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PEGGY MAGDALENO
CABOT JUNIOR HIGH NORTH
RESEARCH SITE:
Impac Learning Systems
LESSON TITLE:
Mr. Cobbler’s Shoe Dilemma
TOPIC: Statistics
SYNOPSIS OF LESSON:
Students will use statistics to help Mr. Cobbler set up his new shoe store. They will devise a survey (or you can use the one provided) to predict the most popular types of shoes to stock the store. They will present the information they discover from the survey and display it in different forms to make inferences and arguments from. The students will discuss whether their sample is a good representation of the general population. (Sometimes during the period that 8th grade football is practicing their are very few boys in the other 5th period classes.) Why are some shoe sizes harder to find than others. This could lead to apparel in general. Why are there more of one size jeans at the store than there are other sizes? If the average American is overweight how would that affect the clothing market?
CONCEPTS:
The students will solve a real-world problem involving statistics.
MATH PROCESS SKILLS:
Students will learn to interpret data and apply to other real-world situations.
MATHEMATICS STANDARDS:
Standard 10: Statistics
TIME FRAME:
One to 3 days depending on how in depth you want to go.
SUGGESTIONS: Students should be familiar with frequency tables, bar charts, and pie charts. Students should know how to find mode and percent.
MATERIALS: Centimeter grid paper for bar graphs. Compass and protractor to make circle graphs.
PROCEDURES:
Mr. Cobbler is thinking about opening a shoe store in town. He is limited on the amount of money he can invest so he wants to make very wise decisions about his stock. What are some of the things he would need to know about his customers before he orders his stock?
Average shoe size for men and for women. Type of shoes most people wear. Average amount people will spend for shoes. Favorite shoe color for the different types.
Do a survey.
What are questions we would need to put on our survey to help Mr. Cobbler?
Find out if male or female.
Find shoe size.
Find the types of shoes worn, i.e., loafers, gym shoes, dress shoes, boots, sandals, etc.
Favorite brand.
Price range.
3. At this point, you can have the students work through the questions to put on the survey or give them the ready-made one.
4. After the survey has been completed, divide the students into 6 groups. Have the students use a frequency table to record the data from each of the 6 questions (or you may want to have 5 groups and have one group do questions 1 and 2 together). Then, assign one of the questions to each group to evaluate. They must use a graph of some type (circle graph, bar graph, box and whisker plot, etc.) to present their data.
5. When all the data have been presented, the groups need to write down advice for Mr. Cobbler instructing him of the types of shoes and service for his new store. The students will discuss whether their sample is a good representation of the general population. Why are some shoe sizes harder to find than others? This could lead to apparel in general. Why are there more of one size jeans at the store than there are other sizes? If the average American is overweight, how would that affect the clothing market? If a manufacturer is opening a market in Japan, what would he need to consider?
EXPECTED RESULTS:
Students will see the need for planning and statistics in the real-world. Students will have a greater understanding of the process of data collection and presentation. See teacher’s key.
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Name:
Date:
THE SHOE PROBLEM
1. Mr. Cobbler is thinking about opening a shoe store in town. He is limited on the amount of money he can invest so he wants to make very wise decisions about his stock. What are some of the things he would need to know about his customers before he orders his stock?
a.
b.
c.
d.
e.
f.
2. Let’s pretend we are part of the town where Mr. Cobbler is establishing his new store. What could we do to find information about the kinds of shoes people are most likely to buy to help Mr. Cobbler?
3. What are questions we would need to put on our survey to help Mr. Cobbler?
a.
b.
c.
d.
e.
f.
4. If this class was the only sample we took for our survey, would it represent the total population of our school? Why?
5. Name a place at school to conduct this survey that would give you a better representation of the town population.
6. Why are some sizes of shoes so hard to find?
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SHOE SURVEY
We are conducting a survey for a possible new shoe store. The answers you give will help the investor know the right type of shoes to stock in the new store. Thank you for taking the time to fill out the following information.
