Author | McGraw-Hill Education | |

Isbn | 9780078604669 | |

File size | 15.1MB | |

Year | 2005 | |

Pages | 381 | |

Language | English | |

File format | ||

Category | mathematics |

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Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of
America. Except as permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or retrieval system,
without prior permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240
ISBN: 0-07-860468-0
1 2 3 4 5 6 111/058 08 07 06 05 04
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TABLE OF CONTENTS
What Does the Data Say?
. . . . . . . . . .2
Graphs and Averages
➤ PHASE ONE Measures of Central Tendency
Lesson 1
Class Survey . . . . . . . . . . . . . . . . . . . . . . . . . .6
Lesson 2
Name Exchange . . . . . . . . . . . . . . . . . . . . . . .8
Lesson 3
TV Shows . . . . . . . . . . . . . . . . . . . . . . . . . . .10
➤ PHASE TWO Representing and Analyzing Data
Lesson 4
Animal Comparisons . . . . . . . . . . . . . . . . . . .14
Lesson 5
Double Data . . . . . . . . . . . . . . . . . . . . . . . . .16
Lesson 6
Across the Ages . . . . . . . . . . . . . . . . . . . . . .18
➤ PHASE THREE Progress over Time
Lesson 7
Are You Improving? . . . . . . . . . . . . . . . . . . . .22
Lesson 8
How Close Can You Get? . . . . . . . . . . . . . . .24
Lesson 9
Stories and Graphs . . . . . . . . . . . . . . . . . . . .26
➤ PHASE FOUR Probability and Sampling
Lesson 10 What Are the Chances? . . . . . . . . . . . . . . . .30
Lesson 11 Changing the Chances . . . . . . . . . . . . . . . . .32
Lesson 12 Which Bag is Which? . . . . . . . . . . . . . . . . . .34
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
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The Language of Numbers
. . . . . . . .48
Inventing and Comparing
Number Systems
➤ PHASE ONE Mystery Device
Lesson 1
Inventing a Mystery Device System . . . . . . . .52
Lesson 2
Comparing Mystery Device Systems . . . . . . .54
Lesson 3
Number Words in Many Languages . . . . . . . .56
Lesson 4
Examining Alisha’s System . . . . . . . . . . . . . . .58
➤ PHASE TWO Chinese Abacus
Lesson 5
Exploring the Chinese Abacus . . . . . . . . . . . .62
Lesson 6
How Close Can You Get? . . . . . . . . . . . . . . .64
Lesson 7
Additive Systems . . . . . . . . . . . . . . . . . . . . . .66
Lesson 8
The MD System . . . . . . . . . . . . . . . . . . . . . .68
➤ PHASE THREE Number Power
Lesson 9
Stacks and Flats . . . . . . . . . . . . . . . . . . . . . . .72
Lesson 10 The Power Up Game . . . . . . . . . . . . . . . . . .74
Lesson 11 Efficient Number Systems . . . . . . . . . . . . . . .76
Lesson 12 A New Number System . . . . . . . . . . . . . . . .78
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80
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From Wholes to Parts . . . . . . . . . . . . .92
Operating with Factors, Multiples,
and Fractions
➤ PHASE ONE The Whole of It
Lesson 1
Shapes and Factors . . . . . . . . . . . . . . . . . . . .96
Lesson 2
The Great Factor Hunt . . . . . . . . . . . . . . . . .98
Lesson 3
Multiple Approaches . . . . . . . . . . . . . . . . . .100
Lesson 4
First Things First . . . . . . . . . . . . . . . . . . . . .102
Lesson 5
Putting It All Together . . . . . . . . . . . . . . . . .104
➤ PHASE TWO Between the Whole Numbers
Lesson 6
Designer Fractions . . . . . . . . . . . . . . . . . . .108
Lesson 7
Area Models and Equivalent Fractions . . . .110
Lesson 8
Fraction Lineup . . . . . . . . . . . . . . . . . . . . . .112
Lesson 9
Focus on Denominators . . . . . . . . . . . . . . .114
➤ PHASE THREE Adding Parts and Taking
Them Away
Lesson 10 Sums and Differences on the Line . . . . . . . .118
