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This activity provides students experience collecting and analyzing data.
Math by All Means: Probability Grades 3-4 by Marilyn Burns
About Teaching Mathematics: A K-8 Resource, 2nd Edition by Marilyn Burns
Part 1 of this lesson introduces children to probability through an experiment in which one outcome is more likely than the others. The experiment provides experience for children to collect and analyze data. The probability of spinning each number provides a context for talking about fractions and percents and engages students in comparing the areas of the regions of a circle. Making their own spinner gives children practice in following directions and helps develop their fine motor skills.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
Invitation to Learn
Hold up the sample spinner you made. Tell students they are going to make a spinner like yours. Ask what they notice about its face. Spin the spinner and point out how the indicator line tells what number the spinner lands on. Demonstrate for the children how to make a spinner.
Directions for making a spinner:
Demonstrate for the students how to do the spinner experiment:
Pose a part of the problem:
Ask, When you spin the spinner, is any number more likely to come up than any other number? Why do you think so? Explain: You can keep track of spins on a graph recording sheet that is 3 squares by 12 squares. Demonstrate for the class how to spin and record on the graph. After three or four spins, ask, What do you think the entire graph will look like when one number reaches the top of the paper? Ask, Which number do you think will reach the top of the recording sheet first? Write your prediction on paper.
Present the problem to be solved:
Explain: Each of you will use your spinner and graph recording sheet to conduct an experiment. When one of the numbers reaches the top, youve completed the experiment. Cut the 3 x 12 recording sheet apart from the graph paper. Then post your 3 x 12 recording sheet on the board under the winning number. (Have students tape their graphs to the board under the heading 1, 2 or 3).
Students should conduct the experiment three times (using their entire graph recording sheet).
Discuss the class results when all students are finished comparing the results to their predictions. Most likely, 3 was the winning number, but there will be instances of 1 or 2 as winner. Ask: how might we find out if 3 actually comes up in half of all the spins?
You could have students take their graph recording sheets and cut apart each column. Then cut off any blank squares. Have small groups of students then tape their 1s end to end. Continue doing this with the 2s and 3s. Next combine each group’s strips of numbers together to get one long strip of 1s, 2s and 3s. Tape one end to the chalkboard. This will provide a visual for students to see which number actually won. See “Homework & Family Connections” to add to this activity.
Homework & Family Connections
Each student can take their spinner and one graph recording sheet home to conduct the experiment again. Explain to students that they are going to gather more data to add to their first experiment. Ask students why this would be helpful. If students do not suggest it, tell them the mathematical theory of probability says that the more times you spin a spinner, the closer the results will match the theoretical distribution.
The next day, have students again cut apart their numbers, discard blank squares, and add to the class strip of 1s, 2s and 3s. Discuss the results. If there is time, have students actually count the number of 1s, 2s and 3s. This could be accomplished by cutting the strips into groups of ten, then compiling the 10s to form hundreds and so on. Some students may devise their own strategies for counting. Divide the strips among small groups for counting, then gather together for a class total.
Discuss the total numbers finding out if there were any surprises with the additional data. Ask, “Does the mathematical theory of probability (gathering more data) seem to be evident in our experiment? How can you tell? Can you find a way to prove that 3 came up in half of the spins?” Add applicable questions and discussion.
Have children write about what they did, what they had predicted and what the results were. Pose these questions to students who might not know how to begin:
How do the class results compare with your prediction?
How did your individual experiments compare with the class results?
Why do you think mathematicians say that a large sample of data is better for analyzing information than a small sample of data?