Students will also be able to perform arithmetic operations using
scientific notation.
Engage
Discuss with students how they would calculate the distance between New York and Los
Angeles. Ask them to write the number in standard form and express that number
using scientific notation. Which form is better to use? Then, ask students to estimate
the distance between Earth and Jupiter. Ask them to write the number and express that
number using scientific notation. Which form do they believe is better to use?
Explore
1.
2.
3.
Using the calculator, model how to use the Scientific Notation key (x10x).
Provide examples of how to input a number expressed in scientific notation and
press "=" to see the number in standard form. (Note: If the number written in
scientific notation is too large for the display, the calculator will express the
number in scientific notation on the answer line.)
Discuss how to use scientific notation to express a number between 0 and 1.
Explain
Have students explain how they can convert any number written in standard form to
scientific notation and vice versa.
Elaborate
Discuss any questions or comments with your students. Have students survey friends
and family members and mention to them that a state lottery jackpot is estimated at
2.5 107. Ask them to correctly identify that amount of money. Have students return
to class and discuss their results and observations.
Extend
1.
2.
Students could perform mathematical operations using a set of numbers written in
scientific notation.
Students could express numbers they use every day in scientific notation in writing
and when verbalizing those numbers to other people in their class.
Evaluate
The students will be given a set of numbers written in standard form and be able to
express them using scientific notation as well as a set of numbers in scientific notation
and be able to express them in standard form.
Copyright © Casio, Inc.
Activity 1 • High School Activities for the Casio fx-300ES
1
Calculator Notes for Activity 1
Steps for Using the Scientific Notation Key
Example:
Enter 5.498 107 and press = to express the number in standard form.
1.
Turn on the calculator and press MODE followed by 1 for COMP.
2.
Enter 5.498 followed by the x10x key.
3.
Enter 7 for the exponent.
D
4.
Press = .
5.
On the answer line of the display you will notice 5.498 107 expressed as
54980000.
D
2
Math
High School Activities for the Casio fx-300ES • Activity 1
Math
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 1 • Spanning the World and the Universe
Introduction
Scientific notation is used to express very large or very small numbers in a simpler form. For example, there are millions of miles between planets and it would
be very difficult to determine place values to read those numbers if they were written in standard form.
A number is expressed in scientific notation when the first number (or coefficient) is between 1 and 10 and is multiplied by a power of ten. For example, it is
approximately 92,000,000 miles between the sun and earth.
Source: Ask a Scientist: Astronomy Achieve
www.newton.dep.anl.gov/newton/askasci/1995/astron?AST045.HTM
May 14, 2005
To express that number in scientific notation, we must first move the decimal
point to make that number between 0 and 10. We could move the decimal point
between the 9 and the 2 making that number 9.2.
Remember, that each time we move the decimal point one place to the left, we
are dividing that number by 10. Since we have moved the decimal point 7 times,
our exponent will be 7 since multiplying 9.2 by 107 will express that number in
standard form. Therefore, the correct way to express 92,000,000 miles in scientific notation is 9.2 107.
Scientific Notation can also be used to express very small numbers. If we
wanted to express the mass of a hydrogen atom in scientific notation it would be
1.6727 10-27 kg.
Source: www.nyu.edu/classes/tuckerman/honors.chem/lectures/lecture_2/node6.html
Whenever we see a negative exponent in scientific notation it indicates that we
must move the decimal point that many places to the left. You can easily see that
if we were to express this number in standard form it would be extremely small.
Objectives
1. Express any number written in standard form in scientific notation.
2. Convert any number written in scientific notation to standard form.
3. Perform mathematical operations with numbers written in scientific notation.
Materials Needed
•
The Casio fx-300ES calculator
•
The tables on the next page
Copyright © Casio, Inc.
Activity 1 • High School Activities for the Casio fx-300ES
3
Name _____________________________________________ Class ________ Date ________________
Activity 1 • Spanning the World and the Universe
The following table lists the distances between two locations. These numbers
are written in standard form. Express each distance using scientific notation. Use
the calculator to check your answers.
Starting Location
Ending Location
Distance
New York
Los Angeles
2,446 miles
Chicago
Tokyo, Japan
6,302 miles
Zurich,
London,
480 miles
Switzerland
England
Earth
Jupiter
628,760,000 km
Earth
Venus
41,440,000 km
Earth
Pluto
5,750,540,000 km
Earth
Mercury
91,700,000 km
Scientific Notation
Source: www.ask.com
The following table lists the distances between two locations. These numbers
are written in scientific notation. Express each distance in standard form. Use
the calculator to check your answers.
Distance
Scientific Notation
Starting Location
Ending Location
Boston, MA
Dallas, TX
1.55 X 103 km
Frankfurt,
Rome, Italy
5.96 X 102 km
Beijing, China
Sydney, Australia
5.571 X 103 km
Saturn
Earth
1.27742 X 109 km
Neptune
Earth
4.3476 X 109 km
Jupiter
Sun
7.786 X 108 km
Earth
Moon
3.84403 X 105 km
Germany
4
High School Activities for the Casio fx-300ES • Activity 1
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 1 • Spanning the World and the Universe
Procedure
1. Turn on the calculator and Press MODE followed by 1 for COMP.
2. If you want to determine a number in standard form, enter the number in
scientific notation by using the x10x key. Enter the decimal between 1 and 10,
press the x10x key, and then input the exponent (the power of ten you are
multiplying the decimal by).
3. If you are given a number in standard from and you want to express that
number using scientific notation, input the number in scientific notation and
press the = key to determine if the display is the same as the number in
standard form.
Problems and Questions
1. Use your calculator to answer the following problems.
a. 2.75431 105 =
_______________
b. 27.5431 104 =
_______________
c. 275.431 103 =
_______________
d. 2754.31 102 =
_______________
e. 27543.1 101 =
_______________
f. 275431 100 =
_______________
g. 2754310 10-1 = _______________
h. 27543100 10-2 = _______________
2. What observations can you make about the products of the problems in #1?
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
3. Express the number 57,600,000 in scientific notation.
____________________________________________________________________________
4. Express the number 0.039 in scientific notation.
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 1 • High School Activities for the Casio fx-300ES
5
Name _____________________________________________ Class ________ Date ________________
Activity 1 • Spanning the World and the Universe
5. What is 3.7 X 104 + 5.2 X 103?
Express your answer in standard form and in scientific notation.
____________________________________________________________________________
6. What is ( 4.17 X 103 )( 5.824 X 104 ) ?
Express your answer in standard form and in scientific notation.
____________________________________________________________________________
7. What is ( 8.75 X 106 ) divided by ( 1.75 X 10-2 ) ?
Express your answer in standard form and in scientific notation.
____________________________________________________________________________
8. What is ( 2.94 X 10-5 ) - ( 7.92 X 10-3 )?
Express your answer in standard form and in scientific notation.
____________________________________________________________________________
6
High School Activities for the Casio fx-300ES • Activity 1
Copyright © Casio, Inc.
Solutions and Answers for Activity 1
Starting Location
Ending Location
Distance
Scientific Notation
New York
Los Angeles
2,446 miles
2.446 X 103 miles
Chicago
Tokyo, Japan
6,302 miles
6.302 X 103 miles
Zurich,
London,
480 miles
4.8 X 102 miles
Switzerland
England
Earth
Jupiter
628,760,000 km
6.2876 X 108 miles
Earth
Venus
41,440,000 km
4.144 X 107 miles
Earth
Pluto
5,750,540,000 km
5.75054 X 109 miles
Earth
Mercury
91,700,000 km
9.17 X 107 miles
Starting Location
Ending Location
Distance
Scientific Notation
Boston, MA
Dallas, TX
1,550 miles
1.55 X 103 km
Frankfurt,
Rome, Italy
596 miles
5.96 X 102 km
Beijing, China
Sydney, Australia
5,571 miles
5.571 X 103 km
Saturn
Earth
1,277,420,000 km
1.27742 X 109 km
Neptune
Earth
4,347,600,000 km
4.3476 X 109 km
Jupiter
Sun
778,600,000 km
7.786 X 108 km
Earth
Moon
384,403 km
3.84403 X 105 km
Germany
1. a. 2.75431 105 =
275,431
b. 27.5431 104 =
275,431
c. 275.431 103 =
275,431
d. 2754.31 102 =
275,431
e. 27543.1 101 =
275,431
f. 275431 100 =
275,431
g. 2754310 10-1 = 275,431
h. 27543100 10-2 = 275,431
Copyright © Casio, Inc.
Activity 1 • High School Activities for the Casio fx-300ES
7
Solutions and Answers for Activity 1
2. All of the products are the same because each time the decimal point is moved
one place to the right in the first factor (coefficient), the exponent for the
power of ten is decreased by 1.
3. 5.76 107
4. 3.9 10-2
5. 42,200 or 4.22 104
6. 242,860,800 or 2.428608 108
7. 500,000,000 or 5 108
8. -0.0078906 or -7.8906 10-3
8
High School Activities for the Casio fx-300ES • Activity 1
Copyright © Casio, Inc.
Activity 2
Trigonometric Ratios
Teaching Notes
Topic Area: Trigonometric Ratios
NCTM Standards: Number and Operations, Algebra, Geometry, Measurement, Reasoning
and Proof, Problem Solving
Objective
Students will demonstrate the ability to solve problems involving various trigonometric
ratios.
Engage
Discuss with students the trigonometric relationships for right triangles. Using a right
triangle, show how to express the sine, cosine, and tangent relationships for each angle.
Explore
1.
2.
3.
Using the calculator, model how to use the trigonometric (sine, cosine, and
tangent) functions.
Using the calculator, model how to use the inverse trigonometric functions.
Using the calculator, model how to switch between the degree mode and radian
mode.
Explain
Students will communicate how they were able to obtain their answers and why their
answers are reasonable.
Elaborate
Incorporate the use of the Law of Sines into further discussions and problem solving.
Extend
1.
2.
3.
Students could create their own problems on an index card and share them with
other students in the class.
Students could draw a right triangle using the Casio ClassPad 300 and manipulate
the sides to witness the change in angle measurements.
Students could construct similar triangles to show how the trigonometric ratios
remain the same.
Evaluate
The students will be given a series of problems and be able to use the knowledge gained
from this activity to solve those problems.
Copyright © Casio, Inc.
Activity 2 • High School Activities for the Casio fx-300ES
9
Calculator Notes for Activity 2
Steps for Using the Scientific Notation Key
10
1.
Turn the calculator on and press MODE followed by 1 for COMP.
2.
Press SHIFT MODE/SETUP followed by 1 for MthIO (Math Input/Output
format).
3.
If you are given the measure of an angle and you want to find its trigonometric
ratio, press SHIFT MODE/SETUP followed by 3 to express your answer in
degrees.
4.
If you are given the value of a trigonometric ratio and you want to find the
measure of the angle, press SHIFT MODE/SETUP followed by 4 for radians.
High School Activities for the Casio fx-300ES • Activity 2
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 2 • Trigonometric Ratios
Introduction
Trigonometric ratios pertain to the angle relationships for right triangles. The
three types of trigonometric ratios are sine, cosine, and tangent. Examine the
diagram below.
B
c
a
C
A
b
Sine of Angle A = leg opposite angle A (a)
Hypotenuse (c)
Cosine of Angle A = leg adjacent to angle A (a)
Hypotenuse (c)
Tangent of Angle A = leg opposite angle A (a)
leg adjacent to angle A (b)
You may be familiar with the mnemonic SOH – CAH – TOA for the trigonometric
ratios where SOH = Sine of an angle = opposite/hypotenuse, CAH = Cosine of an
angle = adjacent/ hypotenuse and TOA = Tangent of an angle = opposite/adjacent.
Objective
Demonstrate the ability to solve problems involving various trigonometric
ratios
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
Copyright © Casio, Inc.
