Overview-  Data, Probability, and Statistics:

     This strand includes statistical investigation: strategies for obtaining data, and analyzing data by use of formats such as pictographs, coordinate graphs, tallies, tables, circle & bar graphs, histograms, box plots, scatterplots, and line graphs.  The display of data becomes more complex as grades increase, as does data collection, which initially is counting, measuring, and conducting simple surveys.  Later, sample size comes into consideration.  Students will eventually investigate via technology.  Spreadsheets, databases, and graphing calculators are used by sixth, seventh and eighth graders in order to analyze the more complex data sets.  Older students also make predictions using tables and charts.  These students are much more involved with data; describing the distribution of data (mean and range), learning about data extremes, representation, bivariate data, and bias free samples.  In general, the chronology of the strand remains the same throughout the years, only becoming more complex as students become older.

Objectives:

K:  Goal 4:  The learner will gather and organize data in a group setting
4.01 collect data to create concrete and pictorial graphs and describe the results as a group activity

1:    Goal 4:  The learner will demonstrate an understanding of data collection, display, and interpretation.
4.01 gather, organize, and display information as a group activity
4.02 answer questions about charts and graphs
4.03 create concrete, pictorial, and symbolic graphs using prepared grids
4.04 create concrete, pictoral, and symbolic graphs using prepared grids

2:   Goal 4:  The learner will demonstrate an understanding of data collection, and interpretation.
4.01 collect, sort, organize, and display information in charts, graphs, and tables with correct labeling
4.02 summarize and interpret information in charts, graphs, and tables – make predictions
4.03 collect and display data over period of time
4.04 locate points on the number line and positions on grid
4.05 complete simple probability experiments; describe results and make predictions

3:    Goal 4:  The learner will demonstrate an understanding of data collection and interpretation.
4.01 gather and organize data from surveys and classroom experiments over a period of time
4.02 display data on charts and graphs:  picture, bar, and line plots; describe data using mode
4.03 construct graphs where symbols or scales represent multiple units
4.04 read and interpret graphs and charts (bar, picture, circle, line, and line plots) as sources of information; identify main idea, draw conclusions, and make predictions
4.05 name the ordered pair for a point on the grid; plot positions named by ordered pairs on a coordinate grid
4.06 construct and use time lines to display sequences of events
4.07 describe the probability of chance events as more, less or equally likely to occur
4.08 list arrangements (permutations) and combinations of up to three items

4:   Goal 4:  The learner will demonstrate an understanding and use of graphing, probability, and data analysis.
4.01 interpret and construct stem-and-leaf plots
4.02 display data in a variety of ways including circle graphs
discuss the advantages and disadvantages of each form including ease of creation and purpose of the graph
4.03 collect, organize, and display data from surveys, research, and classroom experiments, including data collected over time – include data from other disciplines such as science, physical education, social studies, and the media
4.04 interpret information orally and in writing from charts, tables, tallies, and graphs
4.05 use range, median, and mode to describe a set of data
4.06 plot points that represent ordered pairs from many different sources
such as economics, science experiments, and recreational activities
4.07 investigate and discuss probabilities by experimenting with devices that generate random outcomes such as coins, number cubes, and spinners
4.08 use a fraction to describe the probability of an event and report the outcome of an experiment

5:   Goal 4:  The learner will demonstrate an understanding and use of graphing, probability, and data analysis.
4.01 interpret and construct line graphs
4.02 explain the kinds of decisions that need to be made in selecting and constructing appropriate graphs including pictograph, bar, line plot, circle, and line graphs
4.03 systematically collect, organize, display, and interpret data both orally and in writing using information from a variety of content area
4.04 compare increasingly complex displays of data, including multiple sets of data on the same graph, computer applications, and Venn diagrams
4.05 determine the mean of a given set of data using a calculator when appropriate
4.06 use the range, median, mean, and mode to describe a set of data
4.07 show all arrangements (permutations) and combinations of up to four items; list and explain all possible outcomes in a given situation
4.08 compare experimental and theoretical (expected) results for a variety of simple experiments
4.09 use an organized approach and appropriate strategies to solve multi-step problems involving graphing, probability, and statistics-use calculators and computers as appropriate

