Data analysis and probability are two disciplines that utilize mathematics as a basis for prediction (Van de Walle, 2007). In a global society inundated with statistics, and seemingly under continual time constraints, data driven decision making helps one quickly narrow down the field of possibilities while bright lining the most feasible and lucrative selections. This informed and timely ratiocination also obviates the need for tedious trial and error exercises (Van de Walle, 2007).

Probability has been defined as the measure of the chance that a given event will occur (Van de Walle, 2007). Probability is further bifurcated into two individual strands. In certain situations, logical analysis of an event can determine the exact probability (Van de Walle, 2007).This result is styled the theoretical probability. Other times, collecting data on the relative frequency of an event (the number of designated outcomes recorded by the counter) and placing this numeral over the total number of possible outcomes will result in an experimentally derived percentage of probability (Laureate Education, 2010). Incidentally, a larger number of tries will bring the experimental probability into closer proximity to the theoretical probability (Laureate Education, 2010). In other words the probability of an event increases as the number of trials expands.

As part of this application process we were asked to describe a lesson on probability that we once conducted. We were then requested to upgrade the exercise with strategies learned from last week’s reading, discussions and video resources. The first iteration of my third grade lesson on probability contained the following learning

objectives: the students will practice group skills as they conduct a series of probability experiments, collect and record relevant information, as well as predict, discuss and analyze outcomes. In addition, they will understand the definitions of the following terms: less likely, more likely, equally likely, impossible, certain and chance (Ward, 2010).

The materials included spinners, an overhead projector, tally charts, paper and pencils.

To begin the activity I modeled the use of the spinner in which two colors were equally distributed. I then used the overhead projector to discuss the blue and yellow spinner face and its ramifications vis-à-vis probability. The class was next divided into groups. Tally sheets and individual spinners were distributed. Before beginning the students were asked to predict their individual outcomes. Most hypothesized a fifty-fifty breakdown of the two colors. I then asked volunteers to justify this reasoning. After this, each member of the foursomes spun a total of fifteen times. One team member was asked to add up the tally marks for the group. The teacher then recorded the accumulated numbers from all teams and represented these totals on a chart. Finally, we discussed how chance can influence a small collection of tally marks, but as the sample grows the results will move closer to the theoretical probability and more closely match their predictions (Ward, 2010).

After absorbing the concepts presented during my readings, written discussions and video watching, I decided on the following additions and revisions to the previous lesson. Students’ ideas about probability should be developed from personal eventualities (Frykholm, 2001). Rather than having the teacher axiomatically dictate information, it is more profitable to draw ideas about probability from the students. Ultimately, this will result in a greater learning imprint.

Consequently, as a preamble the lesson, we will explore the ideas underpinning the terms “impossible”, “less likely”, “equally likely” ,“more likely” and “certain” (Van de Walle, 2007). This will help move many of the students from a belief that all outcomes are the result of luck, to one in which they realize that some outcomes are clearly ordained and hence predictable. We began this discussion by opening a dialogue about the children’s experiences with board games. In this manner, I intend to link the familiar with the unfamiliar concepts we are about to encounter. The big idea behind this discussion was that luck plays an overarching role in board games but latter in the lesson we may be able to predict outcomes based on the results of our experiments with probability. After activating prior knowledge, the next activity was a read aloud. This short work of fiction will serve as an engaging introduction to the concept of likelihood. “Manga Math Mysteries: the Runaway Puppy: a Mystery with Probability” (Barriman, 2010), presents a personable introduction to the world of probability as well as its attendant vocabulary (Usnick, McCarthy & Alexander, 2001).

After reading this story aloud and discussing it with the class, I will next present the children with a horizontal probability line of spinner faces (Van de Walle, 2007) Above these colored depictions I will delineate a straight line. This will be labeled the “Chances of Spinning Blue” (Van de Walle, 2007). These faces will range from all yellow (impossible) and mostly yellow (less likely) on the left, followed by half yellow, half blue (equally likely) in the middle. As we move further to the right I will include a mostly blue face (more likely) and finally a completely blue image (certain). (Van de Walle, 2007). As the discussion begins, the teacher will encourage the use of the abovementioned content-related terms. As each face is discussed, a consensus will be reached by the students as to the probability of blue occurring. The instructor will subsequently enter a mark on the horizontal line above the faces to indicate this chance of occurrence (less than half, better than half, etc. (Van de Walle, 2007)). To reinforce these concepts the students will then participate in a classroom scavenger hunt for examples of each of the aforementioned events, i.e., certain, unlikely, etc. (Phillips, 2011).