Activity 2 • High School Activities for the Casio fx-300ES
11
Name _____________________________________________ Class ________ Date ________________
Activity 2 • Trigonometric Ratios
Procedure
Steps for Using the Trigonometric Functions:
1. Turn the calculator on and press MODE followed by 1 for COMP.
2. Press SHIFT MODE/SETUP followed by 1 for MthIO (Math Input/Output
format).
3. If you are given the measure of an angle and you want to find its trigonometric
ratio, press SHIFT MODE/SETUP followed by 3 to express your answer in
degrees.
4. If you are given the value of a trigonometric ratio and you want to find the
measure of the angle, press SHIFT MODE/SETUP followed by 4 for radians.
Problems and Questions
1. Find the value of each ratio to the nearest thousandth.
a. sin 82o ________________________
b. cos 53o ________________________
c. tan 35o ________________________
2. Find the measure of each angle to the nearest hundredth of a degree.
a. Cos A = 0.365 ________________________
b. Sin B = 0.871 ________________________
c. Tan C = 3.291 ________________________
3. Given a right triangle where a = 8, b = 15, and c = 17, find the following
measures and express each answer as a fraction and a decimal rounded to the
nearest thousandth. (Hint: use radians.)
B
c
a
C
A
b
(figure not drawn to scale)
12
High School Activities for the Casio fx-300ES • Activity 2
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 2 • Trigonometric Ratios
a. Sin A = _______________
d. Cos B = _______________
b. Sin B = _______________
e. Tan A = _______________
c. Cos A = _______________
f. Tan B = _______________
4. After flying at an altitude of 6 miles an airplane starts its descent when its ground
distance from the landing field is 125 miles. What is the angle of depression for
this portion of the flight? Round your answer to the nearest thousandth.
____________________________________________________________________________
5. A ski slope is 723 yards long with a vertical drop of 119 yards. Find the angle of
depression of the slope. Round your answer to the nearest thousandth.
____________________________________________________________________________
6. Samantha is flying a kite and she has let out 40 feet of string. The string makes
a 27-degree angle with the ground. To the nearest tenth, how high is the kite
above the ground?
____________________________________________________________________________
7. Write an equation that you would use to solve the following problems and round
your answer to the nearest hundredth.
A
B
C
a. Given AB = 5 and BC = 12, find angle C.
_______________________________
b. Given AC = 27 and BC = 18, find angle A.
_______________________________
c. Given angle A = 58o and AB = 7, find BC.
_______________________________
d. Given BC = 9.8 and angle C = 23o, find AC.
_______________________________
e. Given angle A = 18o and BC = 12.9, find AC. _______________________________
8. Given triangle ABC, use the Law of Sines to solve the following problem.
Round your answers to the nearest hundredth.
____________________________________________________________________________
If the measure of angle A = 28o, the measure of angle B = 94o, and
the measure of a = 17 inches, find the measures of angle C, side b and side c.
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 2 • High School Activities for the Casio fx-300ES
13
Solutions and Answers for Activity 2
1. a. sin 82o = 0.990
b. cos 53o = 0.602
c. tan 35o = 0.700
2. a. cos A = 0.365 = 68.59o
b. sin B = 0.871 = 60.58o
c. tan C = 3.291 = 73.10o
3. a. sin A = 8/17 = 0.471
b. sin B = 15/17 = 0.882
c. cos A = 15/17 = 0.882
d. cos B = 8/17 = 0.471
e. tan A = 8/15 = 0.533
f. tan B = 15/8 = 1.875
4. tan-1 (6/125) = 2.748o
5. tan-1 (119/723) = 9.347o
6. sin 27o = x/40 ➞ 40 sin(27o) = x ➞ 18.2 feet.
7. a. tan-1 (5/12) = 22.62o
b. sin-1 (18/27) = 41.81o
c. tan (58o) = x/7 ➞ 7 tan (58o) = 11.20
d. cos (23o) = 9.8/x ➞ x = 9.8/cos (23o) = 10.65
e. sin (18o) = 12.9/x ➞ x = 12.9/sin (18o) = 41.75
8. Law of Sines = Sin A = Sin B = Sin C
a
b
c
angle C = 58o, b = 36.12, c = 30.71
14
High School Activities for the Casio fx-300ES • Activity 2
Copyright © Casio, Inc.
Activity 3
Order in the Court!
Teaching Notes
Topic Area: Combinations and Permutations
NCTM Standards: Standards: Number and Operations, Algebra, Data Analysis and
Probability, Problem Solving, Reasoning and Proof, Connecting, Representations, and
Communications
Objective
Students will demonstrate the ability to use permutations and combinations to solve
problems.
Engage
Ask three students to stand in every possible arrangement. Then, ask four students to
stand in every possible arrangement. Finally, ask the class to determine how many different ways five students can arrange themselves. Ask students to develop a formula or
rule for determining how many possible arrangements there are with "n" students.
Explore
1.
2.
3.
Using the calculator, model how to use the permutation key.
Using the calculator, model how to use the combination key.
Using the calculator, model how to use the factorial key.
Solve: The total number of ways 8 students can arrange themselves.
(Since order is important, you can solve the problem by 8P8 = 40,320. You can
also solve the problem by finding 8!)
Explain
Have students discuss how they obtained their answers to the various scenario
problems indicating whether they need to solve by using a combination or a
permutation.
Elaborate
Discuss the results with your students and ask them:
a. When would you use a permutation and when would you use a combination to
solve for a particular situation?
b. Why is order necessary in certain situations?
Extend
Have students research all of the "number drawn" lottery games in the state and determine the probabilities for each game. (For example, Pick-3, Pick-4, Pick-6, etc…)
Evaluate
Students will be given a series of problems and be able to use the knowledge gained on
combinations and permutations to solve them successfully.
Copyright © Casio, Inc.
Activity 3 • High School Activities for the Casio fx-300ES
15
Calculator Notes for Activity 3
If order is not important, you will need to compute a combination:
•
Turn calculator on and set MODE to 1 (COMP).
•
Enter the total number of items in the set.
•
Press SHIFT and the ÷ key to activate
the Combination key (nCr).
•
Enter the total number of items you
are going to choose from the set.
•
For example, if you wanted to select
three people from a group of 10 and
order was not important, you would
enter 10C3.
D
Math
D
Math
If order is important, you will need to compute a permutation:
•
Turn calculator on and set MODE to
1 (COMP).
•
Enter the total number of items in the
set.
•
Press SHIFT and the key to activate
the Permutation key. (nPr)
•
Enter the total number of items you are going to choose from the set.
•
For example, if you wanted to select three people from a group of 10 in a
particular order, you would enter 10P3.
To use the factorial key:
•
16
Press SHIFT followed by the x-1 key to activate the factorial.
High School Activities for the Casio fx-300ES • Activity 3
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 3 • Order in the Court!
Introduction
In probability, there are certain ways to determine the total number of possibilities in a given situation. Some situations require that order is very important
and others don’t require any need for order within the given arrangement. If we
are calculating the number of possibilities in an arrangement and we must pay
attention to order, that is called a permutation. If order is not important, that is
called a combination.
Sometimes people or things need to be arranged in a particular order. For
example, your teacher might require your class to have a seating chart. That
would be an example of a permutation. A lottery drawing where you have to select
the six winning numbers and the order in which the numbers are drawn is not
important is an example of a combination.
For example, there are 5 people in a group whose names are Andy, Barbara,
Claire, Desiree, and Erik. If you want to arrange 3 of those 5 people in any
particular order, you would use a permutation to find your answer. By finding
5P3, you would be able to determine that there are 60 different ways to order these
people. The first number in our formula indicates the total number of people in
our group and the second number indicates how many people from that group we
are going to choose. However, if order was not important and we could arrange
those three people in any way, then there would only be 10 different combinations.
In a combination, an arrangement of Andy, Barbara, and Erik is the same as Erik,
Andy, and Barbara. You may want to think of a combination as using the same
three people in any order.
Examine the following scenario and see if you can help solve
the problems that arise during this court case.
Judge Jane is entering her courtroom to hear testimony on "The Lottery
Drawing Gone Awry". The bailiff has notified the judge that there is a problem
with the jury. The jury members need to be seated a certain way before any testimony can begin. Four of the jury members are women and three of the jury members are men for a total of 7 members on the jury. Two of the women must sit
together, the three men must sit together and the other two women must sit
together. The arrangement of jury members must look something like this: W W
M M M W W. How many different ways can the jury be seated?
Once the jury members are seated, testimony can begin in the case of "The
Lottery Drawing Gone Awry.
In the state lottery, someone wins the lottery
when they correctly pick 6 out of 52 numbers in any order. The numbers range
from 1 – 52. However, on this particular evening, only the numbers from 1-51
Copyright © Casio, Inc.
Activity 3 • High School Activities for the Casio fx-300ES
17
Name _____________________________________________ Class ________ Date ________________
Activity 3 • Order in the Court!
were placed into the container for the drawing. This means that anyone who
chose the number 52 had no chance of winning the lottery because their number
was not in the container.
What is the difference between the number of combinations where 51 numbers
are to drawn as opposed to the correct number of 52?
Judge Jane rules that the state lottery commission must pay a substantial
amount in penalties and conduct another drawing just for those people who initially chose the number 52. Assuming that everyone who could have chosen the
number 52 did, what is the least amount of numbers in the drawing that will
ensure everyone will have a chance to win?
Objective
•
Demonstrate the ability to use permutations and combinations to solve
problems
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
Procedure
If order is not important, you will need to compute a combination
•
Turn calculator on and set MODE to 1 (COMP).
•
Enter the total number of items in the set.
•
Press SHIFT and the ÷ key to activate the Combination key (nCr).
If order is important, you will need to compute a permutation:
•
Turn calculator on and set MODE to 1 (COMP).
•
Enter the total number of items in the set.
•
Press "Shift" and the multiplication key to activate the Permutation key.
(nPr)
To use the factorial key:
•
18
Press SHIFT followed by the x-1 key to activate the factorial.
High School Activities for the Casio fx-300ES • Activity 3
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 3 • Order in the Court!
Problems and Questions
Directions: Solve each problem and write your calculator keystrokes to show
how you solved each problem.
1. At a very popular game show, 300 people are seated in the audience. Four
people are chosen to participate. How many different arrangements of four
people can be chosen if each person has an equally likely chance of being
selected?
____________________________________________________________________________
2. A state license plate uses three letters and three digits. The first letter cannot
be Q, X, or Z. The second and third letters can be any letter as well as each digit
can be any number from 0 – 9. How many different license plates can be
formed with this criteria? Explain.
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
3. Miki, Judy, John, and Matt are going for a drive. There are four seats in Miki’s
car. Since it is Miki’s car, Miki must drive. If Judy, John, and Matt can sit in
any of the other seats, how many different arrangements are there for them
to sit?
____________________________________________________________________________
4. Wanda has 5 shirts, 3 skirts, and 4 pairs of shoes. How many outfits can
Wanda create if each outfit consists of one shirt, one skirt, and one pair of
shoes?
____________________________________________________________________________
5. At a local dog show, ribbons are awarded for first, second, and third place.
There are 24 different dogs entered into the show. How many different
arrangements of first, second, and third place dogs are possible?
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 3 • High School Activities for the Casio fx-300ES
19
Name _____________________________________________ Class ________ Date ________________
Activity 3 • Order in the Court!
6. A restaurant offers a special menu at a fixed price. Anyone who wants this
special menu must choose one appetizer from a list of 3, one entrée from a
list of 4, and one dessert from a list of 3. How many different dinners can
someone choose?
____________________________________________________________________________
7. 32 students audition for a school play that has 5 parts. How many different
ways can these 5 parts be cast? Explain.
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
8. During your class election, you must choose a president and a vice-president.
If there are 180 people in your class, how many different arrangements are
possible?
