Harcourt Mega Math
Welcome to Harcourt Mega Math: Fraction Action
In Fraction Action, Penny has traveled to an arid land where the action is heating up.
While viewing a volcano, exploring an underground mine, or prospecting in a canyon,
students extend their understanding of fractions, locating numbers on a number line, and
probability. Fraction Action is the third Harcourt Mega Math CD in a series for Grade 3,
Grade 4, Grade 5, and Grade 6 students. It can be used alone, alongside other Harcourt
print and electronic products for these grade levels, or in conjunction with its companion
programs: Harcourt Mega Math The Number Games and Harcourt Mega Math Ice
Station Exploration. Together, the three programs cover the major topics in the third,
fourth, fifth, and sixth grade math curricula.
Figure 89: Fraction Action Welcome Screen
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In Fraction Action, Penny invites students to explore three desert areas, each representing
one of three themes: fractions, a number line, and probability. Each theme, or module,
affords students the opportunity to extend their knowledge from earlier grades; and a
variety of interactivities and manipulatives support and encourage success. Within each
module, students answer questions linked to specific skill levels, and advance to more
challenging levels as they succeed. By using Grow Slides they can monitor the progress
they make, identify the skill levels for the entire module, or navigate to different levels
within the entire module.
A proud eagle, a mining lizard, and an improbable chameleon lead the way in challenging
students to explore and learn. Colorful animations and rewarding interactivities help to
motivate students to explore further and to learn more comprehensively. For example, in
the module Number Line Mine, students answer questions about place value, rounding,
and comparisons to win treasures and their corresponding value. As students answer
questions correctly, they amass a treasure trove and increase their score. The game
motivates students to play on – to better their score and to seek new treasures of
knowledge. In Fraction Action, students learn that math is indeed rewarding.
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What’s Inside Harcourt Mega Math: Fraction Action
1.
At the Main Menu, click
2.
Then choose from three modules by clicking a canyon feature (Figure 80).
3.
From any activity, click
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to return to the Main Menu.
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Fraction Flare Up Overview
The lava and ash from an erupting volcano produce fraction bars and circles to serve as
colorful models in this active module. In Fraction Flare Up, students represent and
compare proper fractions and improper fractions equal to 1. They also use the fraction
models to represent basic arithmetic operations, and to relate simple decimal numbers to
their fractional counterparts.
Figure 91: Opening Fraction Flare Up
Learning Opportunities
The Meaning of Fractions
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Explore and represent parts of a whole and parts of a group
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Represent the whole as the improper fraction
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Represent equivalent fractions to twelfths
Represent and express fractions in simplest form
Represent and compare like and unlike fractions
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Operations with Fractions
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Represent the sum of like and unlike fractions using fraction bars and fractional
notation
Represent the difference between like and unlike fractions using fraction bars and
fractional notation
Multiply a fraction by a fraction and represent it using fractional notation
Divide fractions using fraction bars and represent them using fractional notation
Decimals
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Explore tenths and hundredths
Find equivalent decimals
Relate decimals and fractions
In Fraction Flare Up, students explore the meaning of fractions as representing equal
parts of shapes and groups. They shade the interiors of fraction circles and fraction bars
to show parts of wholes, and click objects or groups to show parts of groups.
Simple fraction bar manipulatives are introduced to help students compare fractions,
identify equivalent fractions, and simplify fractions. For example, to compare and ,
students drag 2 one-third bars and 3 one-fourth bars and align them beneath a unit bar. By
comparing the lengths of the bars, they can see that is less than . To find fractional
equivalents, students manipulate fraction bars until they match the length of the parts in
the two bars. Students work in a similar way to find the simplest form of a given fraction.
Addition and subtraction of like and unlike fractions builds on the skills of finding
equivalent fractions. Multiplying a fraction by a fraction is interpreted geometrically, as
students represent each factor by shading equal parts of a given square first vertically and
then horizontally. To divide by a fraction, students use fraction bars to determine how
many fractional parts are contained in a given quantity. With each operation, students
complete the corresponding number sentences that represent the models.