6:  Goal 4:  The learner will demonstrate an understanding and use of graphing, probability, and data analysis.
4.01 create and evaluate graphing representations of data
4.02 analyze data using spreadsheets
4.03 construct convincing arguments based on analysis of data and interpretation of graphs
4.04 use measures of central tendency to compare two sets of data
4.05 construct convincing arguments based on analysis of data and interpretation of graphs
4.06 design an experiment to test a theoretical probability; record and explain results
4.07 make predictions based on the probabilities of simple events
4.08 use inductive and deductive reasoning to solve problems
4.09 analyze problem situations, use an organized approach, and select appropriate strategies and technology to solve problems involving probability and statistics
 

Teacher Interviews:  “What is hardest for your students when dealing with Data, Probability, and Statistics?”
 
 

Kindergarten-
 Kim Blackman, a home school teacher for children in kindergarten, first, and second grade, has been working recently with manipulatives.  The manipulatives include such items as Unifix Cubes and pattern blocks.  Her kindergartener has been having trouble with visual representation on data.  The student has difficulty with showing amounts with the manipulatives.

First Grade-
 Mrs. Blackman, the same home school teacher used in the Kindergarten example, teaches a first grader and second grader as well.  Currently, her first grader has been using graphs when working with weather, temperature, and soccer games.  The student is struggling with graph representation.

Second Grade-
 The second grade, third grade, and fourth grade combination class at Beech Mountain Elementary School has been working with graphing.  The second graders are battling graphing.  The children do not seem to be able to grasp the concept of categorizing for graph representation.

Third Grade-
 Mrs. Jones, third grade teacher at Bethel Elementary School stated one of the most difficult concepts in the data, probability, and statistics strand for her classes has been representation within pictographs.  If a picture of a flag represents three flags, students typically do not comprehend.  If a student sees four flags and is then asked how many flags were represented, he or she generally responds, “Four,” rather than the correct answer of 12.  Also, Mrs. Jones said test scores show her third graders do poorly on analysis when it deals with measurement.  For example, if given the situation, “Would you pour a mug of hot chocolate into…” with the choices, “a cup, a liter, or a gallon?” the students have much difficulty with that idea.
 On the flip side, Mrs. Jones herself has a “hard spot” teaching a particular area in the data, probability, and stats strand!  She finds it very challenging to create a beneficial lesson plan dealing with stem and leaf plots.

Fourth Grade-
 There is presently a student teacher at Beech Mountain Elementary teaching a combination class including fourth graders.  An observation showed there to be many problems when using the manipulatives.  Students are not understanding number representation when using the Unifix Cubes and 3D cubes.

Fifth Grade-
What a fifth grade teacher said was hardest for her children to understand is the application of information to real-life situations. Using the spinner to have students discuss probability proves this concept of non-applicability. The kids can understand and get correct answers using the spinner, but they cannot apply what they have learned to real life. It is hard for kids to grasp the whole idea of data, probability and statistics.

Sixth Grade-
 The sixth grade teacher at Bethel Elementary School, Ms. Rogers,  felt that her class had the most difficulty with analyzing data in word problems.  Also, producing charts from collected data has typically been quite a challenge.

    There seemed to be a common ground with the difficulty area in the strand of Data, Probability, and Statistics.  Most of the grades are not comprehending the idea of graphing, whether it be representation or categorizing.
 

Related Children’s Literature Books:

Kindergarten & First Grade-

From Head to Toe, Eric Carle, Harper Collins Publishers, Philadelphia, PA, 1997.
 This book is about body parts and how many animals and humans have alike.  The animal introduces itself in the book and tells what one of their body parts can do.  Then, the human replies and says if they can do it or not.  This would be a great book for a kindergarten class to learn to write down the different data of body parts, and then apply it to some sort of graph.  A line graph would be good to start doing.  Goal 4:  4.01

Jump, Frog, Jump!, Robert Kalan, Ill:  Byron Barton.  Mulberry Books, New
     York, NY, 1981.
 This book tells a story of a frog and how well he jumps.  From the very beginning, the frog is able to escape from something that wants to eat him.  Finally at the end of the story, humans try catch him and play with him, but a little boy hides him under a basket.  Then, he does jump away, so he can be safe and out of harm.  Another great book to start sequencing the events into data information.  Goal 4:  4.01

