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Planning Middle School Statistics Lessons

Section A- Planning

Before beginning, remember to consider a) the prior learning do they need to review b) whether the example/data used is interesting and relevant c) providing opportunities for repetition of concepts d) materials that are needed eg graph paper, e) how the students will do the calculating (hand or by calculator) and f) what technology is available/needed.

Here are a few websites which may help you in planning your lesson. This entire document is also available on the website http://www.jackmathsolutions.com/

1.

2.

How does a histogram change in appearance, depending on the width you use for each interval? Demo at http://www.stat.sc.edu/~west/javahtml/Histogram.html

You likely know about this one. It is E-stat, which are lots of statistics for educational purposes: http://www.statcan.gc.ca/estat/licence-eng.htm

3.

Interactive Bar Graphs: This is a clever site that allows young children to easily construct a bar graph. Really good. http://www.amblesideprimary.com/ambleweb/mentalmaths/grapher.html

4.

In a separate document, I am attaching an easy histogram template. Feel free to adjust quantities as needed. Found on Gr 7-10 page of http://www.jackmathsolutions.com/ go down to websites, tips on statistics.

5.

Academy awards data- used in one of my sample lessons http://en.wikipedia.org/wiki/Academy_Award_for_Best_Actor

6.

Download some graph paper? http://incompetech.com/graphpaper/plain/

7.

Ontario Math Curriculum for Grade 8: http://www.edu.gov.on.ca/eng/curriculum/elementary/math.html

8.

Sample learning activities involving Data (has grade 4-8 section) http://www19.statcan.ca/02/02_004_e.htm#02

Section B- Editing, changing and adjusting your lessons to fit the age of the students, the level of ability and the and time limitations (30 minutes)

I am attaching two sample lessons .There are many changes and improvements that need to be made before these would be appropriate. Let’s break up into groups, read them and try to see how they could be improved.

Lesson 1:

Stem and Leaf Plots Date: __________________

Two interviewers were given the task to poll 50 people to record their ages. They recorded the data as shown.

A) One person recorded the data as collected.

39 45 14 36 23 63 12 32 25 35 46 10

49

42

81

91

3

56

15

9

34

50

57

12

33

20

61

77

43

50

82

60

51

32

48

26

22

28

24

21

33

45

31

55

57

45

56

51

8

55

B) The other person recorded her data in a special way on squared paper. This is referred to as a stem-leaf plot. How was the data above written down below?

Explain.

8

6 1

6 5

5 5 6 2

3 3 2 8

3 1 9 8 6

6 5 3 2 6 8

9 1 6 2 5 4 4

7 5 2 1 9 7 1 2

4 2 3 4 4 5 3 8 1 0

3

0 1 2 3 4 5 6 7 8 9

Refer to the stem-leaf plot to answer questions 1) to 3).

1) Which category has the

2) a) greatest number?______________ b) smallest number?_________________ c) same number of people?_______________

In which are there more people,

(circle one)

a) 20 to 29 or

3)

80 to 89? b) 40 to 49 or

How many persons are in each category?

50 to 59? a) 20 to 29______________ c) 40 to 69_________________

4) b) 40 to 49_________________ d) 10 to 59_________________

What is the average (mean) age in each of the following categories? a) 20 to 29? b) 70 to 79?

5) The stem-and-leaf plot shows several hotel room rates, in dollars.

Determine the median, mode and range of the data.

Stem Leaf

7

8

9

10

4 6 7 9

0 1 1 1 2 5 6

2 2 2 4 5

0 5 5

7) The back-to-back plot shows the precipitation recorded during the months of

May and June in 9 Canadian cities.

May

Precipitation (mm)

6 3

2

6 6

5 4

4

5

6

7

8

9

6 2 10

0

4

7

0 0 0 3 6

0

June a) Find the range for each month. _____________________ __________________ b) Find the median for each month. ___________________ c) Find the mode for each month. _____________________ d) Find the mean for each month. ____________________

Stem and Leaf Plots

Homework

1)

__________________

__________________

__________________

Date: __________________

The list shows some adult heights, in centimeters.

155 150 191 170 161 153 182 166 187

169 178 166 179 173 164 174 177 184 a) b) c)

Construct a stem-and-leaf plot. (Hint: the stem would be a two-digit number.)

