Data
and Probability in Upper Elementary School
The study of statistics has gone
from being a university course, to an elective course in high schools,
to being a large part of the study of mathematics at all levels, all within
the past ten years.This is a reflection
of the changing role of mathematics in society and especially the increasing
importance of quantitative reasoning in decision making in business and
government.
The study of
statistics in the Atlantic provinces is outlined in GCOs F and G of the
APEF mathematics curriculum.
Activities
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Word Versions
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Articles
in Teaching Mathematics in the Middle School (in Acadia’s library)
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A Big Gulp
Activity, Nov–Dec 1997, 210–12
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A Nugget of
Gold, May 1997, 408–10
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By Way of
Introduction: Data and Chance, Mar 1999, 347
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Capture and
Recapture Your Students' Interest in Statistics, Mar 1999, 412–18
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Choice and
Chance in Life: the Game of "Skunk.", Apr 1994, 28-33
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Community
Planning through Data Analysis; John Graunt: The Founder of Statistics.
Mar. 2000, 458–64
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Counting Attribute
Blocks: Constructing Meaning for the Multiplication Principle. May 2000,
568–73
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Counting Grass.
Sept. 1999, 7–10
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Data Collection:
Getting to Know Your Students' Attitudes, Mar 1999, 382–84
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Data with
Snap, Crackle, and Pop, Mar-Apr 1996, 760-64
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Displaying
Data Is As Easy As Pie! Polar Area Graphs: Early Pie Charts, Mar 1999,
390–97
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Exploring
Mean, Median, and Mode with a Spreadsheet, Sept-Oct 1995, 490-95
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Exploring
Probability through an Evens-Odds Dice Game, Mar 1999, 358–62
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Free Pizza,
Mar 1999, 389
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Free Pizza?
Slim Chance! Jan. 2000, 320–21
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From The Giver
to The Twenty-One Balloons: Explorations with Probability, May 1999, 504–9
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Genetics as
a Context for the Study of Probability. Dec. 1999, 214–21
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Graphing Calculators
Aren't Just for High School Students, Nov-Dec 1994, 190, 192-96
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Graphing in
the Information Age: Using Data from the World Wide Web, Mar–Apr 1997,
298–304
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Graphs in
Real Time. Oct. 1999, 92–99
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Having Fun
with Baseball, May 1996, 780-85
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How Do Students
Think about Statistical Sampling before Instruction? Dec. 1999, 240–46,
263
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Implementing
Data Analysis in a Sixth-Grade Classroom, Jan-Feb 1996, 622-28
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Improving
Data Analysis through Discourse. Apr. 2000, 548–53
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Investigating
Apples, Gr. 6-8, Nov-Dec 1995, 596
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Learning Statistics
with Technology, Sept-Oct 1994, 130-36
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Looking at
Random Events with Logo Software, Jan-Mar 1995, 318-22
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Making Charts:
Do Your Students Really Understand the Data? Sept. 1999, 16–18
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Mathematical
Connections from Biology: "Killer" Bees Come to Life in the Classroom,
Mar 1999, 350–56
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Mathematics
Fitness, May 1998, 458–62
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Mean and Median:
Are They Really So Easy? Mar. 2000, 436–40
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Means and
MADs, Mar 1999, 398–403
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Mode Code,
Apr 1999, 464–66
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Pennies from
Heaven--Nickels from Where?, Nov–Dec 1997, 240–48
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Preparing
Teachers to Present Techniques of Exploratory Data Analysis, Sept-Oct 1994,
166-72
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Push-Penny:
What Is Your Expected Score?, Feb 1998, 370–77
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Putting Math
in Motion with Calculator-Based Labs, Mar 1999, 364–67
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Racing to
Understand Probability, Oct 1997, 162–70
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Reflecting
on Students' Understanding of Data, Mar 1999, 374–80
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Reinventing
Scrabble with Middle School Students. Dec. 1999, 210–13
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Roll the Dice--an
Introduction to Probability, Oct 1998, 85–89
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Socrates and
the Three Little Pigs: Connecting Patterns, Counting Trees, and Probability.
