• To have a prior understanding of ratio.
• To have a basic knowledge of graphs.
• To have a prior understanding of the terms estimation and data.
• To know how to divide data into appropriate graphs.
• Ten baggies containing 20 Fruit Loops each
• Yarn pieces
• Ten dice
• Data books
• Fruit cards and table labels
• Colored bowls
• Graph paper
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
In problem-solving investigations, students discover trends, formulate conjectures regarding cause-and effect relationships, and demonstrate critical thinking skills to make informed decisions.
1.TLW know how to collect and organize data.
1.1 TLW record data on a chart.
1.2 TLW create a graph using collected data.
2.TLW understand how to calculate the probability using the graph they created.
2.1 TLW record answers to questions about probability pertaining to the graph.
3.TLW know how to find the theoretical probability.
2.1 TLW record estimation of experiments.
2.2 TLW record theoretical probability.
2.3 TLW explain how theoretical probability is determined.
One teacher will sit at the desk and begin making a necklace out of Fruit Loops. The other two teachers will come in and see the first one making the necklace. They will say they really want to make a necklace too. Each one has a favorite color. They say, “I wonder how many (favorite color) I will have on my necklace when I make mine.” They will decide to make a necklace together to find out. TTW use Kid Pix to construct a table. TTW record the number of colors picked for their necklace. Each one will determine the probability of getting their favorite on their necklace. TTW then ask the students if they would like to make a necklace.
1.TTW divide students into five groups of two by letting them pick fruit cards. Each group will go to the table labeled with their fruit picture and the color bowl of their group. The bowls will contain baggies with twenty Fruit Loops in each, two foot yarn pieces, and the students’ data book.
2.TTW instruct the students that when they complete a task, they will remove the spoon from their bowl and place it on their table’s fruit card. TLW begin to fill out the estimation questions in their data book.
3.TLW pick Fruit Loops out of their baggie and place them on their yarn piece one at a time. Each time the student will record the color picked on his/her chart.
4.TTW combine their data chart with that of their partner. They will record their combined answers in their data book. They will record how many of each color was picked in terms of
number of color picked (draw on board) over the
total times picked
TTW ask students to record what they think this number means.
5.After everyone is through with their necklaces and handouts, TLW get a piece of graph paper and the markers from their bowl. The group will combine their answers to construct a bar graph using the data they collected.
6.After groups are through discussing, each group will share their graph and recorded answers with the class. They will explain how they got their answers. TTW record students’ answers on board.
7.TTW ask students if they can think of a ratio to find probability that will work every time. Tell them that mathematicians call this theoretical probability.
Number of outcomes in the event (draw on board) over the
Number of possible outcomes
1.TLW estimate outcomes of experiments using dice rolling. The students will determine the possibilities for rolling a 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. They will each roll their dice twenty times. They will record their data individually and then students will combine their answers with their partners.
2.The students will make a prediction of what they think the class results would be. Each group will give their actual results. TTW write the results for each group on the board. (Ex. 1- 4/40 + 6/40 + 4/40 + 3/40 + 1/40 = 18/40) When they are added, TTW record the total results on the graph she constructed on Kid Pix. Students will compare the actual results with the prediction made before.
1.TTW assess student learning throughout the lesson by observation and questioning.
2.TTW assess student learning through their explanations of charts and graphs.
3.TTW assess student learning by taking up data books.
Van de Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. 5th ed. (2004): 405-407.