Lesson 11 Numbers Only . . . . . . . . . . . . . . . . . . . . . .120
Lesson 12 Not Proper but Still Okay . . . . . . . . . . . . .122
Lesson 13 Sorting Out Subtraction . . . . . . . . . . . . . . .124
Lesson 14 Calc and the Numbers . . . . . . . . . . . . . . . .126
➤ PHASE FOUR Fractions in Groups
Lesson 15 Picturing Fraction Multiplication . . . . . . . . .130
Lesson 16 Fractions of Fractions . . . . . . . . . . . . . . . . .132
Lesson 17 Estimation and Mixed Numbers . . . . . . . . .134
Lesson 18 Fraction Groups within Fractions . . . . . . . .136
Lesson 19 Understanding Fraction Division . . . . . . . . .138
Lesson 20 Multiplication vs. Division . . . . . . . . . . . . . .140
➤
➤
➤
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142
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Designing Spaces . . . . . . . . . . . . . . . . .162
Visualizing, Planning, and Building
➤ PHASE ONE Visualizing and Representing
Cube Structures
Lesson 1
Planning and Building a Modular House . . .166
Lesson 2
Seeing Around the Corners . . . . . . . . . . . .168
Lesson 3
Seeing All Possibilities . . . . . . . . . . . . . . . . .170
Lesson 4
Picture This . . . . . . . . . . . . . . . . . . . . . . . . .172
➤ PHASE TWO Functions and Properties of Shapes
Lesson 5
String Shapes . . . . . . . . . . . . . . . . . . . . . . .176
Lesson 6
Polygon Paths . . . . . . . . . . . . . . . . . . . . . . .178
Lesson 7
Shaping Up . . . . . . . . . . . . . . . . . . . . . . . . .180
Lesson 8
Assembling the Pieces . . . . . . . . . . . . . . . . .182
➤ PHASE THREE Visualizing and Representing
Polyhedrons
Lesson 9
Beyond Boxes . . . . . . . . . . . . . . . . . . . . . . .186
Lesson 10 Drawing Tricks . . . . . . . . . . . . . . . . . . . . . .188
Lesson 11 Mystery Structures . . . . . . . . . . . . . . . . . . .190
Lesson 12 Putting the Pieces Together . . . . . . . . . . . . .192
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194
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Beside the Point . . . . . . . . . . . . . . . . . .206
Operating with Decimals, Percents,
and Integers
➤ PHASE ONE Decimals
Lesson 1
The Fraction-Decimal Connection . . . . . . .210
Lesson 2
What’s the Point? . . . . . . . . . . . . . . . . . . . .212
Lesson 3
Put Them in Order . . . . . . . . . . . . . . . . . . .214
Lesson 4
Get It Close Enough . . . . . . . . . . . . . . . . . .216
➤ PHASE TWO Computing with Decimals
Lesson 5
Place the Point . . . . . . . . . . . . . . . . . . . . . .220
Lesson 6
More to the Point . . . . . . . . . . . . . . . . . . . .222
Lesson 7
Decimal Pinpoint . . . . . . . . . . . . . . . . . . . .224
Lesson 8
Patterns and Predictions . . . . . . . . . . . . . . .226
Lesson 9
It Keeps Going and Going . . . . . . . . . . . . . .228
➤ PHASE THREE Percents
Lesson 10 Moving to Percents . . . . . . . . . . . . . . . . . . .232
Lesson 11 Working with Common Percents . . . . . . . .234
Lesson 12 Percent Power . . . . . . . . . . . . . . . . . . . . . .236
Lesson 13 Less Common Percents . . . . . . . . . . . . . . .238
Lesson 14 Give It to Me Straight . . . . . . . . . . . . . . . . .240
➤ PHASE FOUR The Integers
Lesson 15 The Other End of the Number Line . . . . . .244
Lesson 16 Moving on the Number Line . . . . . . . . . . . .246
Lesson 17 Taking the Challenge . . . . . . . . . . . . . . . . . .248
Lesson 18 The Meaning of the Sign . . . . . . . . . . . . . . .250
Lesson 19 The Cube Model . . . . . . . . . . . . . . . . . . . .252
Lesson 20 Write It Another Way . . . . . . . . . . . . . . . . .254
➤
➤
➤
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256
➤
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Small Town 2:3 (.67:1)