Nov. 1999,156–61
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Sticks to
the Roof of Your Mouth?, Mar 1999, 404–11
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The Case of
the Smash Hit, Mar–Apr 1998, 424–27
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The Human
Scatterplot, Nov–Dec 1997, 208–9
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The Pond:
Doing Research Together, Mar-Apr 1996, 696-702
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Understanding
Students' Understanding of Graphs, Nov–Dec 1997, 224–27
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Using a Database
for Student Research, Jan 1997, 154–59
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Young Women
Experience Mathematics at Work in the Health Professions, Nov–Dec 1997,
198–206
Articles
in Teaching Children Mathematics (aka, the Arithmetic Teacher, in Acadia’s
library)
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A Data "Eggs"ploration,
Apr 1998, 448-51
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A Handy Database
Activity for the Middle School Classroom, Dec 1992, 235-238
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A Television
Programming Challenge: A Cooperative Group Activity That Uses Mathematics,
Jan 1989, 7-9
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Adventures
in Statistics, Mar 1998, 394-400
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Adventures
with Charts and Graphs: Project Zoo, Mar 1989, 54
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All About
Us: Connecting Statistics with Real Life, Sep 1997, 14-19
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An Exploration
of Fifty Nifty States, Feb 1996, 330-34
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Apples! Apples!,
Nov 1992, 172
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Assessing
Students through Data-Exploration Tasks, Feb 1996, 366-71
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Assessing
Young Children’s Mathematical Understandings, Jan 1995, 275-77
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Bingo Math,
May 1990, 44
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Calendar Mathematics:
Extra! Extra! Read All about It!, Sep 1993, 24-25
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Calendar Mathematics:
Getting to Know You, Sep 1991, 24-25
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Calendar Mathematics:
Home Sweet Home, Apr 1993, 452-453
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Calendar Mathematics:
Watch It!, Mar 1994, 392-393
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Calendar Mathematics:
Water, Water Everywhere!, Apr 1994, 474-475
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Cemetery Mathematics,
Dec 1991, 31-36
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Challenging
Codes: Riddles and Jokes, Apr 1991, 55
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Change Partners,
Dec 1989, 21
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Chi Square
Pie Charts and Me, Nov 1988, 61-62
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Classroom
Data, Sep 1994, 28-34
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Collecting
Data Outdoors: Making Connections to the Real World. Sept. 1999, 8-12
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Cookies,
May 1994, 563
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Coordinate
Graphing: Shaping a Sticky Situation, Nov 1987, 6-10
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Coordinate
Math, Sep 1988, 50
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Count on Mathematics
for Number Sense, Feb 1996, 351-56
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Creative Graphing,
Dec 1987, 41
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Curriculum
and Evaluation Standards for School Mathematics: Dealing with Data and
Chance, Dec 1992, 239-240
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Daily Activities
for Data Analysis, Jan 1994, 242-245
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Data Buddies:
Primary-Grade Mathematicians Explore Data, Oct 1994, 80-86
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Data Collection
and Analysis Activities K-8, Sep 1992, 62
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Developing
Concepts in Probability and Statistics-and Much More, Feb 1986, 34-37
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Developing
Graph Comprehension: Elementary and Middle School Activities, Nov 1991,
58-59
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Dinosaurs
Forever!, May 1994, 563-564
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Dolphins or
Wildcats: Exploring Election Statistics, Feb 1996, 386-89
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Elementary
School Activity: Graphing the Stock Market, Mar 1986, 17-20
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Equal Areas,
May 1986, 18
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Exploring
Data: Kindergarten Children Do It Their Way, Feb 1996, 382-85
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Exploring
Measurement, Time and Money-Level 1, Oct 1990, 44-45
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Exploring
Tables and Graphs, Levels 1 and 2, Nov 1985, 53
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Find the Shelf,
Feb 1992, 48
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Finding the
Average with Frisbee Tosses, Jan 1989, 18
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For Our Middle
School, Dec 1984, 40-41
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Functional
Mathematics: Whole and Decimal Numbers, Fractions, Problem Solving, Measurement,