Geometric models are also used to introduce the meaning of decimals. Within square
grids divided into tenths or hundredths, students shade unit squares to show a given
decimal number. Conversely, they enter a decimal and its fractional equivalent for a
given shaded region.
In Fraction Flare Up, audio and animations along with manipulative fraction bars enrich
the interactive nature of the problems posed, and the immediate evaluation of answers
provide students with encouraging feedback and additional guidance where needed.
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Using Fraction Bars
Choose an answer by clicking and dragging a bar to show a fraction.
1.
Follow the directions given. For example, “Use these bars to show a fraction
equivalent to one half.”
2.
Click and drag fraction bars to the answer area to make an equivalent fraction.
3.
Then click
.
Figure 92: Using the Fraction Bar
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Using the Spinner – Numbers
Choose an answer by clicking
to show a fraction or decimal.
¾
Click
to increase the value of the number by one.
¾
Click
to decrease the value of the number by one.
1.
Follow the directions given. For example, “Show the denominator of this fraction.”
2.
Click
3.
Then click
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to show the denominator of the fraction.
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Using the Spinner – Fraction and Decimal Models
Choose an answer by clicking
to shade parts of a fraction or decimal model.
¾
Click
to shade a part.
¾
Click
to remove shading from a part.
1.
Listen to the directions, such as “Show this fraction.”
2.
Click
3.
Then click
to show the fraction.
.
Figure 94: Using the Fraction Action Spinner
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Number Line Mine Overview
Deep inside a mine an assortment of valuable treasures lies buried in the earth. Collecting
these treasures and accumulating their dollar values provides the motivation for solving
the problems in Number Line Mine. The module presents students with a number line
model on which they locate, round, and compare whole numbers, mixed numbers,
fractions, and decimals; and complete operations of addition, subtraction, and
multiplication.
Figure 95: Opening Number Line Mine
Learning Opportunities
Whole Numbers
ƒ Identify place value
ƒ Compare whole numbers using <. =, or > symbols
ƒ Round to the nearest ten, hundred, or thousand
ƒ Complete a multiplication sentence by finding a missing factor
Fractions and Mixed Numbers
ƒ Locate fractions and mixed numbers on the number line
ƒ Compare like and unlike fractions and mixed numbers
ƒ Round fractions and mixed numbers to the nearest whole number or benchmark
number
ƒ Multiply fractions by whole numbers
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Decimals (tenths, hundredths, thousandths)
ƒ Locate decimals on the number line
ƒ Compare decimals and decimals greater than one
ƒ Round decimals
Integers and Rational Numbers
ƒ Locate positive and negative numbers on the number line
ƒ Compare positive and negative numbers
ƒ Locate rational numbers as fractions and decimals
ƒ Add and subtract integers
ƒ Multiply integers
Collecting treasures and accumulating points as dollar values are the extrinsic motivators
in Number Line Mine. Successfully solving problems about numbers using the model of
a number line is the intrinsic motivator. Interactivities within this module are of two
types: those involving hidden treasures and those involving visible treasures.
When treasures are hidden, students first see a problem whose correct answer is the
location of a hidden treasure. To answer the question and collect the treasure, students
drag the mining cart to a specified location. For example, if asked to round a mixed
number to the nearest whole number, students drag the cart to the appropriate number on
the number line. If their answer is correct, the treasure is revealed and loaded into the
mining cart. If the answer is not correct, the treasure remains hidden and the student tries
again.
Visible treasures lie beneath specific numbers within a given interval along the number
line. Treasures are arranged randomly below the number line, and more than one treasure
can be located below the same number. Selecting a treasure highlights the corresponding
number above it on the number line, and the number becomes the focus of a problem to
be solved. For example, in the problem set that deals with multiplication facts, if students
click the treasure below 42, they see an incomplete number sentence, such as __ x 7 = 42.