Quarterville 1:4 (.25:1)
Micropolus 3:8 (.375:1)
Gulliver’s Worlds
. . . . . . . . . . . . . . . . .276
Measuring and Scaling
➤ PHASE ONE Brobdingnag
Lesson 1
The Sizes of Things in Brobdingnag . . . . . . .280
Lesson 2
A Life-Size Object in Brobdingnag . . . . . . . .282
Lesson 3
How Big is “Little” Glumdalclitch? . . . . . . . .284
Lesson 4
Telling Tales in Brobdingnag . . . . . . . . . . . . .286
➤ PHASE TWO Lilliput
Lesson 5
Sizing Up the Lilliputians . . . . . . . . . . . . . . .290
Lesson 6
Glum-gluffs and Mum-gluffs . . . . . . . . . . . . .292
Lesson 7
Housing and Feeding Gulliver . . . . . . . . . . .294
Lesson 8
Seeing Through Lilliputian Eyes . . . . . . . . . .296
➤ PHASE THREE Lands of the Large and Lands
of the Little
Lesson 9
Lands of the Large . . . . . . . . . . . . . . . . . . .300
Lesson 10 Lands of the Little . . . . . . . . . . . . . . . . . . . .302
Lesson 11 Gulliver’s Worlds Cubed . . . . . . . . . . . . . . .304
Lesson 12 Stepping into Gulliver’s Worlds . . . . . . . . . .306
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308
➤
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Patterns in Numbers and Shapes . .320
Using Algebraic Thinking
➤ PHASE ONE Describing Patterns Using Tables
Lesson 1
Calendar Tricks . . . . . . . . . . . . . . . . . . . . . .324
Lesson 2
Painting Faces . . . . . . . . . . . . . . . . . . . . . . .326
Lesson 3
Crossing the River . . . . . . . . . . . . . . . . . . .328
➤ PHASE TWO Describing Patterns Using Variables
and Expressions
Lesson 4
Letter Perfect . . . . . . . . . . . . . . . . . . . . . . .332
Lesson 5
Tiling Garden Beds . . . . . . . . . . . . . . . . . . .334
Lesson 6
Chocolates by the Box . . . . . . . . . . . . . . . .336
➤ PHASE THREE Describing Patterns Using Graphs
Lesson 7
Gridpoint Pictures . . . . . . . . . . . . . . . . . . .340
Lesson 8
Points, Plots, and Patterns . . . . . . . . . . . . . .342
Lesson 9
Payday at Planet Adventure . . . . . . . . . . . . .344
➤ PHASE FOUR Finding and Extending Patterns
Lesson 10 Sneaking Up the Line . . . . . . . . . . . . . . . . .348
Lesson 11 Something Fishy . . . . . . . . . . . . . . . . . . . . .350
Lesson 12 The Will . . . . . . . . . . . . . . . . . . . . . . . . . . .352
Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .354
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TABLE OF CONTENTS • MATHSCAPE
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PHASEONE
Measures of Central Tendency
Super Data Company collects
data, shows data on graphs, and
analyzes data. As an apprentice
statistician, you will conduct a
survey, create a graph of the
data you collect, and analyze it.
These are important skills for
statisticians to know.
How can we use data
to answer questions about
the world around us?
WHAT DOES
THE
DATA SAY?
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PHASETWO
PHASETHREE PHASEFOUR
Representing
and Analyzing Data
You will explore bar graphs.
You will create single bar graphs
and identify errors in several
bar graphs. You will also
investigate how the scale on a
bar graph can affect how the
data is interpreted. At the end
of the phase, you will conduct a
survey of two different age
groups. Then you will make a
double bar graph to represent
the data and compare the
opinions of the two groups.
Progress over Time
Probability and Sampling
Start off with a Memory Game
in which you find out if your
memory improves over time
and with practice. You will
create a broken-line graph to
show your progress. Then you
will analyze the graph to see if
you improved, got worse, or
stayed the same. The phase ends
with a project in which you
measure your progress at a skill
of your choice.