Using Data, Interpreting Graphs, Nov 1988, 60
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Gather, Organize,
Display: Mathematics for the Information Society, Dec 1986, 12-15
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Gender, Ninja
Turtles, and Pizza: Using a Classroom Database for Problem Solving, Dec
1996, 192-199
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Glyphs? Don’t
Let Them Scare You!, Apr 1995, 506-11
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Golf Classic
and Compubar, Oct 1984, 49
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Graphing and
Probability Workshop, Grades 3-8, Nov 1991, 56
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Graphing from
A to Z, Dec 1995, 220-23
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Graphing Primer,
Grades K-2, Oct 1992, 129-130
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Graphs and
Microcomputers: A Middle School Program, Oct 1983, 17-20
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Graphs Can
Motivate Children to Master Basic Facts, Oct 1983, 38-39
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Great Graphing:
More Than 60 Activities for Collecting, Displaying and Using Data, May
1994, 565
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Great Graphing:
More Than 60 Activities for Collecting, Displaying and Using Data, May
1994, 565
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Gummy Bears
in the White House, Feb 1996, 379-81
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Hamster Math:
Authentic Experiences in Data Collection, Feb 1996, 336-39
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Hands On Statistics,
Probability, and Graphing, Oct 1989, 54
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Ideas: Balloons,
Feb 1991, 30-36
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Ideas: Baseball,
Mar 1994, 382-390
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Ideas: Bicycling,
Dec 1990, 23-33
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Ideas: Consumer
Awareness and Judgment, Jan 1991, 26-33
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Ideas: Environment
and Conservation, May 1994, 534-538
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Ideas: Fingerprints,
Mar 1991, 24-33
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Ideas: Games,
Measurement, and Statistics, Apr 1990, 27-32
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Ideas: Graphing,
Oct 1983, 28-32
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Ideas: Graphs,
Jan 1985, 27-32
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Ideas: Hearts,
Feb 1992, 32-39
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Ideas: Information
Represented Graphically, Oct 1991, 26-33
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Ideas: Locating
Objects in Space and on Maps, Jan 1990 19-24, 43
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Ideas: Mathematics
and Children's Literature, May 1993, 512-519
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Ideas: Mathematics
and Environmental Concerns, Sep 1993, 27-39
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Ideas: Mathematics
and Exploration, Oct 1992, 93-101
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Ideas: Mathematics
and Football, Jan 1993, 264-277
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Ideas: Mathematics
and Music, Dec 1992, 215-225
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Ideas: Pizza,
Apr 1991, 26-33
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Ideas: Preference
Tests, Nov 1992, 157-167
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Ideas: Problem
Solving, Apr 1984, 27-30, 35-36
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Ideas: Skittles®
and Statistics, Apr 1993, 454-462
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Ideas: Sports
Balls, Nov 1990, 23-32
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Ideas: Tables,
Charts and Graphs, `Mar 1988 19-24
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Ideas: Television
Viewing, May 1991, 25-33
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Ideas: Uses
of Numbers, Sep 1991, 26-33
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Ideas: Using
and Interpreting Data, Oct 1990, 24-34
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Ideas: Using
and Interpreting Data, Sep 1990, 23-33
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Implementing
the Standards: The Statistics Standards in K-8 Mathematics, Oct 1990, 35-39
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Incredible
Comparisons: Experiences with Data Collection, Sept 1998, 12–16
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Instant Survey
Sampler, No. A-224, Dec 1991, 41
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It's the Berries,
Sep 1997, 30-34
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Jar Lids-An
Unusual Math Manipulative, Nov 1988, 22-25
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Learning Data-Management
Skills Meaningfully, Oct 1997, 82-88
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Learning to
"Ad.", Jan 1996, 284-88
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Let's Do It:
Dealing with Data, May 1984, 9-15
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Let's Do It:
Making Graphs, Jan 1984, 7-11
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Math-O-Graphs:
Critical Thinking through Graphs, May 1991, 47
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Mean or Meaningless?,
Dec 1993 194-197
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Measurement,
Using Data, Interpreting Graphs, Nov 1988, 60