If they enter the correct missing factor, the computer animates the mining cart to that
location and the treasure is collected. If the question is not answered correctly, the cart
does not move and the student tries again. Similarly, with the mining cart located at a
number such as 0.55, students might click a treasure below 0.68. They then see the
incomplete sentence, 0.55 __ 0.68. To collect the treasure at 0.68, students drag the
correct inequality symbol into place.
Number line mine offers students the chance to use a number line to explore whole
number concepts, fractions and mixed numbers, decimals, rational numbers, and integers
in an engaging and supportive environment. Answers are immediately evaluated,
providing students with appropriate feedback and additional instruction where needed.
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Playing the Game
Each treasure represents a question and the number of questions varies within each skill
level. The total possible number of points, expressed as dollar values that can be scored
within the skill is displayed at the top of the screen along with the current score.
Figure 96: Inside the Number Line Mine
If the student answers the question correctly on the first attempt, the corresponding dollar
value of the treasure will appear in the points display area at the top of the screen. After
each incorrect attempt, the number of points possible will be half that of the previous
attempt. For example, if a treasure is worth $200 for a correct answer on the first attempt,
it will be worth $100 if answered correctly on the second attempt. On the third attempt it
will be worth $50, and on the fourth attempt it will be worth $25.
After completing a skill level, a dialogue box will appear giving the final score and
offering the option to repeat the round or continue to the next skill level.
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Playing a Skill Level –Visible Treasures
A number of visible treasures appear beneath the ground. When the mouse rolls over a
treasure its corresponding value in dollars appears beside it.
1.
Click on one of the visible treasures to start the skill.
2.
A number sentence or inequality will appear that relates to the number on the number
line under which the treasure sits (Figure 97).
3.
Complete the number sentence or inequality in order to collect the treasure and
accumulate points in the form of dollar values.
Figure 97: Click a Visible Treasure to See a Question
1.
When the question is answered correctly, the cart will move to the location of the
treasure and the treasure will be pulled up into the cart. The corresponding dollar
value of the treasure will then appear in the points display area at the top of the
screen.
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2.
If the user fails to answer the question correctly on their final attempt, the treasure
will disappear.
Continue to answer questions by clicking treasures until the skill level has been
completed.
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Figure 98: A Correct Answer—Visible Treasures
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Playing a Skill Level—Hidden Treasures
In these skill levels, drag the cart to the correct number on the number line to show the
answer. All hidden treasures have the same value—$200.
1.
Listen to determine the correct answer. For example, “There is a treasure at 2,000
more than 85,000.”
2.
If the answer is correct, the hidden treasure will be revealed and pulled up into the
cart. The corresponding dollar value of the treasure will then appear in the points
display area at the top of the screen.
¾
If the question is not answered correctly on the final attempt, the treasure will not
be revealed.
3. Continue answering questions until the skill level is completed.
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Figure 99: Answering a Hidden Treasures Question
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Last Chance Canyon Overview
Here’s a chance to explore the world of probability - Last Chance Canyon! A colorful
chameleon needs some help in charging up his generator, and students provide assistance
by answering a series of questions about probability. The module focuses on topics such
as certain and impossible events; likely and unlikely outcomes; probability as a fraction,
decimal or percent; and compound events. Students also work with tally or frequency
tables and use them to determine experimental probabilities and predict future outcomes.
Figure 100: Opening Last Chance Canyon
Learning Opportunities
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Predict the likelihood of two more outcomes, including certain and impossible
events
Use tally or frequency tables to predict events
Express the probability of an event as a fraction between 0 and 1
Compare the probabilities of events using fractions, decimals, or percents
Use the Fundamental Counting Principle to determine the probability of
compound events
Use the results of an experiment to express and predict the probability of an event
Express the theoretical probability of two independent events
Express the theoretical probability of two dependent events
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In Last Chance Canyon, students solve problems about experimental and theoretical
probability. In early skill levels, students see a spinner divided into shaded regions and
determine which outcomes might be certain or impossible, likely, or unlikely. They also
drag different-colored beads into a bag so that the chance of pulling either color bead
produces outcomes that are equally likely.