Mr. Gumpy’s Outing, John Burningham, Henry Holt and Company, New York, NY,
     1970.
 Mr. Gumpy wanted to go out on his boat one afternoon for a nice day on the water.  Everyone and every animal wanted to go along with him, but he always had one condition whether they could go or not.  So, he allowed everyone on the boat, and at first, no one argued or fought.  At he end, everyone was fighting, the boat tipped over, and everyone got out of the water.  They all went to have some tea, and everyone had the best manners.  Children could begin comparing their own manners with the manners of the individuals in this book.  On a graph, they could compare by categories of yes, no, and sometimes.  Goal 4: 4.01

Noah’s Ark, Lucy Cousins, Candlewick Press, Cambridge, MA, 1993.
 This is a retold story from the Bible.  Noah had to take two of every animal on the ark with him.  So, two of every animal and his family were the only people on the ark.  It began to rain, and it rained for forty days and nights.  Finally, it stopped raining, and Noah sent a dove out and he returned with an olive branch.  So, they waited, and then another one was sent out and it never returned.  The water began to dry, and finally, everyone could leave off of the ark.  Goal 4: 4.01

Junior’s Colors, Phil Vischer, Ill:  Ron Eddy, Thomas  Nelson, Inc., Nashville,
     TN, 1997.
 This is a great book for a child to start learning their colors.  Veggie Tales help the children discover what each color is, and how many different things ther are in that same color.  There is an average of 2 to 3 things on each page that represent the same color.  The children could use a circle graph and put the data of how many colors and how many items are for each color in the book.  Goal 4: 4.01

Brown Bear, Brown Bear, What Do You See?, Bill Matin Jr. and Eric Carle, Henry Holt
     and Company, New York, NY, 1992.
 This book asks many different animals and humans what they see.  Everyone replies to the question and then asks another question.  Each animal is described with their certain color, so at the end of the book, it would be great to review their colors.  Goal 4: 4.01, 4.02, 4.04

My Visit to the Dinosaurs, Aliki, Harper Collins Publisher, New York, NY, 1985.
 A child, little sister, and father go to the museum to see all the different dinosaurs.  There are statues of some and pictures of others.  This book is a great informational, and one that the students could graph many ideas and things.  One example of a graph that they could begin with is graphing the meat-eating dinosaurs, to the non-meat eating dinosaurs.  Goal 4: 4.01, 4.02, 4.04

Pa Grape’s Shapes, Phil Vischer, Ill:  Ron Eddy, Tommy Nelson, Inc., Nashville,
     TN, 1998.
 Pa Grape is trying to find tires that will fit his car.  So, he uses a new machine that suggests all different types of shapes.  The children could graph the data used in the book to graph which shapes match and which ones do not.  Also, we could allow the bigger kids to apply the different shapes into their every day life.  Goal 4:  4.01, 4.02, 4.03, 4.04

A Time for Singing, Ron Hirschi, Photographs:  Thomas D. Mangelsen, Cobblehill
     Books, New York, NY, 1994.
 This is a beautiful book of real pictures of animals from different types of birds, to a wolf in the snow.  The children would have a great time displaying the data on a graph and dividing the sections by where the animals live at all times.  The animals ranged from living in the air, water, and land.  Goal 4: 4.01, 4.02, 4.04

Underwear!, Mary Elise Monsell, Ill:  Lynn Munsinger, Albert Whitman and
     Company, Morton Grove, Illinois, 1988.
 Bismark the Buffalo tends to not find things in life very funny.  This book is about different types of people’s underwear, and how animals wear different cool ones.   It is very humorous in the fact that each animal wears something different, and in the end they call all laugh together because they look so silly.  The children could graph a couple of ideas.  One graph could be whether all of you laughed or not.  Goal 4: 4.01, 4.02, 4.04