____________________________________________________________________________
20
High School Activities for the Casio fx-300ES • Activity 3
Copyright © Casio, Inc.
Solutions and Answers for Activity 3
Story Solutions:
1. In order to seat the jury in the arrangement W W M M M W W, there are 144
different arrangements. Since there are four women on the jury, any one of four
people can occupy the first seat, with any one of the remaining three women
occupying the second seat. There are three men who are seated together allowing
for 6 different arrangements followed by the remaining two women for 2 different
arrangements. When we multiply all of these arrangements together
(4P2)(3P3)(2P1), it equals 144 different permutations.
2. To choose 6 numbers from 1-52, there are 20,358,520 combinations (52C6). To
choose 6 numbers from 1-51, there are 18,009,460 combinations (51C6). By simply
adding one number to the lottery drawing, there are 2,349,060 more possibilities.
3. Assuming that everyone who could have chosen the number 52 did, there are
2,349,060 people eligible for the special drawing. So that everyone could have one
ticket where he/she chooses 6 different numbers, there must be 38 numbers in the
drawing. When you calculate 38C6 = 2,760,681 different combinations meaning
that each person could be given one ticket leaving 411,621 combinations not
chosen.
Problem Solutions:
1. 330,791,175 different arrangements (300C4)
2. There are 23 possible letters for the first position and 26 letters for the remaining
two positions. Then, any one digit can be chosen for each of three number
positions. Therefore, we can calculate the total number of license plates by
multiplying 23 26 26 10 10 10 = 15,548,000 different license plates.
(23P1)(26P1)2(10P1)3
3. 6 different seating arrangements (1P1)(3P3) = 1 3 2 1
4. 60 different outfits (5C1)(3C1)(4C1)
5. 12,144 different arrangements (24P3)
6. 36 different menu possibilities (3C1)(4C1)(3C1)
7. 24,165,120 different ways these parts can be cast. (Note: Order is important here
because each person is assigned a specific part, thus we use a permutation to
determine the total number of different arrangements. 32P5)
8. 32,220 different arrangements (180P2)
Copyright © Casio, Inc.
Activity 3 • High School Activities for the Casio fx-300ES
21
Activity 4
Exploring Regressions
Teaching Notes
Topic Area: Two-Variable Statistics
NCTM Standards: Number and Operations, Data Analysis and Probability, Problem
Solving, Connecting, Communications, and Representations
Objective
Students will demonstrate the ability to conduct a linear regression and a quadratic
regression as well as perform other statistical calculations using the Casio fx-300ES.
Engage
Discuss with your students how to determine the differences between a linear function
and a quadratic function. Cite the differences between the equations and their graphs.
Then, ask them to provide examples that model linear and quadratic functions. For
example, does earning a salary where you are paid by the hour model a linear equation
or a quadratic equation? What about population growth or bacteria growth?
Explore
1.
2.
3.
Using the calculator, model how to access the statistics application and input data.
Using the calculator, model how to find various statistical information including
the regression, sum, minimum, maximum, and standard deviations.
Discuss how to interpret and analyze the values of various statistical information.
Explain
Have students explain when a particular regression models the data better than another
type of regression. Students should be able to communicate this information through
verbal and written communication.
Elaborate
Discuss the findings with your students:
a. Sum of the data
b. What the value of "r" indicates
c. The significance of the minimum and maximum values
Extend
1.
2.
Have students develop a hypothesis and gather data on a particular topic of
interest. Then, determine which regression best models this hypothesis. Discuss
what each piece of statistical information means in regards to the hypothesis and
study. (For example, students may want to examine the relationship between
population growth of your city/town over the past 50 years.)
Explore different types of regressions such as: logarithmic, exponential, power, and
inverse.
Evaluate
Students will be given a set of data and be able to use the knowledge gained to determine which regression is best as well as to calculate the various statistical information.
22
High School Activities for the Casio fx-300ES • Activity 4
Copyright © Casio, Inc.
Calculator Notes for Activity 4
Data: Points for a Linear Regression: (1,3), (2,5), (3,7), (4,9), (5,11)
To Calculate a Linear Regression:
•
Press MODE 2 to access the Statistics Application.
•
Press 2 (A+Bx) for the Linear Regression.
•
Input the data into the X and Y tables in the STAT Editor Screen. Once you input
the number, press = to store the value in the table.
STAT
D
Note: You may find it easier to input all of the x values first and then input the
y values as each time you input a piece of data, the cursor moves to the line
directly below whichever value you entered.
•
Press AC to exit the table.
•
Press SHIFT 1 to access the STAT Calculation Screen.
Copyright © Casio, Inc.
Activity 4 • High School Activities for the Casio fx-300ES
23
Calculator Notes for Activity 4
•
Press 7 for Regression.
•
Press 1 and = to determine the A value.
STAT
•
Return to the STAT Calculation Screen by pressing SHIFT 1.
•
Press 7 for Regression.
•
Press 2 and = to determine the B value.
STAT
24
D
D
•
Return to the STAT Calculation Screen by pressing SHIFT 1.
•
Press 3 and = to determine the correlation value.
High School Activities for the Casio fx-300ES • Activity 4
Copyright © Casio, Inc.
Calculator Notes for Activity 4
STAT
D
Remember that the closer the correlation values are to 1 or –1 determine how
good a fit the data is to the regression.
To Calculate a Quadratic Regression:
•
Once in the STAT mode, press 3 (____+cx2) to input data and find a quadratic
regression.
•
The keystroking is the same but the regression menu is slightly different.
Useful Hints and Information:
•
To find the sum of the data, enter the STAT Calculation Screen and press 4
for Sum.
•
In the STAT Calculation Screen, press 5 to calculate information for the variables.
Here you can determine the number of pieces of data, the mean of the x variables,
the mean of the y variables, and the standard deviations for each.
Copyright © Casio, Inc.
Activity 4 • High School Activities for the Casio fx-300ES
25
Calculator Notes for Activity 4
•
To find the Minimum or Maximum values of the data, enter the STAT Calculation
Screen and press 6 for MinMax.
To access the STAT mode:
26
•
Press MODE and 2 for the Statistics application.
•
Once in the STAT application, you can select the desired regression and tables to
input data.
High School Activities for the Casio fx-300ES • Activity 4
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 4 • Exploring Regressions
Introduction
Based upon data from the U.S. Census Bureau, the population within the
United States has increased each year. Certainly, there are various factors, which
contribute to the increase in population, but how can we predict what the population will be in 5 years, or 10 years, even 50 years? We can examine a data table
and project what the population will be based upon a regression analysis.
You have been asked to examine the U.S. population data from 1995-2004 and
develop a formula for predicting the U.S. population in the future. The following
data is provided for you.
U.S. Population from 1995-2005
Source: www.census.gov/ipc.www/worldpop.html
Year
Population
1995
5,694,418,460
1996
5,773,464,448
1997
5,852,360,768
1998
5,929,735,977
1999
6,006,163,019
2000
6,081,527,896
2001
6,155,942,526
2002
6,303,112,453
2003
6,376,863,118
2004
6,451,058,790
Objectives
1. Input the data from the table setting year 1995 to equal 1,
2. Determine which regression (linear or quadratic) is best, and
3. Solve problems using the data and the calculations.
Materials Needed
•
The Casio fx-300ES calculator
•
The data table as shown above
•
Pencil and paper
Copyright © Casio, Inc.
Activity 4 • High School Activities for the Casio fx-300ES
27
Name _____________________________________________ Class ________ Date ________________
Activity 4 • Exploring Regressions
Procedure
1.
Turn on the calculator and press MODE followed by 2 to enter the STAT
application.
2.
Input the data in either a linear regression (2) or quadratic regression (3)
based upon your hypothesis.
3.
Enter the data in the X and Y table. Use the X column for the years, setting
1995 to equal 1. Round your population data to the nearest hundredth of a
billion in order to fit in the data column. (1,5.69; 2,5.77; etc.)
4.
Once the data is completely entered, press AC followed by SHIFT 1 to access
the STAT Calculation Screen.
5.
Press 7 to access the regression calculations. Determine the values for each
variable within the equation and to find the correlation of the data.
Problems and Questions
1. Test the U. S. Population data using a linear regression.
a. What is the A value?
_______________________________
b. What is the B value?
_______________________________
c. What is the r-value?
_______________________________
d. Write the equation of the line.
____________________________________________________________________________
2. Test the U.S. Population data using a quadratic regression. Round all answers
to the nearest thousandth.
a. What is the A value?
_______________________________
b. What is the B value?
_______________________________
c. What is the C value?
_______________________________
d. Write the equation of the line.
____________________________________________________________________________
3. Which regression model best fits the data and why?
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
28
High School Activities for the Casio fx-300ES • Activity 4
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 4 • Exploring Regressions
4. Use your equation to predict what the U. S. Population will be in 2020.
Does your predication make sense and why?
____________________________________________________________________________
____________________________________________________________________________
5. Enter the following data table for a quadratic regression and answer the
following questions.
(0, -5), (1, -3), (2, 3), (3, 13), (4, 27), (5, 45), (6, 67), (7, 93)
a. A value:
_______________________________
b. B value:
_______________________________
c. C value:
_______________________________
d. What is the sum of x?
_______________________________
e. What is the sum of y?
_______________________________
f. What is the min Y?
_______________________________
g. What is the max Y?
_______________________________
h. How many pieces of data are in the data set?
_______________________________
i. What is the mean of x?
_______________________________
j. What is the mean of y?
_______________________________
k. What is the standard deviation of x?
_______________________________
l. What is the standard deviation of y?
_______________________________
Copyright © Casio, Inc.
Activity 4 • High School Activities for the Casio fx-300ES
29
Name _____________________________________________ Class ________ Date ________________
Activity 4 • Exploring Regressions
6. Enter the following data for a quadratic regression and determine the values
for a, b, and c. Round all answers to the nearest thousandth.
(-10, -352), (5, -52), (20, -1102), (-2, -70), (12, -374), (9, -200), (27, -2054)
a. A value:
_______________________________
b. B value:
_______________________________
c. C value:
_______________________________
7. A certain bacteria triples every six months. Enter the following data and use an
exponential regression. Write the equation in the space provided.
(0.5, 100), (1, 300), (1.5, 900), (2, 2700), (2.5, 8100)
a. What is the A value?
_______________________________
b. What is the B value?
_______________________________
c. What is the r-value?
_______________________________
d. What is the equation of the regression line?
_______________________________
30
High School Activities for the Casio fx-300ES • Activity 4
Copyright © Casio, Inc.
Solutions and Answers for Activity 4
1. a. 5.591
b. 0.086
c. 0.998
d. y = 5.591 + 0.086x
2. a. 5.621
b. 0.071
c. 1.364 10-3
3. The data best fits a linear regression as the r-value on the linear regression
is very close to 1 indicating that the data and the equation are almost perfectly
correlated.
4. Using a linear regression, the equation is y = 5.591 + 0.086x and x = 21 to
indicate the number of years from 1995 to equal 2020, the estimated population is
7,397,000,000.
5. a. -5
e. 240
b. 0
c. 2
d. 28
f. -5
g. 93
h. 8
i. 3.5
j. 30
k. 2.291287847
l. 33.36165464
6. a. -13.594
b. 5.378
c. -2.992
7. a. 33.33
b. 9
c. 1
d. y = 33.33 • 9X
Copyright © Casio, Inc.
Activity 4 • High School Activities for the Casio fx-300ES
31
Activity 5
So, You Want To Be The
Apprentice?
Teaching Notes
Topic Area: Tables and Graphing
NCTM Standards: Number and Operations, Algebra, Problem Solving, Connecting,
Communications, Representations
Objective
Students will demonstrate the ability to develop income and expense formulas as well
as profit and loss formulas. Students will also develop series of equations and data
tables that will model their break-even points for a particular business plan.