Find the median, mode and range.

How many are taller that the mode?

2) The list gives the durations, in years, of the top 21 longest-running Canadian television shows.

18

18

20

18

38

20

19

25

22

18

23

24

23

24

27

33

36

25

18

25 a) b)

Construct a stem-and-leaf plot.

Find the range of the data.

3) The list shows the peak wind speeds, in kilometers per hour, recorded at 16

Canadian airports.

109 129 127 148 153 129 124 135

161 177 146 132 177 193 106 106 a) b) c) d)

4)

Construct a stem-and-leaf plot.

Find the median, mode and range.

What is the range of the data?

What is the median peak wind speed? a) How many more 14-year-olds than 18-year-olds are represented in this back-to-back plot?

14-Year-Olds

9 7

9 8 8 4 4 2 1

Weekly Television Viewing (h/week)

18-Year-Olds

0

1

7 7 9 9

2 3 4 4 4 8 8 9 9

8 8 6 6 4 3 1

2 2

2

8 8 5 5 5 3

4

5

1 2 3 4 8

6

1

0

Solutions: b) c) d) e)

What is the range of hours of television watched by 14-year-olds.

Find the median viewing habit for each age range.

Describe the difference in viewing habits of the 2 age groups.

What might contribute to the difference in part (c)?

1)

Stem Leaf

15

16

17

18

19

0 3 5

1 4 6 6 9

0 3 4 7 8 9

2 4 7

1

Mean = 171.06

Mode = 166

Median = 171.5

Range = 41

2)

Stem

1

2

3

Leaf

8 8 8 8 8 9

0 0 2 3 3 4 4 5 5 5 7

3 6 8

Mean = 23.7

Mode = 18

Median = 23

Range = 20

3)

Stem Leaf

4) a) 2 b) 35 hours

Median (18) = 18 c) Median (14) = 24

14

15

16

17

10

11

12

13

18

19 3

6 6 9

4 7 9 9

2 5

6 8

3

1

7 7

Lesson 2: Academy Awards

The ages of female and male winners of an academy acting award can be found at http://en.wikipedia.org/wiki/Academy_Award_for_Best_Actor after you have scrolled down to near the end.

a) b)

Once you have opened the link, try and click on the arrow beside the age to rank them by age

Try clicking on the arrow by the year to order them by year.

All of the following questions should be answered on the paper provided.

1)

2)

Determine the youngest and oldest winner for actors and actresses.

Display the ages of the `best actress’ and the `best actor’ winners in a back-toback stem and leaf plot. Calculate the mean, median and mode age.

3) a) Compare the median age of the `best actor’ award winners with the median age of the `best actress’ award winners. b) Why might you expect the `best actress’ award winners to have a younger median age than the `best actor’ award winners? c) Compare the (youngest) lower extreme age of the ‘best actresses’ with the lower extreme age of he ‘best actors’. Why might you expect the lower extreme age of the ‘best actress’ winners to be less than the lower extreme age of the `best actor’ winners? d) Compare the (oldest) upper extreme age for the `best actresses’ with the upper extreme age of the `best actors’. Why might you expect the upper extreme age of the `best actress’ winners to be close to the upper extreme age for the `best actor’ winner? e) Compare and calculate the ranges for the `best actors’ and for the `best actresses’. g) Which difference do you think will be greater: the differences in the median ages of the `best actor’ and `best actresses’, or the difference in their means? Explain.

4) Is there a trend toward selecting older women for the `best actress’ award? a) Construct a scatter plot for the ages of the `best actresses’ spanning the quarter century from 1927 to 1953. b) On the same display, construct a scatter plot for the ages of the `best actresses’ for the quarter century from 1954 to 1970. c) Construct a scatter plot for the ages of the `best actresses’ spanning the quarter century from 1971 to 2007.

d) Compare the scatter plots. Does there appear to be a trend toward selecting older /younger women? Explain.

5)

7) a) What is the modal age for the `best actress’ award winners over the each period? What is the median age for each? The mean age for each?

6) b) What is the modal age for the `best actor’ award winners over the three periods? What is the median age for each? The mean age for each?

What could you conclude about what you have found in #5, #6?

8) Are there any special years where the ages you found were really unexpected compared with other years? Can you explain why?