Second & Third Grade-

Alfie Gets in First, Shirley Hughes, Lothrop, Lee, & Shepard Books, 1981.
 This is a story of Annie Rose, her mom, and her brother, Alfie.  Alfie is a little boy about four or five who is at the age where he likes to be first at everything; everything is a competition!  Alfie eventually is first in his house and closes the door while mom has gone back outside to get Annie Rose and the stroller.    He locked himself in!  While Mom and Annie are outside, Alfie is inside listening to directions from his mother, then to the ladies from across the street, then to the milkman.  Through the illustrations, the reader can see what Alfie is doing on one side of the door, and the adults on the other.  This is an easy book for 2.1.  This book would be a great way to illustrate how one gathers info, analyzes, and then makes a decision.  Goal 4:  4.01, 4.04

A House is a House for Me, Mary Ann Hoberman, Ill:  Betty Fraser, Scholastic, Inc., 1978.
 Easy reading, this book can lead to a more advanced activity for third graders.  The book of poetry about different houses for different things form people to gloves for hands.  Have students put together from one pile, a dwelling, and from the other pile, the dweller.  This deals with analyzing and interpreting data.  Goal 4:  4.04

Chester’s Way, Kevin Henkes, Scholastic, Inc., 1988.
This book is about Chester and Wilson, two mice who were best friends.  They did EVERY, SINGLE thing just alike!  Then Lilly moves to town and does things a little differently.  Good for data gathering:  list differences between Chester, Wilson, and Lilly.  Goal 4:  4.01, 4.02

Everybody Needs a Rock, Byrd Baylor, Ill:  Peter Parnall, An Aladdin Book, 1974.
 This is a book of ten rules to find the perfect rock to keep as a treasure.  Have second graders find a rock at recess.  Each child can collect data and make a list.  For third graders, have five rocks.  Split the class into five groups.  Each group makes a list of qualities of their rock.  Using the collected data, the class will determine which rock is which out of a pile of rocks.  Also, put each rock with two or three others and have groups trade.  Each group will use another group’s list of data, and will find the rock.  Goal 4:  4.01, 4.02, 4.04

Guess Who My Favorite Person Is, Byrd Baylor, Ill:  Robert Andrew Parker, An Aladdin Book, 1977.
This book about a man and his friend, and what their favorite things are, is a great way to introduce bar graphs to third graders.  Formulate a list of what each student’s favorites are (color, thing to touch, sound, etc.).  More than likely, there will be multiples.  If not, begin limiting favorites to things that only do have multiples (except for 1 or 2) ie:  blue=4, red=6, orange=1, yellow=1, brown=1, black=1, purple=7, etc.  Tell class the 3 or 4 most popular colors will be chosen.  Do this for each favorite.  Produce a bar graph.  Kids will love this because graph paper will be new to them an they can be creative with the bars.  Goal 4:  4.01, 4.02, 4.04

The Most Wonderful Egg in the World, Helme Heine, A Margaret K. McElderry Book, 1983.
 This story is about three hens who ultimately wanted to be chosen princess.  This would be a beneficial book to do a math lesson as the book was being read.  Just as the reader thinks the next chicken could not have a better quality, or egg, it does!  An idea would be to list qualities of an average hen (white, short legs, etc.), then list the three names of then hens in the book, all their qualities, then the eggs’ qualities.  Upon gathering data, have class interpret data and hypothesize which will become princess.  Goal 4:  4.01, 4.02, 4.04

Fourth Grade-

A Field Full of Horses, Peter Hansand, Ill: Kenneth Lilly, 1993.
An example of gathering data, this book describes horses and uses horses of many different sizes and colors. This is also a great book for analyzing data. This book could also be used for probability by using the different sizes and colors of the horses.  Goal 4:  4.01, 4.04

Dinosaurs and Other Fun Things, Richard Scary, Sihonspotlikes, 1997.
 Appropriate for data collection.  The beginning of the book explains recycling.  Students could gain an abundance of understanding via gathering their own data on recycling.  Nice way to integrate science, as well.  Children could also evaluate probability, for example, “What is the probability that at least three families in our class recycle cans?”  Goal 4:  4.07

Dragon Scales and Willow Leaves, Terryl Givens, Ill:  Andrew Portwood, G.P. Putnam’s Sons, NY, NY, 1997.
 This is a good book for analyzing two different types of data.  Use the obtained data to decide which seems more realistic.  This gives students the idea that the information should be reasonable.  Goal 4:  4.01, 4.04