Engage
Survey your students to determine who are currently working part-time. Then, survey
your students to learn what they would like to do for a career. Ask students if they are
interested in developing a business or creating a product that they plan to sell. Begin a
discussion as to how businesses determine which product and/or service they might
offer to the general public.
Explore
1.
2.
3.
Using the calculator, explore the Table function and model how to input an
equation and generate a table of values.
Using the calculator, explore the Statistics application to determine the mean of a
set of data.
Model how to interpret linear equations that model income and expense
scenarios.
Explain
Students will discuss the table of values generated by a particular equation. That
equation will model either the income generated by a business, the cost of purchasing
materials to manufacture a product, or to determine the break-even point for a business
venture. Discuss with your students what determines profitability and the success
of a particular business or product.
Elaborate
Discuss the following topics and questions with your students to generate discussion
and further understanding of these topics.
a. Products and/or businesses you believe are successful and why.
b. Products and/or businesses you believe are failures and why.
c. The characteristics that make a good product / good company.
d. The reasons why certain products and/or businesses do not succeed.
Extend
1.
32
Have students develop a business plan for a particular business and/or product.
The business plan must include a marketing strategy, target audience, equations for
expenses, projected income, and break-even point.
High School Activities for the Casio fx-300ES • Activity 5
Copyright © Casio, Inc.
Activity 5:
So, You Want To Be The Apprentice? (continued)
2.
3.
Teaching Notes
Have students research a particular company or product. Determine what
attributed to the success or failure for this product or company. Have students
submit a paper detailing their findings and opinions regarding this company or
product.
Have students interview their parent(s)/guardian(s) and inquire about what they do
for a living. Research their company/product and report to the class what they
have learned. If possible, see if the parent(s)/guardian(s) would be interested in
coming to your class to speak about their business and how they use math in their
profession.
Evaluate
Students will be given a series of scenarios to formulate equations, generate data tables,
and interpret the results.
Copyright © Casio, Inc.
Activity 5 • High School Activities for the Casio fx-300ES
33
Calculator Notes for Activity 5
To Enter a Function and Create a Table of Values:
•
Press MODE.
•
Press 3 for TABLE.
•
Enter the function after f(x)=.
•
Press =.
•
Set a Start Value and press =.
•
•
34
D
Math
D
Math
D
Math
Set an End Value and press =.
Set a Step Value and press =.
High School Activities for the Casio fx-300ES • Activity 5
Copyright © Casio, Inc.
Calculator Notes for Activity 5
D
Math
To Determine the Mean of a Set of Data:
•
Press MODE.
•
Press 2 for STAT.
•
Press 1 for 1-Variable Statistics.
•
Enter the data in the STAT Editor Screen.
STAT
D
•
Once the data is entered, press AC.
•
Press SHIFT 1 to access the STAT Calculation Screen
Copyright © Casio, Inc.
Activity 5 • High School Activities for the Casio fx-300ES
35
Calculator Notes for Activity 5
36
•
Press 5 for Var-Sub Menu to calculate the mean.
•
Press 2 followed by = to display the mean.
High School Activities for the Casio fx-300ES • Activity 5
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 5 • So, You Want To Be The Apprentice?
Introduction
Do you have an interest in developing a product to sell to the general public?
Do you have visions of operating your own business or company and being very
successful? Do you have an invention that you think people will not only use, but
will buy because it’s that good? Well, here’s your chance! It’s time to begin thinking about developing a business plan and what it will take to make it successful.
Think about various products you use everyday. What is it about them that
makes you use them? What is it about that product’s company that makes them
successful? Would you like to create your own company where you provide a service to people, like dog walking, landscaping, a cooking company or perhaps you
have another company in mind? Would you like to manufacture a product that
you will sell to the general public? Whatever it is, how will you generate income?
How will you be able to cover the cost of your expenses such as start-up costs and
supplies? How will you determine your future profits? There is a lot to consider
when starting a business and making it successful. Let’s get to work!
Objectives
1. Examine business scenarios and develop formulas for their expenses, sales, and
break-even points.
2. Calculate the average monthly sales for a particular business.
3. Solve problems involving functions formulas and statistics.
Materials Needed
•
The Casio fx-300ES calculator
•
The table shown below
•
Pencil and paper
Data table with monthly sales figures for
Samantha’s Study Skills Survival Guide
Month
Sales
Month
Sales
January
$20
July
$10
February
$50
August
$40
March
$30
September
$70
April
$90
October
$150
May
$100
November
$130
June
$120
December
$150
Copyright © Casio, Inc.
Activity 5 • High School Activities for the Casio fx-300ES
37
Name _____________________________________________ Class ________ Date ________________
Activity 5 • So, You Want To Be The Apprentice?
Procedure
To Enter a Function and Create a Table of Values:
1. Press MODE followed by 3 for TABLE.
2. Enter the function after f(x)=.
3. Set a Start Value and press =.
4. Set an End Value and press =.
5. Set a Step Value and press =.
To Determine the Mean of a Set of Data:
1. Press MODE followed by 2 for STAT and 1 for 1-Variable Statistics
2. Enter the data in the STAT Editor Screen and once completed press AC.
3. Press SHIFT 1 to access the STAT Calculation Screen
4. Press 5 for Var-Sub Menu, then 2 and = to calculate the mean.
Problems and Questions
1. Samantha is an excellent student and believes that her study skills would be
helpful to her fellow classmates. She decides to write "Samantha’s Study Skills
Survival Guide" and sells it for $10. Her first year’s sales are listed on the
previous page.
a. What is her total sales for the year?
_______________________________
b. What is her sales average for each month?
_______________________________
c. What do you believe are the factors that contribute to more guides being sold
during certain months as opposed to others? State your reasons in the space
provided.
_________________________________________________________________________
_________________________________________________________________________
d. Write an equation that models the income from Samantha’s Study Skills
Survival Guide sales.
_______________________________
38
High School Activities for the Casio fx-300ES • Activity 5
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 5 • So, You Want To Be The Apprentice?
2. Samantha is pleased with her first year sales and decides to create a website where
she can sell her Study Skills Survival Guide on the Internet. She realizes that she
didn’t consider any business expenses such as paper, ink, and use of her computer
when she looked at her first year’s sales figures and doesn’t have a good idea as to
what her profit was during that year. She is going to increase the price of the book
to $15 and determines that each book will cost her $3.25 in expenses.
a. Write a new equation to model the income from the sales of her book.
_______________________________
b. Write a new equation to model the profit from each book.
_______________________________
3. Use the following table to answer these questions.
Month
Books Sold
Sales
Profit
January
11
$165
$129.25
February
15
$225
$176.25
March
20
$300
$235.00
April
25
$375
$293.75
May
35
$525
$411.25
June
42
$630
$493.50
July
8
$120
$94.00
August
11
$165
$129.25
September
21
$315
$246.75
October
25
$375
$293.75
November
33
$495
$387.75
December
39
$585
$458.25
a. What is the total number of books sold?
__________________
b. What is the total sales for her book this year?
__________________
c. What is the total profit for her book this year?
__________________
d. What is her average monthly profit?
__________________
Copyright © Casio, Inc.
Activity 5 • High School Activities for the Casio fx-300ES
39
Name _____________________________________________ Class ________ Date ________________
Activity 5 • So, You Want To Be The Apprentice?
4. Miguel opens a Spa Resort for Dogs. He charges $27.00 per day, per dog and his
services include exercising the dog, two meals, and cleaning service for the kennel.
However, his start up costs are quite high for this business. It will cost him
$15,000 to covert part of his home and backyard to accommodate this spa resort.
a. Write an equation to model Miguel’s business.
_______________________________
b. How many dogs must he care for in order to break-even? (Note: A break-even
point is when your profit formula equals 0 because your expenses or startup
costs have been finally paid.) Explain.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
c. If he increase his daily rate to $31.00 per day, how does that affect his
break-even point?
_______________________________
d. How many dogs must Miguel take care of to have a profit of $10,000 if he
charges $31.00 per day?
_______________________________
5. The school marching band is selling candy as a fundraiser for their next band
competition. They purchase the candy for $ .55 per bar and sell it for $2.00.
a. Write an equation to model the income from the candy sales.
_______________________________
b. Write an equation to model the profit from each candy bar.
_______________________________
c. How many candy bars must they sell in order to raise at least $1,425 for
the trip?
_______________________________
40
High School Activities for the Casio fx-300ES • Activity 5
Copyright © Casio, Inc.
Solutions and Answers for Activity 5
1. a. Total Sales = $960
b. $80 per month
c. Sales decreased during the summer months because school is not in session.
Sales peaked around May and June probably because of final exams and sales
also peaked at the end of the year either due in part to preparation for midterm exams or as gifts for people during the holiday season.
d. F(X) = 10X
2. a. F(X) = 15X
b. F(X) = 15X – 3.25X or F(X) = 11.75X
3. a. 285 books sold
b. $4,275
c. $3,348.75
d. $279.06
4. a. F(X) = 27.00X – 15,000
b. He must take care of 556 dogs in order to break-even. (Note: Since his profit
is -$15 when he takes care of 555 dogs, he must take care of 556 for his profit to
be $12.)
c. When he increases his daily rate to $31, the new profit formula is
F(X) = 31.00X – 15,000. His break-even point is when he takes care of 484 dogs.
That’s a difference of 72 dogs.
d. 807 dogs
5. a. F(X) = 2X
b. F(X) = 2X – 0.55X or F(X) = 1.45X
c. 983 candy bars
Copyright © Casio, Inc.
Activity 5 • High School Activities for the Casio fx-300ES
41
Activity 6
Leaving It All To Chance
Teaching Notes
Topic Area: Probability and Statistics
NCTM Standards: Number and Operations, Data Analysis and Probability, Problem
Solving, Communications, Connecting, Representations
Objective
Students will demonstrate the ability to conduct a probability experiment and process
information gained from that experiment.
Engage
Brainstorm with the class about a definition for probability. Then, ask students to provide various examples in which probability is used. Ask students to determine what
constitutes a fair probability experiment.
Explore
1.
2.
3.
Using the calculator, model how to generate a series of random numbers.
Using the calculator, model how to input a set of data and determine the mean.
Explore how to develop a probability experiment and conduct a fair experiment.
Explain
Students will conduct an experiment with a partner and analyze the results. Guide students towards a discovery and understanding between "experimental probability" and
"theoretical probability."
Elaborate
Discuss their observations and discoveries along with the following:
a. How do you ensure that an event is conducted the same way each time?
b. When does "experimental probability" equal "theoretical probability"?
c. What is the difference between probability events that are "impossible", "equally
likely", and "certain?"
Extend
Have students develop their own game that could be used at a carnival or town fair.
A presentation and report must accompany the probability event detailing the likelihood
of each event occurring, the results of ten people participating in the experiment, and
their observations, discoveries, and critique of the event.
Evaluate
The students will be given a series of probability experiments and will be asked to conduct them, record their data, and summarize their results as well as their observations.
42
High School Activities for the Casio fx-300ES • Activity 6
Copyright © Casio, Inc.
Calculator Notes for Activity 6
A set of data is provided listing the outcomes of a particular probability event. In this
event, a spinner divided into equally likely sections numbered 1 through 8 was spun 10
times. The outcomes are listed. Find the mean of the outcomes and determine
whether or not the probability event is fair based upon the data given.
{2, 8, 3, 1, 5, 2, 7, 4, 6, 2}
Steps for Using the Casio fx-300ES:
To Enter a List of Data and Calculate the Mean:
1.
Press MODE.
2.
Press 2 for STAT.
3.
Press 1 for 1-Variable Statistics.
4.
Enter the data in the STAT Editor Screen.
STAT
5.
D
Once the data is entered, press AC.
Copyright © Casio, Inc.
Activity 6 • High School Activities for the Casio fx-300ES
43
Calculator Notes for Activity 6
STAT
6.
