|Didax "Class Ideas" Newsletter Archive
|Here at Didax, it's our favorite time of year as April showers give way to May flowers and horses are at play in the fields around us. If spring weather makes you frisky, this month's topic will make you friskier. Class Ideas is getting ready to roll the dice with a close-up look at probability.
First up is an article and sample lesson by veteran teacher Mary Saltus on how to use dice play as a probability lesson. Mary is one of the authors of the new Didax math resource, DICE ACTIVITIES FOR MATH. This issue also brings you downloadable activity pages from this unique new book, Internet links to interactive probability activities, and a subscriber-only special that promises big savings on our dice activities book. The fun is just a "dice toss" away!
Cindy O'Neill, Editor
| Introduction to Probability: A Dice/Graph Lesson
|Some Ideas on Randomness and Fair Chance for Grades K-1
by Mary Saltus
Dice Activities for Math, a new Didax publication, has over seventy dice activities for students in grades K?3 that build number sense and generate a conceptual basis for addition and subtraction of number facts. These dice activities can also provide young students opportunities to experience, discover, and dialogue the concept of probability--the chance that an event is likely, unlikely, or impossible to occur.
The scripted lesson below, using the One?Die Graph from Dice Activities for Math, provides a structure for exploring with students the concept of randomness of die tosses and the idea that "fair chance" can appear to be quite unfair. The lesson is completed when one number at the bottom of the graph has been tossed six times and all six boxes above the number are filled in.
In discussion, students will agree that when a die is tossed, each of the number patterns has a "fair chance" of being tossed. Young students enjoy guessing what number will be tossed and sharing their guesses with their peers. Some students frequently guess the number that is tossed. Herein enters the concept of randomness, making the idea of "fair chance" fuzzy. Why do some students guess the correct number and others never do? Or why do the same numbers keep coming up? It seems that not all the numbers have a "fair chance" of being tossed. Students often equate fair with equal.
This lesson involves students working with a partner, communicating their responses and ideas. The use of partners gives each student the opportunity to respond to a teacher?s questioning, thus actively participating in every part of the lesson. Asking students to show the number tossed by holding up that many fingers keeps students engaged, physically and mentally, and gives the teacher an instant check.
Students are asked to guess what dot pattern might be tossed. When tossing a die, one can predict with certainty that a dot pattern 1 through 6 will show, but one cannot predict which dot pattern is more likely or less likely to be tossed. This becomes a guess, at times a lucky guess, but a guess.
As the lesson progresses and the graph boxes are filled in, students predict what number might have all six boxes filled in first. Prediction implies some available information to use to make a judgment, i.e., the numbers on the graph.
The lesson ends with the teacher and the students creating the "story" of the graph, verbalizing the progression of tosses and predictions.
Students then partner up, toss their own die and fill in their own graph, and tell their ?graph story.?
One-Die Graph Activity: A Scripted Lesson
Materials: One-Die Graph overhead, dice
(Students are paired and each pair has a die.)
Teacher says: Look at your die. Tell your partner a fact you notice about the die.
(Teacher lists facts on the board.)
Dot patterns 1 to 6
(Student pairs toss their die.)
What number patterns did you get?
Hold up that many fingers that show the number of dots on the die.
Did any one toss a 7? Tell your partner why not.
(Show the One-Die Graph on the overhead.)
Teacher says: Look at this graph. Tell your partner a fact about the die graph. (Teacher records these facts on the board.)
6 boxes across
Each box has a numeral 1 to 6
Numerals in sequence
6 boxes above each number
I will toss a die.
What number do you think I will toss?
Whisper to your partner.
Show the class your guess by holding up that many fingers.
Can we be sure which number will be tossed?
Why? Why not?
Could we say that there is a "fair chance" that any number from 1 to 6 will be tossed?
(Teacher tosses a 3.)
Teacher says: Thumbs up if you guessed three.
(Teacher writes a 3 in the box above the 3 on the overhead graph.
Students guess the next toss by holding up that many fingers.
Teacher tosses die.)
Teacher says: Thumbs up if you guessed the number.
(Teacher looks around the classroom to see how many guessed the number, then writes the number on the chart.)
After about 5 tosses, teacher asks:
Which number on the graph has the most tosses? Tell your partner.