Part two of the lesson begins with an exploration of “fair” and ‘unfair.” The class will be divided into groups of three. Two like coins are used and the players are assigned points along the following lines: one student earns a point if the result is two tails (Van de Walle, 2007). Another gets a point if the result is two heads. The third player receives a point if the outcome is one head and one tail. At first, the students should generally reach a consensus that each has an equal chance and therefore the game is fair. After a number of trials, it will become apparent that the player with the mixed coins is winning the lion’s share (Van de Walle, 2007). As the teams disperse for a whole class discussion, the class should eventually realize that the mixed-results player has twice the probability of winning (Van de Walle, 2007). This is true because there is only one chance for two heads or two tails to occur, but two chances for a mixed result, i.e., either the first coin comes up heads and the second tails, or the opposite happens (Van de Walle, 2007). Accordingly, this is an example of using hands-on experiments to reach an experimental result that approximates the theoretical probability outcome.

The last addition to the lesson will confirm in the children’s minds the undergirding behind the law of large numbers (Laureate Education, 2010). This dictum states that the relative frequency becomes a closer estimate of the real or theoretical probability as the size of the data sample increases. This concept can be unveiled by simply comparing a small group’s results with the cumulative total of the whole class. Using a half-colored spinner face, some individual outcomes will be skewered to “less likely”, “more likely”, or in rare cases “certain” or “impossible” outcomes on the probability continuum line. However, as these individual results are included in a grand total, the students will watch the experimental probability move very close to an “equally likely” or theoretical stance.

For extension purposes I would have the students identify two different items that can be used to conduct investigations of probability (playing cards, dice, etc.). They would then create an investigation and analyze the collected data determine if the same rule of probability applies using these differentiated manipulatives (Ward, 2010).

Assessment will revolve around how well the students align their performance and products with the objectives. It will also be based on informal observations of their group work, as well as their responses to questions and personal input into the discussions.

In conclusion, I have recently absorbed some very pertinent concepts and strategies to improve my initial lesson plan on probability. To begin, a lesson should relate to the personal experiences of the students (Frykholm, 2001). Secondly, there should be a very gradual sequential outline in place in which the children master basic concepts using a series of multi-sensory experiences (Van de Walle, 2007). There should also be an atypical segment where the students’ initial reasoning is turned upside down (the heads and tails result in the fair and unfair section) (Van de Walle, 2007). This will clear up the misconception that all is as it appears, as well as providing a bridge to the experience of closely scrutinizing results in order to more accurately predict unforeseen results. Finally, I have learned that there is great value in allowing the learners to use different sets of manipulatives to design their own experiments (Ward, 2010). This newly found ownership of the investigation will personalize the activity and therefore reap educational rewards on the highest end of the learning curve.

A Thundercoud of Additional Ideas

Frykholm (2001) suggested, “…[T]hat young children do have intuitive understandings of chance, that these intuitive notions can and should be developed, and that probability explorations in the early grades can enhance children’s probabilistic thinking, number sense, and mathematical connections” (p. 112). The meaningful experience that I have developed for my younger students can also be extended and used with my older Title I students. This experience is perfect for this time of year, as Easter is just around the corner. I believe that anytime we can integrate subject areas, holidays, and real-world experiences with math, students gain more insight to the mathematical concepts being taught.

I would begin to introduce the idea of probability by reading a few stories about Easter eggs. Any stories showing pictures of eggs would spark discussions about the attributes of the eggs in the stories. Next, for my younger students,I would have them conduct an experimental probability event. For this experiment, I would tell the students how many of each color of plastic Easter eggs I put into a bag and ask them to make a prediction about which color they think will get picked most often. Then, I would break my students into groups and ask them to conduct the experiment by drawing out one egg and recording their results; reminding them to replace that egg before drawing a new one. Each group would continue recording their results until they had reached 25 outcomes.Once each group had finished, we would come back together as a group and discuss their results. We could then combine each group’s results to make a class graph. At this time, we would also discuss probability vocabulary; such as, certain, impossible, likely, and unlikely. Finally, we would look back at our predictions and discuss reasons for whether they were correct or incorrect.