Press SHIFT 1 to access the STAT Calculation Screen.
7.
Press 5 for Var-Sub Menu to calculate the mean.
8.
Press 2 to followed by = to display the mean.
STAT
44
D
D
High School Activities for the Casio fx-300ES • Activity 6
Copyright © Casio, Inc.
Calculator Notes for Activity 6
To Generate a Random Number:
1.
Press MODE followed by 1 for the Computation application.
2.
Press SHIFT SETUP and 2 for LineIO (Line Input/Output). (Note: You can
generate a random number in MthIO, but it will appear as a fraction and you
must press the S➞
➞D key to convert it to a decimal.)
3.
Press SHIFT “decimal point” = to generate a random number.
D
Copyright © Casio, Inc.
Activity 6 • High School Activities for the Casio fx-300ES
45
Name _____________________________________________ Class ________ Date ________________
Activity 6 • Leaving It All To Chance
Introduction
Probability is an interesting branch of mathematics because it encompasses
randomness and chance along with an element of fun, interaction, and amazement. There are many games we play that incorporate the use of various probability events such as spinners, dice, or cards. States hold lotteries where millions
of dollars can be awarded to one or more lucky winners who just happen to pick
6 numbers from a specific set. Nevertheless, any probability event has a chance a
particular outcome is going to occur and often times that chance is not as good as
its likelihood it won’t occur.
We refer to an event as a particular probability experiment. With any probability event, there is "theoretical probability" and "experimental probability". We
can define "theoretical probability" as what should occur. For example, if we were
to roll a standard, fair die numbered 1-6, six times we should have each number
appear once and only once. However, once we conduct that experiment and roll
the die six times, our results may be something different. That is what we call
"experimental probability."
Objectives
1. Input a set of data into the STAT Editor Screen and analyze the data.
2. Generate a series of random numbers and analyze the data.
3. Solve probability problems and interpret the results.
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
•
Number cubes or dice
•
Paper clips
•
Protractors and compasses
Procedure
To Enter a List of Data and Calculate the Mean:
1. Press MODE.
2. Press 2 for STAT.
3. Press 1 for 1-Variable Statistics
4. Enter the data in the STAT Editor Screen.
5. Once the data is entered, press AC.
46
High School Activities for the Casio fx-300ES • Activity 6
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 6 • Leaving It All To Chance
6. Press SHIFT 1 to access the STAT Calculation Screen.
7. Press 5 for Var-Sub Menu to calculate the mean.
8. Press 2 to followed by = to display the mean.
To Generate a Random Number:
1. Press MODE followed by 1 for the Computation application.
2. Press SHIFT SETUP and 2 for LineIO (Line Input/Output). (Note: You can
generate a random number in MathIO, but it will appear as a fraction and you
must press the S ➞
➞ D key to convert it to a decimal.)
3. Press SHIFT "decimal point" = to generate a random number.
Problems and Questions
1. Work with a partner and use a number cube or die (numbered 1, 2, 3, 4, 5, 6) to
roll it six times, record the results, and answer the following questions.
(Have one person roll the die and the other person record the outcomes.)
a. List your outcomes of your six rolls.
_______________________________
_______________________________
_______________________________
_______________________________
_______________________________
_______________________________
b. In theory, you should have had each number (1-6) appear once.
Did that happen?
_______________________________
c. Explain how you rolled the number cube or die. Be very specific with your
explanations. For example, did you roll the die the same way each time?
Why or why not?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Copyright © Casio, Inc.
Activity 6 • High School Activities for the Casio fx-300ES
47
Name _____________________________________________ Class ________ Date ________________
Activity 6 • Leaving It All To Chance
2. You and your partner will each roll the number cube or die 10 times. Record the
outcomes for your partner on their worksheet and answer the following questions.
Roll
Outcome
1
2
3
4
5
6
7
8
9
10
11
12
Mean of Outcomes
a. Use your calculator to determine the mean of your outcomes.
_______________________________
b. Did each outcome appear twice? Why or why not?
____________________________________________________________________________
____________________________________________________________________________
c. If each outcome didn’t appear twice, what could you have done differently to
either ensure or be more likely that each outcome would have appeared twice?
____________________________________________________________________________
____________________________________________________________________________
d. Assuming that each outcome appeared twice, what would be the mean of the
data?
_______________________________
48
High School Activities for the Casio fx-300ES • Activity 6
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 6 • Leaving It All To Chance
3. Using your compasses and protractors, construct a spinner divided into 10 equal
segments. Number each segment from 1-10. Using your pencil point, anchor the
paper clip at the center of your circle with one hand and use your other hand to
spin the paper clip making it act like a spinner. Do this for 10 trials and record the
outcomes in the table.
Outcome
Spin
1
2
3
4
5
6
7
8
9
10
Mean of Outcomes
a. Do you believe that this experiment was fair? Why or why not?
____________________________________________________________________________
____________________________________________________________________________
b. What is the angle measurement of each wedge on your spinner?
____________________________________________________________________________
c. Draw a new spinner in the space below that is "not fair".
Copyright © Casio, Inc.
Activity 6 • High School Activities for the Casio fx-300ES
49
Name _____________________________________________ Class ________ Date ________________
Activity 6 • Leaving It All To Chance
4. Create a series of random numbers and record the outcomes in the table.
The calculator will generate a three-digit random number after a decimal point.
For purposes of this probability event, just record the numbers that appear
after the decimal point. However, if a number appears such as 0.32, that
number will be recorded as 320.
Trial
Random Number
1
2
3
4
5
6
7
8
9
10
Mean
a. How many different numbers can be generated in this form?
_______________________________
b. What is the theoretical probability that each number appears in this
experiment?
_________________________________________________________________________
c. What is the probability that a randomly generated number is divisible
by 2?
_________________________________________________________________________
d. What is the probability that a randomly generated number is divisible
by 5?
_________________________________________________________________________
50
High School Activities for the Casio fx-300ES • Activity 6
Copyright © Casio, Inc.
Solutions and Answers for Activity 6
1. All answers will vary by students.
2. a. Answers may vary.
b. Answers may vary.
c. Answers may vary, but some possible explanations may be to roll the number
cube or die at the same speed, release it at the same height, start it with the
same number facing up, and/or prior to the roll, shaking it for the same amount
of time.
d. 3.5
3. a. Answers may vary.
b. The measure of each segment should be 36o.
c. Drawings may vary.
4. a. 1,000 different number can be generated from 000-999.
b. The probability that each numbers appears is 1/1000
1
c. There is a 2 or 50% chance that a number is divisible by 2.
d. There is a 15 or 20% chance that a number is divisible by 5.
Copyright © Casio, Inc.
Activity 6 • High School Activities for the Casio fx-300ES
51
Activity 7
Polar and Rectangular Coordinates
Teaching Notes
Topic Area: Polar and Rectangular Coordinates
NCTM Standards: Number and Operations, Algebra, Geometry, Measurement, Reasoning
and Proof, Connecting, Representations
Objective
Students will demonstrate the ability to define polar and rectangular coordinates and
covert between both forms.
Engage
Discuss with students how to graph on a coordinate plane. Then, make the connection
between the coordinate plane and a polar coordinate system where the points are
defined as (r, ) as r is the polar axis (the length of OP) and is the measure of the
distance from the axis and OP (measured in a counterclockwise direction). Survey
students to determine when such a coordinate system might be used.
Explore
1.
2.
3.
Using the calculator, model how to set the calculator to measure in degrees or
radians.
Using the calculator, model how to use the function application to see a table of
values for the coordinates.
Using the calculator, model how to use the square root function to determine the
distance between two points by solving the distance formula.
Explain
Students will discuss how to convert between polar coordinates and rectangular coordinates and vice versa. They will discuss and interpret their results.
Elaborate
Discuss the problems with your students. Be sure to include:
a. How to interpret each answer.
b. Graph the points on a polar coordinate system.
c. What happens to the graph between 0-90o, 90-180o, 180-270o,
and 270-360o.
Extend
1.
2.
3.
Students could research the locations of particular stars on a polar coordinate
system.
Students could develop a series of equations that when graphed will design a
picture on a polar coordinate system.
Research weather forecasting and how they use polar coordinates to measure the
direction and distance of local storms.
Evaluate
Students will be given a series of problems and successfully convert a polar coordinate
to a rectangular coordinate and vice versa.
52
High School Activities for the Casio fx-300ES • Activity 7
Copyright © Casio, Inc.
Calculator Notes for Activity 7
To Set the Calculator to Degrees or Radians:
•
Press MODE followed by 1 for COMP.
•
Press SHIFT SETUP.
•
Press 3 for Degrees or press 4 for Radians
To Enter a Function and Create a Table of Values:
•
Press MODE.
•
Press 3 for TABLE.
•
Enter the function after f(x)=.
D
•
Math
Press =.
Copyright © Casio, Inc.
Activity 7 • High School Activities for the Casio fx-300ES
53
Calculator Notes for Activity 7
•
•
•
54
Set a Start Value and press =.
D
Math
D
Math
D
Math
Set an End Value and press =.
Set a Step Value and press =.
High School Activities for the Casio fx-300ES • Activity 7
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 7 • Polar and Rectangular Coordinates
Introduction
You are probably used to plotting points on a coordinate plane in the form of
(x, y), but when we plot points on a polar coordinate system we will plot them in
the form of (r, ).
P (r, )
r
O
Polar Axis
In this diagram, the ray extending from point O is called the Polar Axis. Point
P is defined by a set of polar coordinates where r is the length of OP and is the
angle measurement from the Polar Axis to segment OP. There are 360 degrees in
the polar coordinate system indicating a full rotation around point O. The measurement of r parallels the measurement of any x-coordinate in that it is positive in
the first and fourth quadrants and negative in the second and third. The following conversation formulas will help converting between polar and rectangular
coordinates.
From Polar to Rectangular: x = r cos
y = r sin
From Rectangular to Polar: r = + x2 + y2 .
Objectives
1. Convert from polar coordinates to rectangular coordinates
2. Convert from rectangular coordinates to polar coordinates
3. Develop an equation and graph its values on a polar coordinate.
Materials Needed
•
The Casio fx-300ES calculator
•
Polar Coordinate Graph Paper
•
Pencil and paper
Procedure
To Set the Calculator to Degrees or Radians:
•
Press MODE followed by SETUP.
•
Press 3 for Degrees or Press 4 for Radians.
Copyright © Casio, Inc.
Activity 7 • High School Activities for the Casio fx-300ES
55
Name _____________________________________________ Class ________ Date ________________
Activity 7 • Polar and Rectangular Coordinates
To Enter a Function and Create a Table of Values:
•
Press MODE followed by 3 for TABLE.
•
Enter the function after f(x)=.
•
Press =.
•
Set a Start Value and press =.
•
Set an End Value and press =.
•
Set a Step Value and press =.
Problems and Questions
1. Use the distance formula and determine the distance from the origin to the
specified point.
a. (3, 4)
_____________________
b. (-8, 8)
_____________________
c. (2, 0)
_____________________
d. (-10, -24)
_____________________
e. (84, 13)
_____________________
2. Find the value of r for each value of if r = 3 sin (set to degree mode).
a. = 90o
_____________________
b. = 135o
_____________________
c. = 15o
_____________________
d. = 210o
_____________________
e. = 330o
_____________________
56
High School Activities for the Casio fx-300ES • Activity 7
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 7 • Polar and Rectangular Coordinates
3. Complete the table of values for f(x)= 4 cos (4 • ).
4 cos (4 • )
0o
195o
15o
210o
30o
225o
45o
240o
60o
255o
75o
270o
90o
285o
105o
300o
120o
315o
135o
330o
150o
345o
165o
360o
180o
720o
4 cos (4 • )
4. When you plot the points from problem 3, what will the graph look like?
____________________________________________________________________________
____________________________________________________________________________
5. Convert (-6, 60 degrees) to rectangular coordinates.
____________________________________________________________________________
6. Convert ( 3, -1) to polar coordinates.
____________________________________________________________________________
7. Convert (5, 195 degrees) to rectangular coordinates.
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 7 • High School Activities for the Casio fx-300ES
57
Solutions and Answers for Activity 7
1. a. 5
b. 8
2
c. 2
d. 26
e. 85
2. a. 3
b. (3
2) /2
c. (3
6–3
2) /4
d. -3/2
e. -3/2
3.
