Summary:
Students will use fractions to represent the probability of selecting a grid square containing shoreline or pond water.
Materials:
Scissors; Small paper bags; Graph Paper; Blindfolds; Markers; Map of pond on grid paper for each group.
Background For Teachers:
In this activity students will report how likely they are to randomly select a grid square representing shoreline versus a grid square representing pond water. Student groups will carry out the sampling and then create a bar graph to report their findings. Be prepared for different results from the groups. This is to be expected in any activity involving a chance process.A printout of the virtual pond with grid squares can be used. You may wish to print it out and use it as an overhead transparency or a handout. Once you are comfortbable with this approach for exploring probablity, you may desire to find a map of your local pond and photocopy it onto grid paper.
Intended Learning Outcomes:
Students explore chance and probability. Students relate fractions to problem situations. Students organize and report their findings.
Instructional Procedures:
Listening to the news you might hear the statement that there is a 40 chance of rain today. What do you think that means? Explain that this activity will give the students the opportunity to experience chance and discover some things about predicting results (mathematicians call this probability). 1. Assign the students into groups and provide each group with a paper bag, a pair of scissors, graph paper, markers, and a blindfold. Each group will also need a copy of the map of the virtual pond on grid paper. 2. The group should cut their map of the virtual pond into smaller pieces, each piece 2 grid squares wide by 2 grid squares deep. Demonstrate how to do this for the class. 3. Assign the group to count the number of grid pieces that contain at least one full square representing pond water. Teacher note:Depending on how the group divides up the task of cutting the map and depending on where they start to count 2 grids by 2 grids the results will vary.They should have between 25 and 33 (2 by 2) grid pieces that contain at least one full grid of pond water. Remember, we are only counting pond water, not stream water. 4. Have the group count the total number of 2 by 2 grid pieces. There are about 200 complete 2 by 2 grid squares. 5. Ask the groups to calculate the number of 2 by 2 grid pieces that do not contain pond water (call them shoreline pieces for this activity. There should be about (20030=) 170 such pieces. 6. After the groups report their finding to the teacher, the teacher should predict how many 2 by 2 grid squares containing at least one grid of water will be drawn out of ten tries by the students. (Number of Pond Water Pieces/Total Number X 10 or 30/200 X 10 should be about 1.5 or two times in ten tries). 7. One group member can put on the blindfold (or if they promise not to peek) and draw 10 pieces out of the paper bag. Another group member should examine the pieces to see how many 2 by 2 grid pieces contain at least one full grid of pond water. The third group member should record the results. 8. After the groups report their results, compare the teacher's prediction with the actual outcome. Question: Could we possibly draw ten straight pond water 2 by 2 pieces? (Answer: Possible but not likely!). Question: What determined your chance of drawing a pond water 2 by 2 piece? (Answer: The number of pond water pieces in the bag versus the total number of pieces in the bag). 9. Have the students write ratios representing the number of pond water pieces to total pieces (30 to 200 or 30/200). Have the students write the ratio representing the number of pond water pieces to 'shoreline' pieces (30 to 170 or 30/170).
Extensions:
1. Question: 'If I were to randomly select a name from this class (by pulling it out of a paper bag) how likely would I be to draw my own name? (Answer: 1/Total Names). 2. Question: Is it possible that I could randomly draw my own name twice in a row? (Answer: Only if we replace the piece after each draw). 3. Question: What is the ratio of the teacher's name to all class names (1 to 33 or 1/33)
Created Date :
Mar 19 1999 13:38 PM