With my older students, I would not let them know ahead of time what color or how many of each egg I put into the bags. They would conduct the same experiment, only they would be trying to figure out what color and how many of each egg I included in the bag; much like Frykholm (2001) described in the “peek box” experiment (p 114). Again, we would meet as a class to discuss the results, explain the vocabulary as explained in the experiment for the younger grades, as well as, independent versus dependent events. Throughout the discussion students would attempt to identify what colors and how many of each egg I included in the bags. We could then tie this into theoretical probability by observing all the possible outcomes.

Van de Walle, Karp, and Bay-Williams (2010) suggested that, “The use of random devices that can be analyzed can help students make predictions about the likelihood of an event” (p. 457). Therefore, another idea I would incorporate into the experiment with my older Title I students, after we have discussed their results, is the likeliness of each egg being pulled from the bag. I would take one of the bags and ask students what the likelihood is of pulling out each of the different colors. They could respond by telling me the fraction; such as, 4/15, or my chances of pulling a blue egg would be 4 out of the 15 total eggs in the bag. Thus, helping them to gain a better understanding of fractions at the same time they are learning about probability. Another extension for my older students would be to incorporate attributes of the eggs. For example, I could draw dots and/or stripes on the eggs and include these attributes along with the color much like Mrs. Whatsit’s socks probability experiment (Usnick, McCarthy, & Alexander, 2001). By having students conduct the experiment(s), record the results, and compare with the other groups, these experiences should help children, “…begin to develop their intuitions, recognize what “should” happen when an event takes place, and be able to explain unlikely outcomes as products of chance…” (Frykholm, 2001, p. 117).

-Lisa

On Mondays, I have the kids sit in a circle and share their favorite or least favorite thing they did over the weekend. One of my students always tells us that he played video games. Last Monday, however, he chose not to share. After all of the kids had a turn, I asked, “What do you think “child” probably did over the weekend?”. Because of his history giving his weekend update, the whole class responded, “played video games.” He seemed annoyed, but my students used what they knew about “child” to make a valid prediction regarding his weekend activity. Frykholm (2001) says that children have the ability to build inferences based on recognized patterns. My class has definitely recognized a pattern in “child’s” weekend activities!

I have never really given much consideration to “teaching” probability. Data analysis is more the direction of Georgia’s standards in elementary school. However, there is an activity that I have my students complete on the 100th day of school. Using a dice and a teacher made worksheet, the student predicts which number the dice will display on top the most after rolling 100 times. Then, the student marks a tally for the corresponding number each roll until he/she has rolled 100 times. Last the student records the results at the bottom of the page. Because second graders do not fully understand predictions and estimations yet, sometimes, students want to change their original prediction of which number would occur most frequently. Hence, I am able to explain that no matter how many times we roll the dice, the chance that a certain number will appear on top depends on many things. Usually, the students are rotating in centers. So, it is typical for each student to make a different prediction and also have differing results.

After considering this activity, I now understand that I should probably follow the activity with a graph and have the students record each of their results. Using the graph, the class could then determine what number is more likely to be rolled the most when rolling a dice 100 times.

-Jan

As with all mathematics concepts, I begin teaching the concept of probability stressing the importance of my students understanding and being able to fluently use the key vocabulary terms that pertain to the concept. According to Van de Walle, Karp, and Bay-Williams (2010), “To begin refining the concepts that some events are more or less likely to occur than others, introduce the idea of a continuum of likelihood between impossible and certain” (p. 459). Students are first taught the difference between each of the terms. If something must happen it is certain, and if something cannot happen then it is impossible, with likely, equally likely, and unlikely falling in between the terms certain and impossible. My past experiences with probability have shown that most misconceptions occur when students are not sure when an event is impossible or unlikely or when one is certain or likely. I end up having to stress that if there is any chance that an event can happen, but it probably will not, then it is unlikely but not impossible, and if there is any chance that an event will not happen, but it probably will, then it is likely not certain.