1. Please circle the appropriate gender.
(male) (female)
2. What is your shoe size?
3. Circle the two types of shoes you wear the most:
(loafers) (gym shoes) (dress shoes) (boots) (sandals)
4. Circle your favorite brand of gym shoes:
(Nike) (Reebok) (New Balance) (Aasics) (Other)
5. How much do you normally spend on new shoes? Please circle.
(Less than $20 ) ($20 to less than $40) ($40 to $60) (more than $60)
6. Circle the type of shoe store you prefer to buy shoes at:
(self service) (shoe salesperson)
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THE SHOE PROBLEM
Evaluation Worksheet
Name: Teacher’s Key
Date:
1. Use the information in the chart below to make a bar graph on centimeter grid paper.
| SURVEY OF | ATHLETIC | SHOE | BRANDS | ||
| Class | Nike | Reebok | New Balance | Aasics | Other |
| 1st period | 14 | 1 | 2 | 4 | 4 |
| 2nd period | 8 | 2 | 1 | 5 | 8 |
| 4th period | 10 | 1 | 0 | 6 | 9 |
| 5th period | 9 | 0 | 1 | 5 | 10 |
| 6th period | 12 | 2 | 0 | 3 | 5 |
| 7th period | 11 | 2 | 2 | 5 | 7 |
| Total | 64 | 8 | 6 | 28 | 43 |
2. Using the information in the table find the percent of each brand to the total. Make a pie chart.
Nike [42.95%]
Reebok [5.37%]
New Balance [4.03%]
Aasics [18.79%]
Other [28.86%]
3. By looking at the bar graph, what other information might Mr. Cobbler want to know about the brands of shoes? [gender, shoe sizes, types of brands in "other" category.]
4. Which brand of athletic shoes would you recommend to Mr. Cobbler to invest in the most stock? Why? [Nike, most popular]
5. Describe how the survey helped or did not help Mr. Cobbler stock his store. In what ways could the survey been improved? [Helped because he knows the most popular brand. By specifying more brands instead of grouping so many in the "other" brands category.]
6. We’ve seen that a survey can be useful in stocking a store. Name two other circumstances that a survey would be useful and why. [Political race-know opinions of public; product development-know what consumers want.]
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KAYE T. BOUNDS
NORTH PULASKI HIGH SCHOOL
Research: University of Arkansas, School of Pharmacy
LESSON TITLE: Is One Average Better Than the Other?
GRADE LEVEL:
11-12th Statistics--Could be used in a lower level statistics unit.
TOPICS:
Measures of Central Tendency
Comparing Averages
SYNOPSIS LESSON:
Students will use real world data which they will collect from two brands of raisin bran cereals. Students will be divided into two groups based on cereal brands and each student will count the number of raisins per serving. Students will find the average number of raisins per serving of a popular brand and a store brand of raisin cereal. Students will find and compare mean, median, and mode for the best average.
CONCEPT:
Find the best average for the data, after finding mean, mode, and median.
OBJECTIVE:
The students will learn to calculate mean, median, and mode. The student will determine which average is statistically best for these data by using knowledge of outliers and consistency. The average that makes the product look best is also a criteria.
MATH PROCESS SKILLS:
The student will interpret data and use the data to solve a real world problem.
CORRELATION TO NATIONAL STANDARDS:
Statistics
MATERIALS:
MANAGEMENT SUGGESTIONS:
Time required is one 50-minute class. The class is divided into two groups, one for each brand of cereal. Two groups work well with about 16 students. If you have more students, go to three cereals brands and three groups.
SAFETY CAUTIONS:
There should be few problems, but you may want to put down paper towels and caution them not to eat.
PROCEDURES:
1. Ask the students the following questions: Is one average better than another? Is there a difference between brands of raisin bran cereal?
2. Divide the class equally into two groups.
3. Each student is to get a small cup of his/her cereal and a paper plate.
4. Each student is to count his/her raisins per cup serving.
5. Members of each group are to combine their findings to determine the mean, mode and median of the data.
6. The two groups are to share their results.
7. Each group is to select the best average to use in an advertising slogan. The group is to write a slogan with the selected average and compare to the other brand.
8. Each student is to write an explanation of why the group selected the average.
EXPECTED OR ACTUAL RESULTS:
The students get hands-on experience of finding the mean, mode, and median and determining the best average for the situation.
EXTENSIONS:
ASSESSMENT SUGGESTIONS:
1. Observation of each group.
2. Each student's written explanation of why an average was selected.
3. Students can be given different data such as different brands of tires to compare averages.
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Student worksheet: IS ONE AVERAGE BETTER THAN THE OTHER?
Suppose that you are to write the advertising slogan for a raisin bran cereal. You want to include the average number of raisins per serving and compare your brand to other brands.
1. The number of raisins in your serving cup =
2. The number of raisins in each cup in your group: a____, b____, c____, d____, e____, f____, g____, h____, i____, j____, k____, l____.
3. Mean number of raisins =
Mode =
Median =
4. Best average to use for advertising:
5. Your group is to write an advertising slogan using the selected average and information from the other brand. (Cost is on the box)
6. Evaluation: each person is to write an explanation of why your group selected the average used in the advertising slogan. Tell which cereal you would buy and why.
Keep these data for further use.
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