Easy Braids, Barrettes, and Bows, Judy Ann Sadler, Ill:  Sarah Jane English, Kids Can Press, Ltd., 1997.
 This book would tie in great in a math class.   You can collect and analyze data about different hairstyles in the book, and then analyze how many people in class have one of these hairstyles.  Goal 4:  4.01, 4.02, 4.03, 4.04

Grandpa Bud, Siobhan Dodds, Candlewick Press, 1993.
 Good to use for collecting and analyzing data.  Compare this data with data obtained from class.  Use question, “Does your grandpa do this for you?”  If not Grandpa, use Grandma, Mother, Father, etc.  Goal 4:  4.01, 4.04

Ida Fan Fancy, Dick Gackenbach, Harper and Rowe Publishers, NY, NY, 1978.
 This book would be good to analyze different types of weather such as raining, sunny, and even floods.  This could be incorporated into a lesson on weather and the probability that two or three days will be sunny.  Goal 4:  4.01, 4.07

If Anything Ever Goes Wrong at the Zoo, Mary Jean Hendrich, Ill:  Jane Dyer, Voyager Books, 1993.
 This book is good to use for collecting and analyzing data.  The children can collect data about animals at the beginning and then analyze data as it unfolds near the end.  The kids could also relate this book to zoo trips they have been on.  Goal 4:  4.01, 4.04

The Log Cabin Quilt, Ellen Howard, Ill:  Ronald Himler, Holiday House, NY, NY, 1996.
 This book would be great for collecting data.  The lady in the book has a bag of cloth pieces.  The students could help gather “cloth pieces” within the classroom.  This could also deal with probability, for example, “If I reach in this bag, what is the probability the piece I pull out will be a blue diamond?”  Goal 4:  4.01, 4.07

The Mommy Exchange, Amy Hest, Ill: Dyanne DiSalvo- Ryan, 1988.
This book can be used for gathering and analyzing data, and probability. The children can gather data about the two different family lives and compare it to their family. Probability can be used if children try to find the probability that at least one child will have a family that is described in the book.  Goal 4:  4.01, 4.07

Sweet Clara and the Freedom Quilt, Deborah Hopkins, Ill: James Ransome.
Beneficial to describe collecting data to get an end product. Clara collected data from many sources to make her quilt, which was actually a map. The children can see as Clara collects her data and puts it together that there is a useful and needed end product.  Goal 4:  4.01

Fifth Grade-

Do You Wanna Bet?, Jean Cushman.  Ill:  Martha Weston, Clarion Books, New York , NY, 1991.
This is an interesting fifth grade level book.  It addresses topics like one out of two, forecasting, ABC’s of probability- making and breaking codes, birthday party, sampling and statistics- baseball statistics and strategies, PTA carnival- addresses chance and luck, winners and losers-playing cards and rolling dice, and last chance.  Students will be interested and involved with this statistics book.  Goal 4:  4.01

G is for Googol, David M. Schwartz, Ill:  Marissa Moss, Tricycle Press, Berkeley, CA, 1998.
This book goes through the alphabet, and provides in-depth descriptions and definitions for each new math term.  This is a very factual book, and introduces many new concepts of math to the teacher and the student.  There are endless possibilities for creative activities involving this book in the classroom setting.  Goal 4:  4.01
 

Graph Games, Frederique & Papy, Ill:  Susan Holding;  Thomas V. Crowell Co.,  New York, NY, 1971.
This provides games that can make graphs interesting and fun.  This is a book that provides adequate information to students about graphs while allowing them to learn through playing games.  The students will enjoy learning through these games and fun activities.  Goal 4:  4.01, 4.02

Math Projects in the Computer Age, David A. Thomas, 1995.
 An interesting statistics, probability, and data collecting/analyzing book filled with great web ideas.  A perfect book for understanding the use of computers and data analyzing.  Goal 4:  4.01, 4.07

Modern Mathematics, Harry Henderson, Facts on File, Inc., 1996.
 This is an introductory statistics book that applies math into the modern world and a world of technology.  This is a great book to tie in technology, math, and statistics.  Goal 4:  4.01

