Source:  Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
                For further information about Backward Design refer to http://www.ubdexchange.org/

 

Title: Statistics & Probability  Subject/Course: Pre-Algebra Topic: Measures of Central Tendency Grade(s): 7 Designer(s): Lillian Laster

Stage 1 – Desired Results

Established Goal(s)

Students will demonstrate understanding of data analysis by posing questions, collecting data, analyzing the data using measures of central tendency and variation, and using the data to answer the questions posed.

     QCC:  42

         Strand:  Statistics & Probability

         Topic:  Measures of Central Tendency and Spread

         Standard:  Uses mean, median, and mode to describe central tendencies of a data set, and uses range to describe spread of the data.

Understanding(s) Students will understand that...

1.      In statistics there are three measures that tell how the data cluster near the center of the data.  These averages  (mean, median, mode) are called measures of central tendency.

2.      Average and arithmetic mean are equivalent.

3.      For sets of data with no very high or low numbers, mean may be a better description.

4.      For sets of data with a couple of points much higher or lower than most of the others, median may be a better description.

5.      For sets of data with many identical data points, mode may be a better description.

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Essential Question(s)

1.      If you were to pick a number that best describes all the data in a set, what number would you pick?

2.      How is the mean (average) affect when all the data are close to each other, or when one piece of data is much bigger or much smaller than the rest?

3.      How is the median (middle) determined when there is an even number of numbers in a set of data?

4.      How can the measures of central tendency be used to describe tendencies and make predictions?

 

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Students will know...

1.      Average and arithmetic mean are equivalent.

2.      Mean is found by adding all the values in a set and dividing by the number

      of values.

3.      Median is the number that falls exactly in the middle of a set of data when the data are arranged in order from least to greatest.

4.      Mode is the value that occurs the most often in a set of data.

5.      Range is the difference between the greatest and least numbers in a set of data.

 

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Students will be able to...

1.      State measures which describe central tendency of a set of  numbers.

2.      To define data and range of a set of data.  To find the range.

3.      To define arithmetic mean of a set of data.  To compute the mean.

4.      To find the median of a set of data.

5.      To find the mode(s) of a set of data.

6.      Produce sets of numbers whose statistical measures are specified.

7.      To organize, plot and analyze statistical data.

Stage 2 – Assessment Evidence

 

Performance Task(s) Summary in G.R.A.S.P.S. form

1.      Divide class into groups of  4 and 5 students.

2.       Ask each group to list each member’s favorite number between 1-20 also show data using a stem-and-leaf plot.

3.       Have each group write the definition of range in their own words and determine the range for their set of date.  Compare range for all groups.

4.       Have each group write the definition of median in their own words and determine the median of their set of data.  Compare medians for all groups.

5.       Have each group write the definition of mode in their own words and determine the mode of their set of data.  Compare modes for all groups.

6.       Have each group write the definition of mean in their own words and determine the mean of their set of data.  Compare means for all groups.

7.       Class extension exercise:  Have each group determine if any central tendency is affected if the teacher’s favorite number is added to their group’s data.

 

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Key Criteria:

Students will participate in verbal responses and questioning.  Each cooperative group will show and summarize all work.  Teacher observation

Other Evidence

Learning activity, quiz

 

 

Stage 3 – Learning Plan

Learning Activities Consider the W.H.E.R.E.T.O. elements.

 

Your local newspaper has reported standardized test scores for seventh-graders.  Your class had the following raw scores on the test:  95, 101, 82, 150, 178, 164, 103, 181, 97, 154, 144, 130, 133,159, 177, 99, 124, 127, 151. 

·         Make a stem-and-leaf plot from the data.

·         Solve for all measures (range, mean, median, mode) of the nineteen scores.

The newspaper realizes that a score was omitted.  The score was 149.

·         Which of the measures of central tendency, mean, median, or mode, changes the most as a result of the last score?

 

Extension:  If you happen to know that your score was 150, compare how well you did to other test-takers by finding your percentile ranking.

       Note:  Students should be able to arrange the data in order from least to greatest.  Find the total number of scores: n=20.  Find how many scores are less than or equal to their score (150); 13 of the 20 scores are less than or equal to 150.  Find out what percent 13 is of 20:  65%.  Therefore, their score of 150 is in the 65th percentile.  Their score is at least as good as the scores of 65% of their classmates.

 

 

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