Probability does not show up in the standards until 6th grade, but even my 4th graders love it and have an understanding after the unit is completed. I use a unit on Probability to teach critical thinking skills and data analysis (MP1 - make sense of problems and persevere in solving them).
In this lesson your students will become what I call mathematical scientists - predicting (students will need to use correct vocabulary or MP 6) which number will be rolled most often (2-12), gathering data and analyzing the data. Starting with a small sample size(individual) and then putting together a larger sample (whole class). This directly aligns with MP7 where students look for and make use of structure.
In this lesson students are exploring how many times they roll all possible sums on a pair of dice. I first read the story Jumanji by Chris Van Allsberg to get them interested. Students need to feel connected to their learning and what child has not played a game where they roll the dice to win? I read the story bringing out vocabulary words and asking scientific questions about monsoons and hot lava hitting the water causing steam to rise. I pull out items specifically tied to what we are learning – water into a gas, water cycle, monsoons = precipitation and rapid erosion.
When you get to the part where is says “If you roll a 12, you can get out of the jungle,’ said Peter.'” Stop and ask your students, “Do you think it is unlikely or likely Judy will roll a 12?”There are many ways you can have your students share their answers but this time I have mine talk to a partner and I listen in as I circulate. After the conversation dies down, I ask the same question and toss the Koosh ball to a student and they answer and then toss the Koosh to another student. Student answers will be something like (MP2):
I think it is unlikely because it is a big number.
I think it is unlikely because there is only one way to get 12, six plus six.
I think it is likely because I always roll doubles.
I think it is likely because it is the biggest number.
From these answers, and the conversations I overhear, I know my students are all over the board with this type of math. I am looking forward to the "Ah Ha" moments I know are about to happen.
I finish reading the story and bring the students back to page where Judy wants to roll a 12 to get out of the jungle.
I ask “What sum do you think she will most likely roll?” and tell them to talk with a partner. I do not have them share because I want the excitement of discovery as they do the activity. I give each student the handout Roll to Win and a pair of dice. I picked up a bag of dice inside a dice or you could use two different colors for each student. There is an important reason for the two colors later on.
Explain to your students they will be recording the sum of the dice roll to create a graph (MP4). They can put an X or they can record the addition sentence in the box. Each time they roll they must record the answer. If they roll 2 and 3 they will put an X or 2 + 3 in a box next to the 5. You will have questions such as, “I rolled a 2 and 3 last time and then I rolled it again do I record it?” Yes they need to record it because they are recording which sum appears the most often. “If I roll a 2 and 3 and then a 3 and 2, do I write both of them because back in the beginning of the year you said this was the same thing or the commutative property?” Here is the reason for the two different colors. I point out that they are using two different dice so the answers are different and both can be recorded.
Many of my students were able to do more than one page giving us a larger sample size.
After each student completes one handout, some can do more than one giving a larger sample of data to analyze, have your students share with you the number that "won." I did this following a pattern I created in my class I call the "Whip Around." There is an order the students follow from one person to the next in giving their answers. I recorded these on another blank Roll to Win handout.
I had to add a second page to be able to include all of the data.
After I have the answer from the last students I say "You can say it out loud. Which one won?" In unison they say "seven!"
Then ask your students to discuss why 7 is the most often rolled number.
Give your students some time to talk about why 7 is the most often rolled and then walk them through all the possible ways to get the sums from 2-12. You can also ask why 1 is not an answer on the Roll to Win record sheet - there is no possible way to get a 1 when two dice are rolled.
You can see how I recorded their answers in the picture (MP4 and 5). Seven is the sum with the most possible addends.
Students need to reflect on what they have learned to increase comprehension and retention.
I ask my students three questions for them to reflect on, verbally this time.
1. What did you learn about probability?
I am looking for an answer that reflects analytic thinking about likely/less likely outcomes - 7 had a more likely probability of being rolled because it has more addends.
2. What did you notice about your thinking while you were doing this lesson?
There isn't really any wrong answer to this question because it is based in opinion. I hear answers such as, "I started thinking about patterns." "I had to really think, and I could feel myself thinking, when I was trying to figure out why 7 happened more."
3. What did you to help this lesson be successful?
With this question I am having the students think about their own behavior and if it was positive or negative towards a learning classroom environment. If a student responds with a positive comment I thank them. If they respond with a not so positive comment I ask them what their plan was for doing better the next time.