Sixth Grade-

The Red Badge of Courage, Steven Crane, Mass Market Paperback, NY, NY, 1997.
 This is the classic story of a soldier’s first two days in battle during the Civil War.  This novel would be a wonderful way to integrate history into a math lesson.  Create a graph with three bars comparing the number of Union soldiers, the number of Confederates killed in battle in the Civil War, and also the number who died of disease.  What percentage of the general population at the time do these represent?  Leave room for adding more statistics later.  Goal 4:  4.01, 4.02

Cat Running, Zilpha Keatley Snyder, Dell Publishing Company, NY, NY, 1996.
 Cat is the fastest runner at Brownwood School.  Everyone expects her to win the sixth grade race.  However, Cat’s dad will not allow her to wear slacks in the competition.  Being stubborn, Cat decides not to race at all.  When Zane Perkins, a “dirty, barefooted Okie” wins the race, Cat is furious with herself and suffers ridicule from her classmates.  Cat befriends Samantha, Zane’s sister, and her attitude towards the Okie situation changes.  When there is emergency in the Perkin’s family, Cat’s ability to run could make the difference between life and death.  Good book to use with an almanac.  Have students list the female runners who have received gold medals in the Olympics.  Ask them to calculate what percentage of these women are from the United States and graph these results.  Goal 4: 4.01, 4.07

Driver’s Education, Caroline B. Cooney, Bantam Books, NY, NY, 1996.
 Getting a driver’s license is the one thing that would make Remy’s and Morgan’s lives nearly perfect.  And it seems as if it’s going to be easy and fun.  After all, Mr. Fielding, the Driver’s Education teacher, thinks his course is a joke.  With their already licensed friend, Nickie Budie, Remy and Morgan take the stop sign at the corner.  When this action has fatal consequences, they are forced to deal with death, guilt, and the responses of their friends and families.  The teenagers struggle to do the right thing in the face of their crime.  This book is excellent for statistical purposes.  Have students look up statistics regarding traffic fatalities caused by young drivers in your county.  Compare the statistics with those of neighboring counties.  Goal 4:  4.01, 4.04

Hatchet, Gary Paulsen, Viking Penguin Press, NY, NY, 1988.
 In Hatchet, thirteen year old Brian Robeson learns to survive alone in the Canadian wilderness after a plane crash.  He only has his hatchet and his own resourcefulness to survive in the woods.  Brian draws on various math skills to help himself survive.  He has to calculate how many days his food will last, and he must estimate distances when he is hunting.  Ask students to create math problems and graphs on specific situations or incidents.  Goal 4:  4.01, 4.02, 4.03

The War With Grandpa, Robert Kimmel Smith, Delacarte Press, NY, NY, 1984.
 When 10-year-old Peter Stokes finds out that his newly widowed grandfather is coming to live with the family, he is glad because he really like his grandfather.  However, when he discovers that the plan is for his grandfather to take Peter’s room, Peter declares war upon his grandfather to recover his rightful property.  Family love is not destroyed, but attacks and counterattacks escalate until Peter finally surrenders—or does he win?  Peter Stokes had lived in the same house all his life.  Many people move one or more times while they are growing up.  Record how many students were born in your town, how many have moved once, twice, etc.  Make a bar graph of the results, or use the scale on a map to figure students’ moves “as the crow flies”.  Make a bar graph of the distances from zero to the highest number.  Goal 4:  4.01
 

 Chronology of Text-  Data, Probability, and Statistics:

Kindergarten-
Willoughby, Steven S., et al., SRA Math Explorations & Applications Level K, McGraw-Hill Company, Ohio, 1998.
 Students will begin by sorting and describing objects according to attributes such as size, color, weight, etc.  Students will create floor and table graphs with actual objects.  The students will have the opportunity to experience organizing data and interpreting bar graphs.  Children will gain knowledge in constructing bar graphs.

First Grade-
Willoughby, Steven S., et al., SRA Math Explorations & Applications Level 1, McGraw-Hill Company, Ohio, 1998.
 Students will collect data and record using tally marks.  Class will make their own bar graphs using manipulatives.  There are opportunities to collect data and report it using picture graphs, which are all supplied.  The teacher will teach how tally marks, numbers, and bar graphs are related.  Students will learn to use bar graphs to record data from exploration of probability.  Graphing is used as a method of analyzing data and representing statistical relationships collected through simple surveys.  Bar graphs created with physical objects are often used to generate discussion and explore fundamental concepts in probability and statistics.