In this module, students also begin to quantify probability. They examine various
spinners to represent the probability of a likely outcome as a fraction between 0 and 1,
and the probability of impossible and certain events as 0 or 1, respectively.
The computer provides a unique opportunity for students to simulate probability
experiments. For example, given a spinner, students first predict the probability of a
given event, and then spin the pointer of the spinner 10 times. The computer displays the
results of the spins in a frequency table, and students compare the experimental results to
the earlier prediction. They then simulate spinning the pointer 100 times, and compare
the two experimental probabilities and the theoretical probability determined at the
outset.
Students also use experimental results to identify the model used to generate a set of
outcomes displayed in a frequency table. Similarly, given the frequency data of about 20
spins, students express the experimental probability of an outcome and use that value to
predict the number of outcomes in a second trial.
In more advanced problems sets, students use probability notation and the Fundamental
Counting Principle to calculate and compare probabilities. They also complete tree
diagrams by dragging labels into place to show all possible outcomes in an experiment.
Finally, students calculate the probability of two independent or dependent events using
the corresponding formula for each.
All the problem sets in Last Chance Canyon offer students engaging and supportive
interactivities. Answers are immediately evaluated, providing students with appropriate
feedback and additional instruction where needed. Audio and animations, along with onscreen models and representations, provide students with a rich and interactive learning
environment in which to explore ideas in theoretical and experimental probability.
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Conducting a Probability Experiment
Conduct a probability experiment by clicking to spin a pointer.
1.
Follow the directions given. For example, “Click the button to see the results of
spinning the pointer ten times.”
2.
Click
3.
Then click
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Grow Slide Levels for Fraction Action
Each of the three learning activities in Fraction Action has a Grow Slide with progressive
difficulty levels.
Fraction Flare Up
Last Chance Canyon
A. Unit Fractions
B. Parts of a Whole
C. Parts of a Group
D. Equivalent Fractions
E. Simplest Form
F. Compare Fractions Using <, >, or =
G. Add Like Fractions
H. Subtract Like Fractions
I. Add Unlike Fractions
J. Subtract Unlike Fractions
K. Add and Subtract Unlike Fractions
L. Tenths and Hundredths
M. Equivalent Decimals
N. Relate Fractions and Decimals
O. Multiply a Fraction by a Fraction
P. Divide Fractions
Q. Review
A. Certain, Impossible, Likely, Unlikely Outcomes
B. Most Likely, Least Likely, Equally Likely
C. Possible Outcomes for a Single Event
D. Predict Probability
E. Predict Future Events
F. Probability as a Fraction
G. Probability as a Fraction-Advanced
H. Theoretical Probability
I. Experimental Probability
J. Predict Probability - Advanced
K. Compare Probability
L. Express Probability as Fractions, Decimals, Percents
M. Compound Events
N. Probability of Independent Events
O. Probability of Dependent Events
Number Line Mine
A. Place Value: Tens, Hundreds, Thousands
B. Compare Whole Numbers Using <, >, or =
C. Round Whole Numbers to 10s, 100s and 1,000s
D. Multiplication Facts
E. Locate Equivalent Fractions
F. Locate Like Mixed Numbers
G. Locate Unlike Fractions
H. Locate Unlike Mixed Numbers
I. Compare Like and Unlike Fractions
J. Compare Like and Unlike Mixed Numbers
K. Round Fractions and Mixed Numbers
L. Multiply a Fraction by a Whole Number
M. Locate Decimals
N. Relate Fractions and Decimals
O. Locate Decimals Greater Than 1
P. Compare Decimals
Q. Compare Decimals Greater Than 1
R. Round Decimals
S. Locate Positive and Negative Numbers
T. Compare Positive and Negative Numbers
U. Locate Rational Numbers as Fractions
V. Locate Rational Numbers as Decimals
W. Add and Subtract Integers
X. Multiply Integers
Y. Review
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