4 cos (4 • )
4 cos (4 • )
0
4
195
2
15
2
210
-2
30
-2
225
-4
45
-4
240
-2
60
-2
255
2
75
2
270
4
90
4
285
2
105
2
300
-2
120
-2
315
-4
135
-4
330
-2
150
-2
345
2
165
2
360
4
180
4
720
4
4. The graph will look like an 8-petal flower.
5. (-3, -3
3)
6. (2, 330o)
7. -5
58
6 –5
4
2 , -5
6+5
4
2
High School Activities for the Casio fx-300ES • Activity 7
Copyright © Casio, Inc.
Activity 8
Exploring π
Teaching Notes
Topic Area: π (Area and Circumference)
NCTM Standards: Number and Operations, Algebra, Geometry, Measurement, Problem
Solving, Reasoning and Proof, Connecting, Communications
Objective
Students will demonstrate how to calculate the circumference and area of a circle as
well as explore its effects on these measures when the radius is changed.
Engage
Discuss with your students the differences between a radius and a diameter. Based on
prior knowledge, ask students to define how to determine the circumference and area of
a circle. Ask students how to determine the value of π, which is defined as the circumference divided by the diameter.
Explore
1.
2.
3.
Using the calculator, model how to use the calculator to find the circumference and
area of a circle and to use the π key.
Using the calculator, model how to input a function in the table application using
the π symbol.
Using the calculator, model how to add and subtract values of π that students
might see in problems focusing on composite figures.
Explain
Explain why it is acceptable to express a circle’s circumference and area in terms of π
rather substituting with values of 22/7 or 3.14.
Elaborate
Discuss any questions or comments with students. Have students use string to measure
the bases of various cylinders and express π as the circumference divided by the diameter to see that the all values of π are equal.
Extend
1.
2.
Have students describe the changes in the area and circumference of a circle when
the diameter is doubled, tripled, multiplied by a particular number, etc…
Have students draw composite figures and determine the area and circumference
of those figures.
Evaluate
Students will be given a series of problems in which they must find the area and
circumference of various circles.
Copyright © Casio, Inc.
Activity 8 • High School Activities for the Casio fx-300ES
59
Calculator Notes for Activity 8
Solve 3π + 5π
Steps for Using the π key:
1.
Press MODE followed by 1 for COMP application.
2.
Press SHIFT SETUP 1 for MthIO (Input/Output).
3.
Enter the problem as 3 π + 5 π and press =.
D
Math
4.
See the answer as 8π on the answer line.
5.
To display the decimal equivalent, press the S➞D key.
D
Math
To Enter a Function and Create a Table of Values:
60
1.
Press MODE.
2.
Press 3 for TABLE.
High School Activities for the Casio fx-300ES • Activity 8
Copyright © Casio, Inc.
Calculator Notes for Activity 8
3.
Enter the function after f(x)=.
D
4.
Press =.
5.
Set a Start Value and press =.
6.
Set an End Value and press =.
7.
Set a Step Value and press =.
Math
(Note: When using the π key in the TABLE application, the values of f(x) will be
displayed as the decimal approximation rather than in terms of π.)
Copyright © Casio, Inc.
Activity 8 • High School Activities for the Casio fx-300ES
61
Name _____________________________________________ Class ________ Date ________________
Activity 8 • Exploring π
Introduction
When we examine a circle, we must differentiate between the radius and the
diameter. A radius is a line segment from the center point to one point on the circle while the diameter is a line segment connecting two points on the circle and
passing through the center point. Examine the diagrams below.
radius
diameter
To calculate the circumference of the circle, we need to know the measurement
of the radius and multiply it by 2 times π. (C = 2•π•r) For some, it might be easier to determine the circumference as π times the diameter. (C = π•d) However,
when calculating the area, we must use the radius as the formula is A = π•r2. It is
helpful to remember that the circumference of the circle is a linear measurement,
which measures the distance around the circle. The area measures the amount of
space inside of the circle measured in square units.
The big mystery here is the definition of π. When we were first introduced to
π we might have been simply told that it equaled 3.14 in decimal form or 22/7 as
a fraction. That was it! However, π is an irrational number meaning that in its
decimal form, it does not terminate or repeat. But, with all circles, the relationship of π remains the same. It might help to gain a better understanding of π if
we transform each formula.
The circumference of a circle is calculated as C = 2•π•r and we can express π
as π=C/2r. For the area of a circle, we can express π as π=A/r2.
Examine these two circles.
Radius = 5 units
62
Radius = 12 units
C = 2•π•r
A = π•r2
A = π•52
C = 2•π•12
A = π•122
A = 25π
C = 24π
A = 144π
C = 2•π•r
A=
C = 2•π•5
C = 10π
π•r2
High School Activities for the Casio fx-300ES • Activity 8
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 8 • Exploring π
Now that we have measured the circumference and area of each circle, lets
transform each of these equations and solve for π. To do this, we need to substitute the values of the circumference and area of each circle to solve for π.
Radius = 5 units
Radius = 12 units
π = C/2r
π=A/r2
π = C/2r
π=A/r2
π = 10π/10
π=25π/25
π = 24π/24
π = 144π/144
π=π
π=π
π=π
π=π
We can conclude from the above examples that regardless of the circle’s radius,
the value of π is always the same for each circle whether we are calculating its circumference or its area.
Let’s explore this concept further by completing a chart for the area and circumference of circles with radii of various lengths. Once you have completed the
chart, see if you can notice any patterns within the data. For all calculations,
express your answers in terms of π.
Radius
1 unit
2 units
4 units
8 units
16 units
32 units
Circumference
(C = 2 • π • r)
Area
(A = π • r2)
Objective
Demonstrate how to calculate the circumference and area of a circle as well as explore
its effects on these measures when the radius is changed.
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
Copyright © Casio, Inc.
Activity 8 • High School Activities for the Casio fx-300ES
63
Name _____________________________________________ Class ________ Date ________________
Activity 8 • Exploring π
Procedure
Steps for Using the π key:
1. Press MODE followed by 1 for COMP application.
2. Press SHIFT SETUP 1 for MthIO (Input/Output).
3. Enter the problem as 3π + 5π and press "=".
4. See the answer as 8π on the answer line.
5. To display the decimal equivalent, press the S ➞
➞ D key.
To Enter a Function and Create a Table of Values:
1. Press MODE.
2. Press 3 for TABLE.
3. Enter the function after f(x)=.
4. Press =.
5. Set a Start Value and press =.
6. Set an End Value and press =.
6. Set a Step Value and press =.
(Note: When using the π key in the
TABLE application, the values of f(x)
will be displayed as the decimal approximation rather than in terms of π).
Problems and Questions
1. Using the TABLE application on your calculator, enter f(x) = 2•π•X to calculate
the circumference of a circle, where X = the measure of the radius. Set a start
value of 1, an end value of 10, and a step value of 1. Write the values of the table
in the chart provided as well as the answers in terms of π.
F(x) = 2•π•X
Answer in Terms of π
Answer in Decimal Form
X=1
X=2
X=3
X=4
X=5
X=6
X=7
X=8
X=9
X = 10
64
High School Activities for the Casio fx-300ES • Activity 8
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 8 • Exploring π
2. Calculate the area and circumference of this circle.
D=14cm
Circumference = _____________________
Area = ______________________________
3. Calculate the area and circumference of this circle.
R=0.9m
Circumference = _____________________
Area = ______________________________
4. Calculate the area and circumference of a circle with a radius that measures
(8X).
Circumference = __________________
Area = __________________
5. Find the area of the shaded region when the circle has a radius that measures
7 inches. Express your answer in terms of π as well as in decimal form.
Area = ____________________________(π form)
_______________________(decimal form)
6. Find the perimeter of the rectangular region as well as the area of the shaded
region. In the space below, describe how you obtained your solution and show the
calculations you used to determine your answers.
r = 3.5 inches
7. In terms of π, what is the total circumference of a circle that has a radius of 3 cm,
a circle with a radius of 5.5 cm, and a circle with a radius of 9.25 cm.?
____________________________________
Copyright © Casio, Inc.
Activity 8 • High School Activities for the Casio fx-300ES
65
Solutions and Answers for Activity 8
Radius
Circumference
(C = 2 • π • r)
Area
(A = π • r2)
1.
1 unit
2 units
4 units
8 units
16 units
32 units
2π
4π
8π
16π
32π
64π
1π
4π
16π
64π
256π
1024π
F(x) = 2•π•X
Answer in Terms of π
Answer in Decimal Form
X=1
2π
6.2831
X=2
4π
12.566
X=3
6π
18.849
X=4
8π
25.132
X=5
10π
31.415
X=6
12π
37.699
X=7
14π
43.982
X=8
16π
50.265
X=9
18π
56.548
X = 10
20π
62.831
2. Circumference = 14π = 43.982297; Area = 49π = 153.93804
3. Circumference = 1.8π = 5.654866776; Area = 0.81π = 2.544690049
4. Circumference = 16Xπ; Area = 64Xπ
5. Area of Square = 196 in2
Area of Circle = 49π in2
Area of Shaded Region = (196 – 49π) in2 = 42.06195997 in2
6. Since the radius of each circle measures 3.5 inches, we can determine that the
width of the rectangle is the same as the diameter of the circle, which equals 7
inches. The length of the rectangle is equivalent to 5 times the diameter of each
circle, which equals 35 inches. Therefore, the area of the rectangle is
(35 7)=245 in2. The area of each circle is 12.25 π in2. There are five circles in
this rectangle so their combined areas equal 61.25 π in2. To calculate the area of
the shaded region, subtract the area of the circles from the area of the rectangle to
equal 245 in2 – 61.25 π in2, which in decimal form equals 52.57744997 in2.
7. The total circumference is 6π + 11π + 18.5π which equals (71/2)π cm2 or
111.5265392 cm2.
66
High School Activities for the Casio fx-300ES • Activity 8
Copyright © Casio, Inc.
Activity 9
Measuring Polygons
Teaching Notes
Topic Area: Finding Area and Perimeter
NCTM Standards: Number and Operations, Algebra, Geometry, Measurement, Problem
Solving, Reasoning and Proof, Communications, Connections, Representations
Objective
Students will demonstrate the ability to find the area and perimeter of various polygons
and explore the changes on these measurements when a dimension is changed.
Engage
Discuss with students the differences between area and perimeter. Provide examples
where these measurements are needed and if possible, use manipulatives to reinforce
your presentation. Then, ask students to derive a method of determining the perimeter
and area for polygons other than triangles and quadrilaterals.
Explore
1.
2.
Using the calculator, model how to input calculations within the MthIO (Math
Input/Output) format.
Using the calculator, model how to use the TABLE application to provide data for
the perimeter and area when a function is entered.
Explain
Have students explain how the perimeter and area of a polygon change as the values of
a dimension increase or decrease.
Elaborate
Discuss any questions or comments with your students. Provide students with a formula for finding the areas of polygons other than triangles and quadrilaterals and have
them calculate those areas.
Extend
Have students construct 5 different regular polygons all with the same side length and
explore the changes which occur within their areas and perimeters. Have students construct 5 regular polygons of different side lengths and explore the changes that occur
within their areas and perimeters.
Evaluate
Students will be given a series of area and perimeter problems and will provide calculations as well as rationales behind their calculations. Emphasis should be placed on estimation strategies to ensure that their solutions make mathematical sense.