Second Grade-
Willoughby, Steven S., et al., SRA Math Explorations Level 2, McGraw-Hill Company, Ohio, 1998.
 Students will create and interpret picture graphs and bar graphs, and use them to predict.  Students will identify information on a labeled picture map. Students will understand how to use a pictograph.  There will be a focus on maps where students will draw conclusions from a pictograph. As the year progresses, students will learn to read and make bar graphs, and horizontal bar graphs.  Students will learn to draw graphs on grids, and will understand how to base conclusions on graphs.  In this text, picture graphs serve as a means of transition between concrete and bar graphs.

Third Grade-
Burton, Grace M., et al., Mathematics Plus, Harcourt Brace Jovanovich, Inc., NY, NY, 1992.
Initially, third graders will learn about collecting data.  Collecting data in this grade level includes gathering information from surveys and class experiments.  After students have learned to effectively collect data according to standards, they will analyze data given a situation or a table.  Students will then begin to organize the data they collected into tally tables with the complexity increasing to schedules and pictographs.  Children will do graph plotting/points on a grid/coordinating before they use bar graphs for analysis.  The text ends the strand with constructing bar graphs.

Fourth Grade-
Kanter, Patsy F., et al.,  Math Central, Houghton Mifflin, 1999.
The fourth grade data portion of this book begins with basic collecting and recording data. The next few lessons include organizing data by bar graphs, stem and leaf plots, circle graphs, and even using some algebra for line graphs. Algebra problem solving strategies are also used to begin the process by making a list. The teacher should lead the children through how to use data and problem solving decisions such as," Is the answer reasonable?" There is a mid-chapter review before going further. Once past this point you begin making predictions and comparing probabilities. At this point they go back to using lists, line plots, and other ways to display data. This ends the fourth grade data chapter and there is a chapter test. To close the chapter there is a cumulative review and time for analyzing errors.

Fifth Grade-
Math Central, Houghton Mifflin, New York, NY, 1998.
 This fifth grade textbook is an excellent source for teaching math, and particularly data collection and organization through probability and statistics.  The textbook provides this information in primarily two chapters in the book.  Chapter four discusses collecting, organizing, and using data, and chapter twelve talks about ratio, percent, and probability.  Throughout the text the themes of data collection and organization, graphs, measuring data, and probability interrelate to provide a solid foundation for students to understand probability and statistics.
In the topic of data collection and organization the focuses include:  experiments and sampling activities, counting, surveys and questioning, outside resources, tallies, tables and charts, frequency tables, stem-and-leaf plot, and systematic counting- tree diagrams or lists.  The topic of graphs- readiness for median, mode, and range includes:  pictographs, bar graphs, line graphs, circle graphs, scales/intervals, double-bar graphs, double-line graphs, plotting data- line plots, and choosing appropriate graphs to make.
Measuring data includes:  averages or means, range, median and mode, and clustered and un-clustered data.  Lastly, probability includes:  concept of chance- games, combinations, likely or unlikely events, certain or impossible events, predicting and guessing, probability and area- using spinners, probability ratio or fraction, multiple outcomes, experimental probability, and theoretical probability.  This textbook gives a thorough approach to probability and statistics that challenges and motivates teachers and students alike.

Sixth Grade-
Charles, Randall I., et al., Math, Scott Foresman-Addison Wesley, 1988.
 In this textbook, Chapter 1 was completely dedicated to “Collecting, Analyzing, and Displaying Data.”  The authors of this textbook divided the chapter into three sections.  Section A discussed “Statistics-Real World Use of Whole Numbers, Section B “Displaying Data”, and Section C “Describing Data.”  Section A’s main focuses is learning to read graphs, understand simple data, and applying the information for the graph.  The three lessons for this section include reading graphs, misleading graphs, and scatter plots and trends.  The more in depth way of displaying different data comes in Section B game.  The types of graphs discussed were tallies, frequency charts, line plots, scales, bar graphs, and stem-and-leaf diagrams.  There are several ways in describing data, and section C has all of the ways to apply the data and be able to understand what information is being produced.   The median and the mode are describe in detail, along with ways of incorporating this idea with other topics.  Also, to sum up the chapter on data, the effects of outliers are discussed.