The probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event.

Each sock has three tiles.

Each tile is the same size.

A tile must be one of three colors.

Each tile has an equal chance of being drawn.

The possible combinations are: all one color, two the same color and one different, three different colors.

The more objects of one color, the greater the chance of that color being selected.

The more trials, the more accurate the theoretical values that are obtained.

I can cause a certain tile to be selected. (think real hard, pick a certain way...).

One tile always gets chosen.

It is magic.

Diagnostic

Have students predict the probability for the sock with three tiles.

Summative

Have students predict the probability for selection of tiles with different combinations.

Generative

Use a spinner with equal partitions of different colors and have the students predict the probability for each colored section to be selected.

Accuracy of prediction may be increased with more trials.

Each selection increases the possibility of selecting all tiles at least once.

Predictions are derived from possibilities.

Some possibilities have a better chance of occurring than others.

Some possibilities are not likely to happen.

Some possibilities are impossible to happen.

Young students do not understand proportion. They might look at their individual data and see that the numbers are closer to the actual numbers, than the sum of all the class numbers and not see how it is more accurate.

Diagnostic

How many times do think you would have to pick a tile and put it back into the sock, before you would have a pretty good guess as to the color of the three tiles in the sock?

Summative

Have students predict the number of times they would want to draw for different amounts of tiles.

Generative

Have the students predict the number of times a person would have to call out the colors on it before a person could predict the different colors of the sections accurately.

Activity Objective

Students will make a specific number of random selections with replacement and draw a conclusion about the tile population in a sock.

1. Ask students if they think they can predict exactly what the population of tiles in a sock is without dumping all of the objects.
2. Record all ideas on the board.
3. Ask them to explain how they think their answer is a good one.
4. Ask if they would like to try.
5. Show the socks and explain that each sock has identical colored tiles.
6. Tell the students that they will predict the color of each tile for the sock population.
7. Divide the class into groups of three.
8. Outline the following directions on the board.

   Each student will rotate the following roles: selector, counter, recorder.

   Selector: Draws the tile from the sock, announces its color, returns the tile to the sock, and shakes the sock.

   Counter: Keeps track of the number of trials the selector has taken.

   Recorder: Records the color of each tile on the group paper.

   Selector: Returns the tile to the sock.

   Each person selects a tile four (4) times.

   Each group thinks about, discusses the results and then writes a group prediction.

9. Ask someone to repeat the instructions
10. Students complete the task.
11. Cruise the room and observe interactions, note critical comments, answer questions about procedures, and make sure groups record the necessary information.

1. Ask students how to display data. If students do not know how to arrange data have them record the number of each color selected on a chart with the colors labeled across the top or bottom, each group’s name on the side and the number of times a certain color was drawn in the cells.
2. Students put their data on the chart and explain how they arrived at their predictions.
3. Have the students decide that more draws would help to obtain a more accurate prediction.

1. Have students repeat the process with four draws.
2. Ask students if they think they the additional draws will help.
3. Record all ideas on the board.
4. Ask them to explain how they think their answer is a good one.
5. Ask if they would like to try.
6. Remind them about the directions on the board.
7. Check for understanding.
8. Students complete the task.
9. Cruise the room and observe interactions, note critical comments, answer questions about procedures, and make sure groups record the necessary information.

1. Ask students how to display the data. If students do not know how to arrange data have them record the number of each color selected on a chart with the colors labeled across the top or bottom, each group’s name on the side and the number of times a certain color was drawn in the cells.
2. Students put their data on the chart and explain how they arrived at their predictions
3. Ask student what would happen if all the classes data was put on one chart.
4. Create a class chart by having all students place a colored polka - dot or sticky - notes for each colored tile on a graph.
5. Have the students explain the graph.
6. Have students predict the probability for selection of tiles with different combinations.
7. Use a spinner with equal partitions of different colors and have the students predict the probability for each colored section to be selected.