Birthdays

By David Reid

Activities

 

1.     Remind the class of the definition of theoretical probability: the number of successful events possible divided by the total number of possible events.  To check ask:

a.      what is the theoretical probability of rolling 5 on a dice (1/6),

b.     what is the theoretical probability of rolling and odd number on a dice (3/6 or 1/2),

c.     what is the theoretical probability of rolling 7 on a dice (0/6).

2.     Ask what is the theoretical probability of someone being born in January.  Encourage discussion.  Possible answers are “About 1/12” (discuss whether it is exactly 1/12; are all months equally likely?); “about 31/365” (Is this exact?  Are all years 365 days long?  Are all days equally likely?)

3.     Collect data from the class on birth month. 

a.      Display as both a bar chart and a line chart (and for grade 6 a circle chart). 

b.     Discuss advantages and disadvantages of each type of display.

4.     Have the class calculate, based on the data displayed, the experimental probability of being born in each month (If needed remind them that experimental probability is the number of successful events observed divided by the total number of observed events. 

5.     Discuss what they would do to get experimental results that were closer to the theoretical values (Use a larger sample).

6.     Have each person calculate their age in days.  Include yourself.

a.      Assemble this data into a sorted list. 

b.     Ask them what the average age is in the class. 

c.     Discuss the difference between the mean and the median.

d.     Discuss the effect of removing the outlier (you).

e.      Ask if mode would be useful for this data.

7.     Ask them what the average birth month is.  Suggest coding the moths with numbers.  Does the mean mean anything?  What about the median?  What about the mode?

 

Outcomes

 

Grade 4

F1- recognize and use a variety of methods for the collection and organization of data

F3- read and interpret bar graphs, line graphs, pictographs, and stem-and-leaf plots

F5- construct bar graphs, pictographs, and stem-and-leaf plots

F7- describe data, using the mean

F8- explore real-world issues of interest to students and for which data collection is necessary to determine an answer

G1- predict probabilities as either close to 0, near 1, or near ½

G2- cite examples of everyday events with very high or very low probabilities

G3- predict whether one simple outcome is more or less likely than another

G4- use fractions to describe experimental probabilities

 

Grade 5

F2- use pictographs and bar graphs to display and interpret data

F4- create and interpret line graphs

F6- recognize and explain the effect of certain changes in data on the mean of that data

F7- explore relevant issues for which data collection assists in reaching conclusions

G1- conduct simple experiments to determine probabilities

G2- Determine simple theoretical probabilities and use fractions to describe them

 

Grade 6

F1- choose and evaluate appropriate samples for data collection

F4- use bar graphs, double bar graphs and stem-and-leaf plots to display data

F5- use circle graphs to represent data proportionally

F7- make inferences from data displays

F8- demonstrate an understanding of the differences among mean, median, and mode

F9- explore relevant issues for which data collection assists in reaching conclusions

G1- conduct simple simulations to determine probabilities

G2- evaluate the reliability of sampling results

G3- analyze simple probabilistic claims

G4- determine theoretical probabilities