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Measuring:
From Paces to Feet, Grades 3-4, from Used Numbers: Real Data in the Classroom,
May 1991, 48
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Model Right,
Oct 1991, 52
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Multicultural
Mathematics Education for the Middle Grades, Feb 1991, 8-13
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Not Just an
Average Unit, Dec 1990, 54-58
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Nuts about
Mathematics, Dec 1995, 228-32
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Pairing Up,
Apr 1994, 444
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Paper Route:
A Coordinate Graphing Activity, Sep 1987, 51
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Pictograms:
Graphing Pictures for a Reusable Classroom, Oct 1992, 130
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Pictures,
Tables, Graphs, and Questions: Statistical Processes, Feb 1996, 340-45
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Plotting Margo's
Party, Nov 1995, 176-79
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Polishing
a Data Task: Seeking Better Assessment, Feb 1996, 372-78
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Primary Graphing
and Probability Workshop, Grades K-2, Dec 1991, 41-42
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Problem Solving:
Dealing with Data in the Elementary School, Jan 1995, 256-60
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Problem Solving:
Tips for Teachers, Nov 1984, 46-47
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Reading and
Making Graphs: Volume 1, Bar Graphs, Dec 1988, 53
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Reading and
Making Graphs: Volume 2, Line Graphs, Dec 1988, 53-54
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Reading and
Making Graphs: Volume 3, Circle Graphs, Dec 1988, 54
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Research into
Practice: Teaching Statistics: Mean, Median, and Mode, Mar 1988, 25-26
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Sampling Treats
from a School of Fish, Mar 1987, 36-37
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Skills, Oct
1993, 129-135
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Some Like
It Hot: Promoting Measurement and Graphical Thinking by Using Temperature,
May 1999, 538–43
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Sports Math,
Mar 1985, 58
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Statistics,
Probability and Graphing, Apr 1989, 59-60
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Statistics:
The Shape of Data, Grades 4-6: from Used Numbers: Real Data in the Classroom,
May 1991, 49
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Supermarket
Challenge, Oct 1992, 84-88
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Surveys Unlimited:
A Tool for Survey Takers, Dec 1987, 38
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Taste That
Graph!, Dec 1990, 53
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Teacher to
Teacher: Learn about Statistics-Math League Baseball, Apr 1994, 459-461
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Teaching Arithmetic
Averaging: An Activity Approach, Mar 1990, 38-43
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Teaching Mathematics
with Technology: A Graphing Tool for the Primary Grades, Oct 1990, 40-43
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Teaching Mathematics
with Technology: Statistics and Graphing, Apr 1992, 48-52
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Telling Tales:
Creating Graphs Using Multicultural Literature, Oct 1994, 87-91
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The Children's
Rain Forest, Nov 1995, 144-48
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The Class
Survey: A Problem-Solving Activity, May 1985, 10-12
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The Tangram-It's
More Than an Ancient Puzzle, May 1991, 38-43
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Up Fractions!
Up n/m!, Apr 1985, 42-43
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Using a Polar
Coordinate System in the Classroom, Apr 1990, 42-45
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Using Data
to Make Decisions about Chance, Feb 1996, 346-50
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Using Plastic
Recycling Numbers, May 1994, 553
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Weather Mathematics:
Integrating Science and Mathematics, Sept 1998, 19–22
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What Do Children
Understand about Average?, Feb 1996, 360-64
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What Do You
Like to Read? Sept. 1999, 34-37
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What's Going
On…, Dec 1984, 25
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What's in
a Glyph?, Feb 1996, 324-28
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What's In
a Name?, May 1990, 44
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Ya Gotta Play
to Win: A Probability and Statistics Unit for the Middle Grades, Mar 1984,
26-30
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Young Children
Deal with Data, Nov 1997, 146-49
Background
Averages:What
are they and what are they for?
·Mean-
if the total were evenly distributed, everyone would have this amount
·Median-
if everyone is ranked the person in the middle has this amount
·Mode-
most people have this amount
The mean is
the most commonly use average. It is appropriate for numerical data
in which every number is possible.Use
with data that include outliers can be misleading. Measurements are often
averaged using the mean.