As a 4th and 5th grade mathematics teacher, when teaching the concept of probability I try to make the learning experience as meaningful as possible by including the students as much as possible. When discussing the terms, I give the students an example of each term while at the same time allowing volunteers to come up with some events as well. For example, I might tell the students that it is certain that tomorrow will be whatever the next day of the week will be and then ask them to think of something that they are certain of. This year, I even followed up that activity by having the students work in groups to come up with an example of each type event, certain, likely, equally likely, unlikely, and impossible. Prior to the activity, I posted five pieces of chart paper around the classroom, one for each of the terms, and had the students go around the room as a group from one chart to another adding an example of each term as they went. The students enjoyed participating in the activity and coming up with examples that were different from the other groups before them, and I felt that it really helped them to develop a better understanding of probability.

-Crystal

I would start my students with an activity similar to the peek box that Frykholm (2001) introduced. I would try to link this idea to another math standard that the students had previously worked on. For example using a box or a bag which students could reach into and pull a three dimensional shape from. Placing a set amount of each kind of shape into the bag, such as three cubes, two cylinders, and 1 sphere, would give the students an opportunity to explore chance as the students with the marbles did. This type of activity was recommended for kindergarten to second grade students, but third graders who hadn’t been exposed to probability could start here and quickly progress.

The next step then would be to be to move to an activity such as the sock activity presented by Usnick, McCarthy, and Alexander (2001). The authors used probability with an attribute set to examine possible combinations of characteristics of socks. I could continue to use the three dimensional shapes and combine other attributes rather than just the shape itself. I could use different colors of the same shapes, or even use the properties of the shapes, such as flat surfaces or curved surfaces, and number of edges or vertices. Students could continue to pull the shapes from the bag and record the results to analyze the data they collect.

It seems that there are many activities available for introducing probability that involve spinners, pulling from bags, or dice. I am interested in finding additional ways to engage and involve students in the process of exploring probability.

-Jen

Van De Walle, Karp, and Bay-Williams,(2010) states that probability is a measure of the chance of an event occurring. It is a skill that most students use very frequently inside and outside of the classroom environment without really realizing they are using a mathematical concept. Students must be exposed to probability concepts through seeing and hearing the language of it everyday in the classroom (Frykholm,2001). I adhere to his beliefs, because as a 4th grade mathematics and reading teacher, I have found many opportunities to introduce the skill to my students during reading. Students are often allowed opportunities to ask questions, make predictions, and discuss the likely hood or unlikely hood that an event will occur or not occur, such as what are the chances that all of the girls in the 4th grade will tryout to become a cheerleader this Fall.

As a 4th grade mathematics teacher,I believe that it is imperative that students are introduced and taught the mathematical terms and synonyms to all concepts being learned. They need to understand that chance, probability, likeliness, odds, and etc means the same thing. As stated by Frykholm, (2001) helping young children think of probability in terms of chance is fruitful, which I also agree.

I have introduced the concept of probability to my students with a hands on activity. I had a red and blue bag. The bags were labeled bag A and bag B. Bag A had 28 red marbles and 2 blue marbles and bag B had 15 red marbles and 15 blue marbles. I had students make a prediction about what colors they thought that I would pull from each bag.I believe that the majority of the students in my class, as well as the students in the peek box and two dice game activity were successful because of the hands on activities involved in learning the concept.

-Cindy

Fourth grade students will be placed into groups of two. They will play the game of “Eenie, Meenie, Minie, Moe” recording their outcomes (Frykholm, J., 2001). They will play and record the game 10 times on a chart showing the outcome when the rhyme starts with the person saying the rhyme. Next they will play the game starting with the person who was not saying the rhyme and record the results. Students will then be divided into groups of three. They will play the game recording the results when the rhyme is started by the person saying the rhyme. The process will be repeated starting the rhyme with the second player and the outcome of all 10 games will be recorded. The game will be repeated starting with the third player and the results will be recorded. The game will be played a 3rd time. The students will be divided into groups of four and the steps stated above would be repeated for each student. Students will return to their desk and combine the results on a chart when the game was played with 2, 3, and 4 players. The chart would be used to help students recognize all the possible outcomes and discover how the activity falls under theoretical probability. Students will discuss the outcome and determine if the results could be predictable. From the information on the chart students will be asked if the group continued to increase in size could they predict the outcome for a group of five, seven, and ten. Students would be asked to explore how the results changed when the starting of the rhyme changed from the person saying the rhyme to the 2nd person, 3rd person, and 4th person. Words related to probability such as independent and dependent circumstances will be explored using the chart to guide students toward explaining how the outcome depends on how many students are in the group and what player the game started with.