Copyright © Casio, Inc.
Activity 9 • High School Activities for the Casio fx-300ES
67
Calculator Notes for Activity 9
Steps for Solving the Problems:
To Use the MthIO Format:
1.
Press MODE and then 1 for COMP.
2.
Press SHIFT MODE to access the SETUP menu followed by
1 for MthIO (Math Input/Output).
To Enter a Function and Create a Table of Values:
1.
Press MODE.
2.
Press 3 for TABLE.
D
68
3.
Enter the function after f(x)=.
4.
Press =.
Math
High School Activities for the Casio fx-300ES • Activity 9
Copyright © Casio, Inc.
Calculator Notes for Activity 9
5.
6.
7.
Set a Start Value and press =.
D
Math
D
Math
D
Math
Set an End Value and press =.
Set a Step Value and press =.
Copyright © Casio, Inc.
Activity 9 • High School Activities for the Casio fx-300ES
69
Name _____________________________________________ Class ________ Date ________________
Activity 9 • Measuring Polygons
Introduction
By definition, a polygon is a closed figure made up of at least three line segments. With any polygon, we can measures its perimeter and area. The perimeter will measure the distance around the figure while the area will measure the
space inside of the line segments measured in square units.
If we were to take any polygon and separate its sides to place each line segment
in a continuous line, we would find a linear measurement for its perimeter.
However, when we measure a polygon’s area, it would be as if we were placing
square tiles inside the figure’s space and that’s why we express any polygon’s area
as a measure in square units.
While these definitions provide a general understanding of how to determine
the area and perimeter of a polygon, their formulas for performing these calculations are different. You have been learning how to calculate the perimeter and
area of various polygons, but what happens when we change a dimension or
measure within each polygon? Let’s make that connection as we explore the
perimeters and areas of these figures.
Objectives
Demonstrate the ability to find the area and perimeter of various polygons
and explore the changes on these measurements when a dimension is
changed.
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
Procedure
Steps for Solving the Problems:
To Use the MthIO Format:
1.
Press MODE and then 1 for COMP.
2.
Press SHIFT MODE to access the SETUP menu followed by
1 for MthIO (Math Input/Output).
To Enter a Function and Create a Table of Values:
70
1.
Press MODE.
2.
Press 3 for TABLE.
3.
Enter the function after f(x)=.
High School Activities for the Casio fx-300ES • Activity 9
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 9 • Measuring Polygons
4.
Press =.
5.
Set a Start Value and press =.
6.
Set an End Value and press =.
7.
Set a Step Value and press =.
Problems and Questions
1. Complete the table of values for the area of rectangle with a perimeter of 28 units.
a. Designate the width of this rectangle to equal X. Express the length in
terms of X.
_______________________________
b. What does the length need to be in order to maximize the area of this
rectangle?
_______________________________
c. What do you notice about this rectangle when you maximize the area?
_________________________________________________________________________
_________________________________________________________________________
2. Examine this region.
16 cm
9 cm
5 cm
7 cm
a. What is the perimeter of this region?
____________________________________
b. What is the area of this region?
____________________________________
c. Using complete sentences, explain how you derived the perimeter and area
of this region?
_________________________________________________________________________
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 9 • High School Activities for the Casio fx-300ES
71
Name _____________________________________________ Class ________ Date ________________
Activity 9 • Measuring Polygons
d. Draw a new figure doubling each dimension. Since you have doubled the
perimeter of this figure, have you doubled the area? Explain.
_________________________________________________________________________
_________________________________________________________________________
3. Find the perimeter and area of this regular polygon.
8 in
a. What is the perimeter of this figure?
____________________________________
b. What is the area of this figure?
____________________________________
c. Using complete sentences, explain how you calculated the area of this figure.
_________________________________________________________________________
_________________________________________________________________________
4. Find the perimeter and area of this figure polygon.
4 mm
a. What is the perimeter of this figure?
____________________________________
b. What is the area of this figure?
____________________________________
c. Using complete sentences, explain how you calculated the area of this figure.
_________________________________________________________________________
_________________________________________________________________________
72
High School Activities for the Casio fx-300ES • Activity 9
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 9 • Measuring Polygons
5. Determine the area and perimeter of this regular figure.
X cm
a. In terms of X, what is the perimeter of this figure?
_______________________________
b. In terms of X, what is the area of this figure?
_______________________________
c. Complete the following table for the perimeter and area of this figure.
(Set MODE to LineIO)
X=
Perimeter
Area
2
5
8
12
21
(X + 3)
Copyright © Casio, Inc.
Activity 9 • High School Activities for the Casio fx-300ES
73
Solutions and Answers for Activity 9
1. a. 14 – X
b. 7
c. When the length is 7, the width is also 7 making this rectangle a square.
2. a. 50 cm
b. 99 cm2
c. Answers may vary.
d. Answers may vary.
3. a. 40 cm
b. approximately 110.11 cm2
c. Answers may vary
4. a. 48 cm
b. approximately 124.71 cm2
c. Answers may vary
5. a. 8X
b. (1/2)(8X)(0.5X/tan 22.5o)
c.
X=
Perimeter
Area
2
16
19.313
5
40
120.71
8
64
309.01
12
96
695.29
21
168
(X + 3)
74
8X + 24
High School Activities for the Casio fx-300ES • Activity 9
2129.3
(2X2
+ 12X + 18) /
tan 22.5
Copyright © Casio, Inc.
Activity 10
It’s Uncanny!
Teaching Notes
Topic Area: Finding Surface Area and Volume
NCTM Standards: Number and Operations, Algebra, Geometry, Measurement, Problem
Solving, Process Standards, Problem Solving, Reasoning and Proof, Communications,
Connecting, Representations
Objective
Students will demonstrate the ability to find the surface area and volume of a soup can.
Students will have to explore various dimensions of the soup can so that it will be able
to maximize shelf space at a supermarket.
Engage
Show students two different sized soup cans. Describe each of the products and explain
that you bought these items at a local supermarket where they were displayed on a
shelf. Have students work in cooperative groups to calculate the volume and surface
area of each can. Have students determine how many cans could be neatly placed on a
rectangular store shelf that measures 3 feet by 1 foot.
Explore
1.
2.
Using the calculator, model how to calculate the volume and surface area of a right
cylinder in the COMP application.
Using the calculator, model how to replace one dimension of a right cylinder with a
variable and input that function into the TABLE application. This will create a
table of values with a specified range of the dimension indicated by the variable.
Explain
Have students explain how they calculated the volume and surface area of a right cylinder and how they determined the number of cans that can be placed on the store shelf.
Elaborate
Discuss any questions or problems with your students. Then, have students go to the
supermarket or convenience store and count the different brands of soup cans on a
store display. Have students note whether or not these cans are appropriately displayed
on the store shelves and if not, what could they do to display them better?
Extend
1.
2.
Have students design a new soup can. The soup can must contain a graphic label
design for their product and must be accompanied by a sheet stating the volume
and surface area of the can.
Have students go to a local supermarket and sketch the allocated space for all soup
cans. Students must take appropriate measurements and re-design the space to
make it more appealing and more effective for the products displayed.
Evaluate
Students will be given a series of problems and be asked to solve them correctly.
Students will be assessed on how well they communicate their reasoning.
Copyright © Casio, Inc.
Activity 10 • High School Activities for the Casio fx-300ES
75
Calculator Notes for Activity 10
Steps for Solving the Problem:
To Enter a Function and Create a Table of Values:
1.
Press MODE.
2.
Press 3 for TABLE.
3.
Enter the function after f(x)=.
4.
Press =.
5.
6.
76
D
Math
D
Math
D
Math
Set a Start Value and press =.
Set an End Value and press =.
High School Activities for the Casio fx-300ES • Activity 10
Copyright © Casio, Inc.
Calculator Notes for Activity 10
7.
Set a Step Value and press =.
D
Math
Note: When using a formula for volume or surface area, you can only replace one
dimension with a variable. If you decide to change both dimensions (radius and
height) you must perform those calculations in the COMP application.
Copyright © Casio, Inc.
Activity 10 • High School Activities for the Casio fx-300ES
77
Name _____________________________________________ Class ________ Date ________________
Activity 10 • It’s Uncanny!
Introduction
Containers come in various shapes and sizes but their purpose is very simple.
Containers are designed to hold things whether they are solid or liquid. Take an
ordinary soup can that you might have in your kitchen or could find at a local
supermarket. Soup cans come in different sizes but they are cylindrical in shape
and they hold various amounts of soup. However, when you go to the store, they
must be neatly and appropriately displayed on the shelf so customers can purchase them. Companies who distribute the product pay for space on the supermarket shelf to display their items and be purchased by consumer. And because
people have different tastes, that’s why there are so many different kinds of soup.
Imagine the planning that must be involved in simply arranging all of those different kinds of soup cans!
Examine the soup cans within your group. Measure its height and radius.
Once you have those measurements, you can calculate the volume and surface
area of the soup can. The formulas are:
Volume = π • r2h
Surface Area = 2π • rh + 2π • r2
Obviously, the larger the can, the more soup it can hold. However, why do
think the soup can must have those measurements? Do you think it makes any
difference if the can was designed differently?
Objectives
Demonstrate the ability to find the surface area and volume of a soup can. Students
will have to explore various dimensions of the soup can so that it will be able to maximize shelf space at a supermarket.
Materials Needed
78
•
The Casio fx-300ES calculator
•
Pencil and paper
•
Compass
•
Soup cans
•
Measuring Tape, Ruler
High School Activities for the Casio fx-300ES • Activity 10
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 10 • It’s Uncanny!
Procedure
Steps for Solving the Problem:
To Enter a Function and Create a Table of Values:
1.
Press MODE.
2.
Press 3 for TABLE.
3.
Enter the function after f(x)=.
4.
Press =.
5.
Set a Start Value and press =.
6.
Set an End Value and press =.
7.
Set a Step Value and press =.
Note: When using a formula for volume or surface area, you can only replace one
dimension with a variable. If you decide to change both dimensions (radius and
height) you must perform those calculations in the COMP application.
Problems and Questions
Directions: Solve the following problems and express all answers in terms of π and
where necessary, rounded to the nearest hundredth. Use the π key on your calculator
for all calculations.
1. Calculate the volume and surface area of a soup can that measures 5 inches in
height and 3 inches in diameter.
Volume:
____________________
Surface Area:
____________________
2. Which soup can has the larger surface area?
Soup Can A:
Height = 4.5 inches; Diameter = 2 inches
Soup Can B:
Height = 6 inches; Diameter = 1.5 inches
____________________________________________________________________________
3. Refer to question 2, find the volume of each soup can.
Soup Can A:
____________________
Soup Can B:
____________________
Copyright © Casio, Inc.
Activity 10 • High School Activities for the Casio fx-300ES
79
Name _____________________________________________ Class ________ Date ________________
Activity 10 • It’s Uncanny!
4. Given a soup can that measures 8 inches in height and 4 inches in diameter, find
the dimensions of a new soup can that has the same volume and record those
dimensions.
____________________________________________________________________________
Using complete sentences, explain how you were able to find the dimensions of a
soup can that has the same volume.
____________________________________________________________________________
____________________________________________________________________________
5. Mom’s Homemade Chicken Soup comes in a can that measures 6 inches in height
and 4 inches in diameter. How much soup can the can contain? What is the
surface area of this can?
____________________________________________________________________________
____________________________________________________________________________
6. You have been hired by Mom’s Homemade Chicken Soup to design a new
container for their product. The product has a good price point and the
company does not want to increase the cost of the product. Provide two different
sets of measurements that will yield the same volume but different surface areas.
____________________________________________________________________________
Explain how you were able to determine these measurements.