Which number has the least tosses? Tell your partner.
Do any of the numbers have the same amount of tosses? Tell your partner.
Which number has more than __ but less than __? Tell your partner.
How many more would __ need to have 10?
Which number do you and your partner think will reach the top first?
Show the class with your fingers.
(Teacher writes the students' predictions on the board.)
Teacher says: Show with your fingers which number you think I will toss next.
(Continue. After 4 to 6 more tosses, teacher again asks the questions:)
What number do you think will reach the top first now? Tell your partner.
Who wants to change their number that is written on the board?
(Teacher crosses off prediction for each pair of students on the board and writes new prediction next to crossed-off prediction.)
(Continue tossing die until one number is almost to the top of the graph. Again have students predict which number will reach the top first. Change their predictions on the board. Some students might have been "lucky," and many of their guesses were tossed. Emphasize fair chance.)
Teacher asks: Do you think there is a number that does not have a fair chance of being tossed? Tell your partner.
(Ask for explanations as to why it doesn?t have a fair chance.)
Teacher asks: When I toss the die, what numbers are certain to be tossed? (either 1, 2, 3, 4, 5, or 6)
What one number is likely to be tossed? (any one of the 6)
(Teacher continues tossing the die until a number is almost at the top of the graph.)
Teacher says: Look at the graph. Tell your partner which number or numbers you do not think have a chance of winning? Why?
Number _____ has the fewest boxes filled in. Is it likely or unlikely to reach the top first?
Is it possible? What would need to happen for number ___ to reach the top first?
Is it likely? Is it possible? (possible but unlikely)
Number _____ has the most boxes filled in on the chart. It is almost to the top. Can we be sure that it will reach the top first? Is it likely to, unlikely, or don?t we know?
Who wants to change their prediction? Talk to your partner. (Teacher changes prediction numbers on the board.)
Letting students change their predictions of the winning number gives them the opportunity to experience the randomness of events and that "fair chance" is not the same as equal opportunity. Rather it is just as likely as unlikely that a number will be tossed.
When the activity is over, model telling the "graph story":
?At first 3 had more spaces filled in than the other numbers, so I thought it would get to the top first. But then 5 almost caught up, so then I didn?t know which number would get to the top first. Six was just below 5. Two didn?t have any spaces filled in. My last prediction I said 3 would win because 3 and 5 both needed only one more. The next toss was a 2, and then another 2, and then a 6 and a 4, and then a 6, so 6 got to the top first. None of my predictions won and neither of the numbers in the lead won.?
Questions to ask about the graph:
(Students talk to their partners before responding.)
Do any numbers have the same amount of boxes filled in?
How many more does __ have than __?
How many more would __ have if you added 5 to it?
What number would have 9 boxes filled in if you added 4 more boxes to it?
If you add the column 3 and column 6 boxes, how many do you have in all?
Talk to your partner. Make up a question to ask the class about the graph.
About the Author
Mary Saltus holds a CAS degree in human development from Harvard Graduate School of Education and a master's degree from Wheelock College. An elementary school teacher for many years in Sudbury, Massachusetts, she is now retired from teaching and is currently researching the links between understanding math concepts and reading comprehension.
| Downloadable Probability Activity Pages
|Dice activities are a great way to get your students excited about learning math concepts, including probability. See for yourself by downloading these sample pages from DICE ACTIVITIES FOR MATH, a great new math resource from Didax Education. Created and tested by experienced teachers, these engaging, challenging, and fun activities build number sense and generate a conceptual base for number facts. Just copy and distribute the downloaded pages, hand out the dice, and let the games begin!
| Probability Internet Links
|The Internet is a great place to find interactive activities that really bring the concept of probability to life. To get you started, we're providing links to just a few of the clever, original, and instructive activities you can find there. The odds are high that you'll find them worthwhile!
| June Newsletter Theme: Phonics
|Join us in June, when Class Ideas takes a fresh look at phonics. We'll have an article by Liz Baldwin, author of the new phonics game book I Hear with my Little Ear, available from Didax. We'll also have downloadable activity pages and a fantastic special on this practical little book, which aims to enrich the development of children's speech, language, and literacy skill by taking a multi-sensory approach. It's a great way to gear up for summer vacation!