Dr. Warrick explains there are two types of probability problems which are theoretical and experimental (Laureate, 2010). The game “Eenie, Meenie, Minie, Moe” is predictable. The person who is saying the rhyme is able to manipulate who wins by knowing how many players are in the game and knowing where to start the rhyme. As Van de Walle, Karp, & Bay-Williams (2010) conveys the need to create a chart that list all the possible outcomes when working with theoretical probability problems. Implementing the above activity would improve the way I teach probability since students’ are directly involved with each step of probability. By having students illustrate the outcome in a variety of ways, students gain a deeper understanding about probability due to being involved solving the problem, making sense of the outcome, listing the outcome eliminates guessing, provides experience with probability, and stimulates an interest in probability (Van de Walle, Karp, & Bay-Williams, 2010). Students create a personal experience as they plan, predict, carry out, list, analyze, discuss, and explain the results (Manchester, P. 2002).

-Jan

Probability, the chance or likelihood of an event happening, is an essential skill and always fun to teach! I begin this topic by reading a book and drawing a likelihood line on the board, which offers a great introduction into the vocabulary of probability. Since I teach math and science, the vocabulary is something that I use all year long so the students are familiar with the terms, however they are expected to use them from this point forward. Frykholm (2001) reveals, “we might foster this development [language] by using the following words as descriptions of the likelihood of events: certain, impossible, likely, or unlikely…children continue to develop their probabilistic thinking by beginning to predict expected outcomes” (p. 113).

Literature plays an important role in my classroom, in any subject. This unit is usually begun by reading “Probably Pistachio” by Stuart J. Murphy (2001). This book offers a great start to probability, predictions, and the vocabulary I want my students to use. After reading the book and asking questions to generate good discussions, I draw a horizontal line on the board and ask students if it will rain gumdrops today. My questions and statements guide them to say, “it is impossible.” I then write the word impossible on the extreme left end of the line. Next I ask the students if it will get dark tonight, again guiding them to say “it is definite or certain” and write the word certain on the extreme right end of the line. From here we list one or two other ideas that fall into those two categories. The next step is to add likely and unlikely onto our line, discussing their meanings. Students are then divided into small groups, given little post-it notes and asked to come up with three events for each word on our likelihood line. Once the allotted time has ended, students alternate coming to the board with a sticky-note event from another group, placing it in the appropriate spot on the likelihood line and telling the class why they chose that location. This activity, along with the book, provides the opportunity for an excellent introduction into probability. Usnick, McCarthy, & Alexander (2001) remind us, “using children’s literature in the mathematics classroom is a wonderful way to integrate the curriculum and give students opportunities to view specific content knowledge, such as probability, as part of a connected whole” (p. 249).

-Shelby

Probability can be a difficult concept for young students, if they are taught on level too high for them to understand. Students need to grasp the meaning of the vocabulary associated with probability and why probability is an important life skill. I like how the teachers presented and taught the meaningful concepts of probability in this week’s resources. “The story of [Eenie, meenie, minie, moe] points toward the premises that young children do have intuitive understandings of chance, that these intuitive notions can and should be developed, and that probability explorations in the early grades can enhance children’s probabilistic thinking, number sense, and mathematical connections” (Frykholm, 2001).

To teach my students probability I embed the vocabulary in daily lessons. For example, my students earn tickets for good behavior, classwork, and preparedness. I often explain that the more tickets they earn the more likely their ticket will be pulled on Friday for a prize. I often pose questions, for example, who has more of a chance of winning a prize? Or, is likely that “Alex’s” ticket will be pulled if he was absent three out of the five days this week? These questions make them think about their behavior more, but it is also gearing them up for our probability unit. Introducing my students to the vocabulary and real contextual usage of probability gives them more confidence for learning the more in-depth concepts of probability, such as, expressing probability as a faction or tree diagram.