____________________________________________________________________________
____________________________________________________________________________
7. A soup can has a height of 5 inches. Using the TABLE application on your
calculator, set the radius to equal X with a range from 2 to 5 and a step value of
0.5 and record the volume and surface area as displayed in the table.
Radius = X
Volume
Surface Area
2.0
2.5
3.0
3.5
4.0
4.5
5.0
80
High School Activities for the Casio fx-300ES • Activity 10
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 10 • It’s Uncanny!
8. Using the COMP application of your calculator, record the volume and surface
area of the following cylinders as one measure increases while the other
decreases. Express all answers rounded to the nearest tenth.
Measurements
Volume
Surface Area
R = 1; H = 5
R = 2; H = 4
R = 3; H = 3
R = 4; H = 2
R = 5; H = 1
What measurements from this table do you believe will create the best soup
can and why?
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Copyright © Casio, Inc.
Activity 10 • High School Activities for the Casio fx-300ES
81
Solutions and Answers for Activity 10
1. Volume = (45/4)π in3; 35.34 in3
Surface Area = (39/2)π in2; 61.26 in2
2. Surface Area of Soup Can A = 11π in2; 34.56 in2
Surface Area of Soup Can B = (81/8)π in2; 31.81 in2
Soup Can A has the largest
surface area.
3. Volume of Soup Can A = (9/2)π in3; 14.14 in3
Volume of Soup Can B = (27/8)π in3; 10.60 in3
4. Answers may vary. The volume must equal 32π in3. One possible solution to
this problem is a right cylinder with a radius of 4 inches and a height of 2 inches.
5. A can of Mom’s Homemade Chicken Soup has a volume of 24π3 (75.40in3) and a
surface area of 32π in2 (100.53 in2).
6. Two different sets of measurements that will have same volume of 24π3 and
different surface area are:
a. Radius = 1, Height = 24; SA = 50π in2; 157.08 in2
b. Radius = 4, Height = 1.5; SA = 44π in2; 138.23 in2
7.
8.
Radius = X
Volume
Surface Area
2.0
62.831 in3
87.964 in2
2.5
98.174 in3
117.8 in2
3.0
141.37 in3
150.79 in2
3.5
192.42 in3
186.92 in2
4.0
251.32 in3
226.19 in2
4.5
318.08 in3
268.60 in2
5.0
392.69 in3
314.15 in2
Measurements
Volume
Surface Area
R = 1; H = 5
15.71 u3
37.7 u2
R = 2; H = 4
50.27 u3
75.4 u2
R = 3; H = 3
84.82 u3
113.1 u2
R = 4; H = 2
100.53 u3
150.8 u2
R = 5; H = 1
78.54 u3
188.5 u2
Answer may vary regarding the best dimensions for the soup can.
82
High School Activities for the Casio fx-300ES • Activity 10
Copyright © Casio, Inc.
Activity 11
Small Town, U.S.A.
Teaching Notes
Topic Area: Exponential Functions
NCTM Standards: Number and Operations, Algebra, Data Analysis and Probability,
Problem Solving, Communications, Connecting, Representations
Objective
Students will demonstrate the ability to project the population for a town experiencing
an annual rate of growth. Students will demonstrate the ability to explore exponential
growth and decay functions.
Engage
Read the following scenario to the students. "At the present time, the population of
Small Town U.S.A. is 8,950 and the town is experiencing an annual population growth
of 7.25% each year. People are attracted to this town because of its affordable housing,
phenomenal business opportunities, and excellent school system."
Discuss with students the residual factors this town might experience such as new housing, demands on the school system, recreational and business opportunities, increased
demands for medical professionals, etc…
Have students work in small groups to discuss what other types of planning, projecting,
and preparation must be considered with the anticipated population growth? Once
each group has generated these ideas, have them give priority to these suggestions and
present this list to the class.
Explore
1.
2.
Using the calculator, model how to use the TABLE application to input a function,
set a starting, ending, and step value, and create a table of values.
Using the calculator, model how to seed a number or expression and generate
information pertaining to a specific problem.
Explain
Have students explain the data generated by an exponential growth function and interpret the results. Have students explain how to determine the growth factor for an exponential growth function.
Elaborate
Discuss any questions or comments with your students. Obtain a copy of your school’s
population from the past 5 years and examine the increases or decreases. Dialogue with
your students to determine an estimated rate of growth or decay within the data.
Extend
1.
2.
Have students do an extensive analysis of population growth for a major city.
Students must present a set of data for the past 15 years and derive a rate of
population growth or decay. Then, students must create a two-minute presentation
detailing the results and the impact on the city’s business and industry.
Have students research compound interest. Have students calculate a $5,000
principal invested at 3% compounded annually, semi-annually, quarterly, monthly,
Copyright © Casio, Inc.
Activity 11 • High School Activities for the Casio fx-300ES
83
Activity 11:
Small Town, U.S.A (continued)
3.
Teaching Notes
and daily over a period of 20 years. Students can use the TABLE application the
generate data for these 5 different scenarios. Have students discover which method
of compounding is best.
Have students examine the change in population of Small Town, U.S.A. when the
growth rate is 7.5%, 8%, 8.5% and 14.5% over a period of 10 years. Have students
identify at which point the population will double.
Evaluate
Students will be given a series of problems to solve exploring exponential growth and
decay. Students will be asked to communicate their results through verbal and written
communication.
84
High School Activities for the Casio fx-300ES • Activity 11
Copyright © Casio, Inc.
Calculator Notes for Activity 11
Steps for Solving the Problems:
To Enter a Function and Create a Table of Values:
1.
Press MODE.
2.
Press 3 for TABLE.
3.
Enter the function after f(x)=.
4.
Press =.
5.
Set a Start Value and press =.
6.
Set an End Value and press =.
7.
Set a Step Value and press =.
To Seed a Number or Expression into the Calculator:
1.
Press MODE followed by 1 for the COMP application.
2.
Press SHIFT SETUP followed by 2 for the LineIO format.
3.
To seed a number, input a starting amount into calculator and press =.
4.
Press an operation sign followed by the number you want to repeatedly add,
subtract, multiply of divide by.
5.
Press =.
Copyright © Casio, Inc.
Activity 11 • High School Activities for the Casio fx-300ES
85
Calculator Notes for Activity 11
6.
Each time you press = , you will generate the next number in that sequence.
For example, start with the number 9 and generate the first 10 numbers in a
pattern that adds 7 each time. (Answers: 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, 79)
86
D
Math
D
Math
D
Math
High School Activities for the Casio fx-300ES • Activity 11
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 11 • Small Town, U.S.A.
Introduction
The population of Small Town U.S.A. is currently 8,950 and the town is experiencing an annual population growth of 7.25% each year. People are attracted to
this town because of its affordable housing, many business opportunities, and an
excellent school system. While the projected growth is wonderful for the town,
you as the town mayor must ensure that it will be able to handle such growth in
a short period of time. In your opinion, how can the town prepare for such growth
and opportunity? What are the immediate impacts of such growth? What types
of business should the town have in order to increase its appeal to the public?
In order to plan accordingly, you consult with the town’s financial advisor and
invest $250,000 in an account, which generates interest at 4.35% compounded
annually. This money is designated for special projects within the town. It is
anticipated that you will need this money in 8 years.
What other types of planning, projecting, and preparation must you consider
with the anticipated population growth? Discuss with other members of your
group and compile a list of things to consider. Once you have generated such a
list, give priority to these suggestions and present this list to the class.
Objectives
Demonstrate the ability to project the population for a town experiencing an annual
rate of growth. Students will demonstrate the ability to explore exponential growth
and decay functions.
Materials Needed
•
The Casio fx-300ES calculator
•
Pencil and paper
Procedure
Steps for Solving the Problems:
To Enter a Function and Create a Table of Values:
1.
Press MODE.
2.
Press 3 for TABLE.
3.
Enter the function after f(x)=.
4.
Press =.
5.
Set a Start Value and press =.
6.
Set an End Value and press =.
7.
Set a Step Value and press =.
Copyright © Casio, Inc.
Activity 11 • High School Activities for the Casio fx-300ES
87
Name _____________________________________________ Class ________ Date ________________
Activity 11 • Small Town, U.S.A.
To Seed a Number or Expression into the Calculator:
1.
Press MODE followed by 1 for the COMP application.
2.
Press SHIFT SETUP followed by 2 for the LineIO format.
3.
To seed a number, input a starting amount into calculator and press =.
4.
Press an operation sign followed by the number you want to repeatedly add,
subtract, multiply of divide by.
5.
Press =.
6.
Each time you press = , you will generate the next number in that sequence.
For example, start with the number 9 and generate the first 10 numbers in a
pattern that adds 7 each time. (Answers: 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, 79)
Problems and Questions
1. Generate a table of values for Small Town, U.S.A. that shows the projected
population growth over the next 5 years. Write a function and complete the table.
__________________________________
Year
Population
1
2
3
4
5
2. Using an exponential growth formula of f(x) = a • bx where a = starting amount,
b = growth factor, and x = number of times the compounding is taken, what would
be the formula that would model a town whose population is 158,900 and is
experiencing a growth rate of 5.4% annually?
__________________________________
3. Project the population for a town with a starting population of 49,598 that is
experiencing an annual decay of 3.7%. Input a function into the TABLE
application and complete the population for the years indicated within the
table.
88
High School Activities for the Casio fx-300ES • Activity 11
Copyright © Casio, Inc.
Name _____________________________________________ Class ________ Date ________________
Activity 11 • Small Town, U.S.A.
Year
Population
1
3
5
10
25
a. Write the function to determine the projected population.
__________________________________
b. Will the population of this town ever reach 0? Using complete sentences,
explain why or why not.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
4. You have invested $250,000 of the town’s funds in an account that gets an
estimated 4.35% interest compounded monthly. Complete the table to project
how much money will be in the account at the end of 8 years (96 months)
Time
Amount
6 months
2 years
40 months
5 years
70 months
7 years
8 years
5. With the projected population increase in Small Town, U.S.A., property values
will also increase. It is estimated that property values will increase 10.9% for
each of the next five years. If a home is currently valued at $100,000, complete a
table to show the property values over the next 5 years.
Copyright © Casio, Inc.
Activity 11 • High School Activities for the Casio fx-300ES
89
Name _____________________________________________ Class ________ Date ________________
Activity 11 • Small Town, U.S.A.
Year
Est. Property Value
1
2
3
4
5
a. How many years will it take the property value to double at the current rate
of growth?
__________________________________
b. How many years will it take the property value to triple at the current rate
of growth?
__________________________________
c. If a family’s home is currently valued at $250,000, will it take the same amount
of time to double its value at the current growth rate of 10.9%?
Explain why or why not.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
90
High School Activities for the Casio fx-300ES • Activity 11
Copyright © Casio, Inc.
Solutions and Answers for Activity 11
1.
Year
Population
F(x) = 8750 • 1.0725X
1
9384
2
10064
3
10794
4
11577
5
12416
2. f(x) = 158,900 • 1.054X
3.
4.
Copyright © Casio, Inc.
Year
Population
1
47762
3
44293
5
41076
10
34019
25
19325
Time
Amount
6 months
$255,487.02
2 years
$272,681.27
40 months
$288,934.13
5 years
$310,619.18
70 months
$322,064.59
7 years
$338,800.13
8 years
$353,835.35
3a. f(x) = 49598 • 0.963X
b. In theory, the town’s
population will never equal
0, though it will approach 0.
Activity 11 • High School Activities for the Casio fx-300ES
91
Solutions and Answers for Activity 11
5.
Year
Est. Property Value
1
$110,900
2
$122,988
3
$136,393
4
$151,260
5
$167,748
a. 7 years
b. 11 years
c. Yes, it will still take the same amount of years to double the property value
because while the starting amount is different, the rate is the same and it will
exponentially double in its 7th year.
92
High School Activities for the Casio fx-300ES • Activity 11
Copyright © Casio, Inc.