You will investigate the chances
of choosing a green cube out
of a bag of green and yellow
cubes. Then you will explore
how changing the number of
cubes in the bag can change the
probability of picking a green
cube. At the end of the phase,
you will apply what you’ve
learned so far by helping one
of Super Data Company’s
clients solve the Jelly Bean Bag
Mix-Up.
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PHASE ONE
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A statistician collects and organizes data. Surveys,
questionnaires, polls, and graphs are tools that
statisticians use to gather and analyze the information.
In Phase One, you will begin your new job as an apprentice
statistician by collecting data about your class. You will
learn ways to organize the data you collect. Then you will
analyze the data and present your findings to the class.
Measures
of Central
Tendency
WHAT’S THE MATH?
Investigations in this section focus on:
COLLECTING DATA
■
Conducting surveys to collect data
■
Collecting numerical data
GRAPHING
■
Making and interpreting frequency graphs
ANALYZING DATA
■
Finding the mean, median, mode, and range of a
data set
■
Using mean, median, mode, and range to analyze
data
mathscape1.com/self_check_quiz
WHAT DOES THE DATA SAY?
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ANALYZING DATA
TO FIND MODES
AND RANGES
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Class
Survey
How well do you know your class? Taking a survey is one
way to get information about a group of people. You and your
classmates will answer some survey questions. Then you will graph
the class data and analyze it. You may be surprised by what you find
out about your class.
Find the Mode and Range
How can you find the
mode and range for a
set of data?
The data your class tallied from the Class Survey Questions is a
list of numbers. The number that shows up most often in a set of
data like this is called the mode. The range is the difference
between the greatest number and the least number in a set of
data. For the data in the class frequency graph you see here, the
mode is 10. The range is 9.
Look at the frequency graph your class created for Question A.
Find the mode and the range for your class data.
How Many Glasses of Soda We Drink
6
X
X
X
X
X
X
X
X
X
1
2
X
X
X
X
3
X
X
X
X
X
X
4 5 6 7 8
Number of glasses
WHAT DOES THE DATA SAY? • LESSON 1
X
X
X
X
X
X
X
X
X
X
9
10
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Analyze the Class Data
Your teacher will give your group the class’s responses for one of
the survey questions you answered at the beginning of the lesson.
Follow these steps to find out everything you can about your
class.
1
How can you use
mode and range
to analyze data?
Create a frequency graph of the data.
a. Include everyone’s answer on your graph.
b. Don’t forget to label the graph and give it a title.
2
Analyze the data from your graph.
a. Find the mode.
b. Find the range.
Write About the Class Data
Write a summary that clearly states what you learned about your
class from the data. Be sure to include answers to the following
questions:
■
What does the data tell you about the class? Make a list of
statements about the data. For example, “Only one student in
the class has 7 pets.”
■
What information did you find out about the class from the
mode and range?
hot
words
mode
range
frequency graph
W
Homework
page 36
WHAT DOES THE DATA SAY? • LESSON 1
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EXPLORING MEANS
AND MEDIANS
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Name
Exchange
One of the questions often asked about a set of data is,
“What is typical?” You have learned to find the mode of a list of
numbers. Two other measures of what’s typical are the mean and
the median. Here you will use mean, median, and mode to analyze
data on the names in your class.
Find the Mean
How can you find the
mean length of a
name in the class?
One way to find the mean length of a set of first names is to do
the Name Exchange. Follow these steps to find the mean, or
average, length of the first names of members in your group.
1
Write each letter of your first name on a different sheet of
paper.
2
Members of your group should exchange just enough letters so
that either:
a. each member has the same number of letters, or
b. some group members have just one letter more than other
members.
You may find that some members of the group do not need to
change letters at all.
3
Record the mean, or average, length of the first names in your
group.
How does the mean for your group compare to the mean for the
class?