-Natalie

Research tells us that children have intuitive understandings of chance (Frykholm, 2001). Consequently rudimentary probability explorations in the early grades enable the learners to tap into this innate ability. These investigations result in the child’s acquiring a sharpened sense of numbers as well as a stronger grasp on ideas related to probability (Frykholm, 2001).

In the first and second grade a productive initial step in introducing probability is to use simple phrases such as “the chance of such and such happening is more likely, less likely, certain or impossible” (Frykholm, 2001). Next, we should use the students’ every day experiences as a canvas to introduce probabilistic thinking. These might include, “What are the chances you will be older next year?” (Certain). “What are the chances it will snow next July?” (Impossible). And so on (Frykholm, 2001).

A short lesson that introduces some of these basic ideas follows.

Here the students will construct spinners on a sheet of paper. They will use a pre-drawn wheel which has three quarter of its area colored blue and the remaining quarter shaded yellow. Each child (after appropriate modeling by the teacher) will then construct a spinner using a dot in the center of the wheel, a pencil and a paper clip (Power to Learn, n.d.). The instructor will explain that this will be a group effort and that all the tally marks will be added together for a class total. After making a prediction as to which color will collect the most marks (and justifying their reasoning), each pair of students will spin a total of twenty-five times and use a table to record their tally marks. Once all the data has been collected and “blue” declared the overwhelming winner, the class will discuss the reasons for this outcome. At this point the teacher again encourages the use of “more or less likely.”

Lastly they will revisit their prediction in order to validate or negate that preliminary hypothesis. Afterwards the children can use another template-created wheel and choose different colors and ratios to further explore the embedded concepts (Power to Learn, n.d.).

Summing up, this is a very basic introductory lesson. At its conclusion, the children will understand the concepts of more or less likely, certain, and impossible. They will also realize the connection between more likely scenarios and more likely outcomes, as well as perceive the link between less likely, certain and impossible scenarios and their respective results.

-Dennis

As noted by Frykholm (2001), early studies of probability should focus on such experiences involving the likelihood of events, chance, fairness, and uncertainty, “as opposed to asking children prematurely to view probabilities as numbers, calculations, and ratios” (p. 113). Moving students along on the “probability continuum” requires the appropriate development of basic skills and concepts (Frykholm, 2001). Once the beginnings of probability concepts have been fostered, students can move into deeper probabilistic concepts and skills.

Once I have ensured that my 4th graders have had experience with simple experiments involving probability, such as with number cubes, coin tossing or determining the likelihood of events using a spinner, I would have them work with probability at a higher level. An experience that would be meaningful for students is working with tree diagrams to determine possible outcomes for various situations. Students would be given probability problems in which they would need to determine possible outcomes of independent events. One probability problem that I could have students use a tree diagram to solve is determining the number of choices for a snack one would have if the choices were orange juice or apple juice and cookies or chips. I would first have these items present in the room and ask students to come up and demonstrate all of the choices they could have. Providing students with real items to manipulate helps them bring the problem into perspective. Of course, as students work with the drinks and foods, they may begin to realize that some students are repeating choices that have already been shown or that they can not remember all of the combinations that have been made. Here is where I would introduce the idea of using a tree diagram to solve the problem. Using a tree diagram makes probability problems simpler to solve because it gives students a visual of all possibilities. Furthermore, the diagram helps students organize the combinations they make

-Cassondra

One activity that I use with my students is the exploration of mini M&M packages. We look at the number of candies in each package and the color of each candy to determine the likelihood of pulling each type of candy out of the bag. I use this experiment to discuss the concept of theoretical probability based on the fact that there are six different colored produced by the company. Based on this information we can conclude that there is a one in six chance of getting each color out of the bag. I then challenge the students to test this theory by figuring out how many candies of each are in their bag and the students discuss the comparison of the experimental probability verse the theoretical chance. This discussion takes place in order to guide the students to determine reasons for the differences in probability.

