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## Investigation - How Tall is the Average Sixth Grader?

### Materials

Yard sticks, tape measures, meter sticks, calculators

### Authors

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team

1 - 2 lessons

### Procedure

DOING THE INVESTIGATION

1. Introduce the problem.
2. Elicit that the mean height is the average height.
3. Have each student measure his/her partner using a tape measure or yard stick. (Use total inches.)
4. Organize data on a stem and leaf plot on chart paper for the class.
e.g. (using 11 students)
stem leaf
5 5 5 6 7
6 0 0 0 8 9
7 1 1

(Stem is tens place and the leaf is the ones place for height in inches.)

5. Elicit the average (MEAN) height of the students.

POSSIBLE SOLUTIONS

Answer for the example is 62 inches. Answers will vary from class to class.

### Vocabulary

Mean, median, mode, average, data, stem and leaf plot

### Description

Students will measure each other and record the data in inches. Students will use a stem and leaf plot to display data. Figure out the average height of the students in your class.

WHAT'S THE MATHEMATICS?

• mean
• median
• mode
• add, subtract, multiply and divide whole numbers
• stem and leaf plot

### Extending the Activity

Extension 1: Eliciting the median and mode of the data.

1. Elicit from students which height appears most often. (In example the answer is 60 inches. Answer in your classes will vary.)
2. Discuss that this number is the MODE.
3. Elicit the importance of understanding the mode. (e.g., knowing what you need to order if you work in a store or restaurant.)
4. Elicit from the students which height is the middle. (in the example above, 60 inches.)
5. Discuss that this number is the MEDIAN.
6. Discuss the difference between mean, median and mode.

Extension 2: Do this same activity using metric measurement.

### Assessment 1

Your math scores so far this year have been: 80, 100, 92 and 87. What is the lowest score you can get on your final test in order to still receive an A. (A is 90% or more)

a) 90
b) 85
c) 91
d) 89

Ans. c)

### Assessment 2

Part A: Organize the following test scores on a stem and leaf plot:
86, 43, 92, 67, 90, 87, 86, 71, 94, 73, 90, 86, 77, 71, 100.

Part B: What is the mean, mode, and median of these test scores?

Ans. a)

stem leaf
4 3
6 7
7 1 1 3 7
8 6 6 6 7
9 0 0 2 4
10 0

Ans. b)

Mode = 86
Median = 86
Mean = 80.87

For additional information and activities, see pages 72, 73, and 84 in the Core Curriculum/Mathematics Resource Guide.

• About The Core Curriculum Companion
• ### Source

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team. “HOW TALL IS THE AVERAGE SIXTH GRADER?” In The Core Curriculum Companion For The New York State Mathematics Resource Guide, 171-173.

### Related New York City Performance Standards

• M1a Consistently and accurately add, subtract, multiply, and divide rational numbers.
• M4a Organize and display data.
• M4b Analyze data with respect to frequency and distribution.
• M4c Analyze central tendencies of data.
• M4d Make conclusions and recommendations based on data analysis.
• M5a - Formulation
• M5b - Implementation
• M5c - Conclusion
• M6a - Compute accurately with arithmetic operations on rational numbers.
• M6g - Read and organize data on charts and graphs.