8
WHAT DOES THE DATA SAY? • LESSON 2
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Find the Median
When the numbers in a set of data are arranged in order from
least to greatest, the number in the middle is the median. If there
is an even number of numbers in a set of data, the median is the
mean of the two middle numbers. Use the frequency graph your
class made for the lengths of names to answer these questions.
■
What is the median length of a first name for your class?
■
What does the median tell you?
How can you find the
median for a data set?
How does the mean compare to the median for the class?
Write About the Class Data
You have learned about the mean, median, mode, and range.
Think about what you have learned to answer the following
questions about your class:
■
What do each of the measures (mean, median, mode, and
range) tell you about the lengths of the first names in the class?
■
Which of the measures (mean, median, or mode) do you think
gives the best sense of what is typical for the class? Why?
■
What are some situations where it would be helpful to know
the mean, median, mode, or range for the class?
Ms. Bryan’s Class
1
2
3
4
5 6 7 8 9
Number of letters
10 11 12
hot
words
mean
median
W
Homework
page 37
WHAT DOES THE DATA SAY? • LESSON 2
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INVESTIGATING
RATINGS AND
DISTRIBUTIONS
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TV
Shows
Rating scales are often used to find out about people’s
opinions. After your class rates some television shows, you will
look at some data on how another group of students rated other
television shows. Then you will apply everything you have learned
so far to conduct and analyze a survey of your own.
Analyze Mystery Graphs
What information
can you get by
analyzing the
distribution of
data in a graph?
The graphs below show how some middle school students rated
four TV shows. Use the information in the graphs to answer the
following questions:
■
Overall, how do students feel about each show?
■
Do the students agree on their feelings about each show?
Explain your answer.
■
Which TV shows that you watch might give the same results if
your classmates rated the shows?
Mystery Graphs
TV Show A
X
X
1
Terrible
10
X
X
X
X
2
X
X
X
X
X
X
X
X
X
X
3 4
Okay
TV Show B
X
X
5
Great
X
X
X
X
X
X
X
1
Terrible
X
X
X
X
2
3 4
Okay
TV Show C
X
X
X
X
X
X
X
5
Great
WHAT DOES THE DATA SAY? • LESSON 3
X
1
Terrible
2
X
X
X
X
X
X
X
X
X
3 4
Okay
TV Show D
X
X
X
X
X
X
X
X
5
Great
X
X
X
1
Terrible
X
X
X
X
2
X
X
X
X
X
X
X
X
3 4
Okay
X
X
X
5
Great
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Collect and Analyze Data, Part 1
Now it’s your turn! You will apply what you have learned about
collecting, representing, and analyzing data to find out about a
topic of your choice. Follow these steps.
1
2
3
How can you conduct
and analyze a survey?
Make a data collection plan
Choose a topic
On what topic would you like
to collect data?
Choose a population to
survey
Whom do you want to survey?
For example, do you want to
ask 6th graders or 1st graders?
How will you find at least 10
people from your population to
survey?
Write survey questions
Write four different survey
questions that can be answered
with numbers. At least one of
the questions should use a
rating scale. Make sure that the
questions are easy to understand.
Identify an audience
Who might be interested in the
information you will collect?
Why might they be interested?
Collect and represent data
Collect data
Collect data for just one of the
survey questions. Ask at least 10
people from the population you
chose. Record your data.
Graph data
Create an accurate frequency
graph of your data.
Analyze the data
Write a report that answers
these questions:
What are the mean, median,
mode, and range? How would
you describe the distribution,
or shape, of the data? What did
you find out? Make a list of
statements that are clearly
supported by the data.
hot
words
frequency graph
distribution
W
Homework
page 38
WHAT DOES THE DATA SAY? • LESSON 3
11
12/19/03
P H A S E TWO
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Author McGraw-Hill Education Isbn 9780078604669 File size 15.1MB Year 2005 Pages 381 Language English File format PDF Category Mathematics Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare NSF-funded program helps you meet your state standards in an engaging and student friendly format. Download (15.1MB) Rich and Engaging Mathematical Tasks: Grades 5-9 California Algebra 1: Concepts, Skills, and Problem Solving California Algebra 2: Concepts, Skills, and Problem Solving Elementary Number Theory Category Theory, 2 edition Load more posts