Once this activity is complete extensions can take place. Students can explore the concept of “and” and “or” much like in Usnick, McCarthy, and Alexander's experiment with Mrs. Whatsit’s socks (2001). Here students would determine the theoretical possibilities by charting out all of the possible candy color pairs. From here the students would be challenged to determine the possibility of pulling out different pairs of combinations to determine if “and” combinations would be more likely to occur than “or” combinations.

-Caitlin

As a first grade teacher, when developing meaningful experiences to teach probability concepts, I would use manipulatives that would allow students to “engage in probabilistic thinking through the use of hands-on models…” (Frykholm, 2001, p. 113). All of my first grade students love candy! They enjoy any opportunity that they might have to eat it, not alone use it during math. I was thinking about having my students investigate how many of each color Skittles candies are in a single bag. Skittles are made to be red, green, yellow, orange, and purple. But, how many of each color would you find in each bag? I will begin the lesson by asking students “What is your favorite flavor of Skittles?” I will chart the students’ responses using a tally chart. I would then ask “How many of each color do you believe would be inside a single bag of Skittles?” Students will write their predictions on a piece of paper. I will probe more by asking students “Which color are we more likely to find inside the bag?”

As a class, we will open up a bag of Skittles candy. We will sort the various colors in order to count them. Students will check to see if their predictions were correct. I would then ask “Do you think that the same amount of each color is inside of each Skittles bag?” Also, “Do you think that the same color would be more likely to have the most inside of the bag?” Once students think about these questions, I will open up another bag of Skittles candy. We will repeat the same process of sorting the colors and determining which color appeared the most. Students will then have a discussion about if they think that the company makes each bag the same or different. Students will also make suggestions as to why they feel their responses are correct. To extend this activity further, students will write a letter to the Skittles Company to discuss their findings after opening six bags of Skittles.

I believe this activity allows students to make connections to real-world experiences. Students are not only able to make predictions about what they expect to see, but they were able to sort and graph their responses. Students also will have the opportunity to write their results in a letter to the company addressing their findings and suggest their thoughts about if they thought that each bag was fair or unfair.

-Mary

Recently, I taught a lesson on probability utilizing the terms equally likely, unlikely, likely, certain, and impossible. As a whole group we went over the definitions of each term. I had a jar of different colored marbles and a brown paper bag. I put ten white, four black, and one yellow marble in the bag. These colored marbles were also written on the white board so students would remember what was in the bag. Before pulling the marbles out of the bag, I made a statement about the probability of pulling out a marble using the new vocabulary. For example, It is unlikely to pull out a yellow marble because there are not as many as the other colors.

After the activity was modeled I gave each cooperative group the same materials as I used. Each student had a chance to put a selection of marbles into the bag. The other students in the group had to state an outcome using the new vocabulary. The students then pulled out the marbles and recorded the color pulled out on a tally table. They each were able to pull out a marble five times. Every time it was pulled out it had to go back in the bag before the next pull.

My third grade students really enjoyed this activity. For closure we came back as a whole group and each cooperative group shared about their probability experiences.

-Cherie

References

Barriman, L. (2010). Manga math mysteries: the runaway puppy: a mystery with probability. New York NY: Graphic Universe.

Frykholm, J. A. (2001). Eenie, meenie, minie, moe . . . Building on intuitive notions of

chance. *Teaching Children Mathematics, 8*(2), 112–121.

Laureate Education, Inc, (Producer). (2010) [Motion picture]. Program Two, “Making

Predictions and Probability” Baltimore: Warrick, Pamela.

National Council of Teachers of Mathematics, (2000). Principals and standards of mathematics.

Reston VA: Author.

Phillips, C. (2010). Retrieved on March 12, 2011 from the website:sylvan.live.college.

Usnick, V., McCarthy, J., & Alexander, S. (2001). Mrs. Whatsit “socks” it to probability.

*Teaching Children Mathematics, 8*(4), 246–250

Van der Walle, J.A. (2007). Elementary and middle school mathematics. Upper Saddle River NJ: Pearson.

Ward, M. (2010). Retrieved on October 19, 2010 from the website:

www.athens.edu/vinsobm/lesson_25.htm