The median is
useful for numerical data where not every number is possible, or
where there are outliers. Income data (which often has outliers)
is often averaged using the median.Data
from Likert scales should also be averaged using the median (but sloppy
social scientists often use the mean).
The mode is
the only average you can use with non-numerical categorical data.If
you wanted to average “Favouritecolour”
you’d use the mode.
Measures
of dispersion: What are they and what are they for?
·Maximum
(plural maxima) refers to the largest value in the data
·Minimum
(plural minima) refers to the smallest value in the data
·Range
refers to the difference between the maximum and the minimum.The
bigger the range the more dispersed (spread out) the data is. If the data
is widely dispersed then few values will be close to the mean and median.
·Frequency
refers to the number of times each value occurs in the data.If
the frequencies are all about the same them the data is more dispersed
than if there are a few values of high frequency close together.
All of these
are used to decide if an average is a good representation of the whole
data set. If the data is widely dispersed then the average doesn’t tell
you much about most of the data.The
class average might be 75%, but if the range is big and the frequencies
are small, then most people don’t have marks of about 75%.On
the other hand if the range is small and the frequencies relatively high,
then most people probably do have marks close to 75%
Graphs and plots: What are they and what are they for?
Pictographs display
categorical data by representing each member (or groups of n members)
of a category with a picture of it.
Preferred means
of communication
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Letters
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Phone calls
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Emails
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Bombs thrown
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Line
graphs represent
categorical data by representing the total number of members with a point,
and joining the points.It is
often used to trace events over time.
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Bar
graphs display categorical data using bars to represent the total number
of members in each group.
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Double
bar graphs are used when two sets of data are being compared.
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Stem-and-leaf
plots are useful for displaying the distribution of numerical data, and
displaying the data at the same time.
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Final marks
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6
7
8
9
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7889
13356788
00234445677788889999
0000001111122333467 |
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Circle
graphs are used to display proportional data where the amount in
each category is compared to the total.
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Coordinate
graphs are used to display the relationship between two sets of
numbers.
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Scatter
plots are used to display data so a judgment can be made about whether
or not there is a relationship between two sets of numbers.
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Curriculum
outcomes (GCOs F&G)
Grade
4
F1-
recognize and use a variety of methods for the collection and organization
of data
F2-
describe data maxima, minima, range and frequency
F3-
read and interpret bar graphs, line graphs, pictographs, and stem-and-leaf
plots
F4-
display position, using ordered pairs on a grid
F5-
construct bar graphs, pictographs, and stem-and-leaf plots
F6-
interpolate data from a display
F7-
describe data, using the mean
F8-
explore real-world issues of interest to students and for which data collection
is necessary to determine an answer
G1-
predict probabilities as either close to 0, near 1, or near ½
G2-
cite examples of everyday events with very high or very low probabilities
G3-
predict whether one simple outcome is more or less likely than another
G4-
use fractions to describe experimental probabilities
Grade
5
F1-
use double bar graphs to display data
F2-
use pictographs and bar graphs to display and interpret data
F3-
use coordinate graphs to display data
F4-
create and interpret line graphs
F5-
groups data appropriately and use stem-and-leaf plots to describe the data
F6-
recognize and explain the effect of certain changes in data on the mean
of that data
F7-
explore relevant issues for which data collection assists in reaching conclusions
G1-
conduct simple experiments to determine probabilities
G2-
Determine simple theoretical probabilities and use fractions to describe
them
Grade
6
F1-
choose and evaluate appropriate samples for data collection
F2-
identify various types of data sources
F3-
plot coordinates in four quadrants
F4-
use bar graphs, double bar graphs and stem-and-leaf plots to display data
F5-
use circle graphs to represent data proportionally
F6-
interpret data represented in scatter plots
F7-
make inferences from data displays
F8-
demonstrate an understanding of the differences among mean, median, and
mode
F9-
explore relevant issues for which data collection assists in reaching conclusions
G1-
conduct simple simulations to determine probabilities
G2-
evaluate the reliability of sampling results
G3-
analyze simple probabilistic claims
G4-
determine theoretical probabilities
G5-
identify events that could be associated with a particular theoretical
probability
[Copyright --
David
A Reid] [School of
Education] [Acadia University]