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									              CAHSEE Math Problem of the Day -- Week 1
                                      Teacher Notes
Week & Day        Week 1 – Day 1
Concept/Skill     Mean
   Standard       6.SP:1.1 Compute the range, mean, median, and mode of data sets.
   Materials      CAHSEE Math Released Item #35

Overview for Week 1
Students were introduced to mean, median, and mode in fourth grade, however, they
often forget or become confused between these three words. This week will provide
students with a quick review of the vocabulary, methods for finding mean, median and
mode, and some practice problems from the CAHSEE released items. Note that students
do not need to answer any questions about the range on the CAHSEE.

 Review what the word mean means. Students probably are more familiar with the term
 average. Ask students where they have heard the word average? Some possible replies
 are grade point average (GPA), batting average, or average height.

 Have students review how to compute the mean.
  1. Find the sum of all of the numbers
  2. Divide the sum by the number of numbers you added up

  Have students do the guided practice on Day 1 of the student CAHSEE Math
  Problem of the Day -- Week 1 worksheet.

        Find the average of 10, 25, 20 and 5.

        Step 1: 10 + 25 + 20 + 5 = 60
        Step 2: 60 / 4 = 15

        Have the students state the ANSWER as “The mean is 15”

 Have students do the CAHSEE released test item on Day 1 of the student CAHSEE
 Math Problem of the Day -- Week 1 worksheet.

      Rico’s first three test scores in biology were
      65, 90, and 73. What was his mean score?


                                          The mean is the same as the average.
     A 65
                                                 65+90+73=228
     B 73
                                                 228/3=76
     C 76
     D 90                                 The mean is 76




Laura Westermeier, Ed.D.                                                          Fall 2007
SAUSD, Educational Services                                 Week 1 – Teacher - Page 1 of 5
              CAHSEE Math Problem of the Day -- Week 1
                                    Teacher Notes

      Week        Week 1 – Day 2
Concept/Skill     Median
   Standard       6.SP:1.1 Compute the range, mean, median, and mode of data sets.
   Materials      CAHSEE Math Released Item #34

 Review what the word median means. Students may have hear the word used in
 “median house price” for a certain zip code in the real estate section of the newspaper.
 Explain that median means the “middle” price when all the prices are put in order from
 least to most. For example, if the houses in a neighborhood have sold for $400,000,
 $400,000, $500, 000, $550,000 and $950,000 the median price is the one in the middle,
 $500,000. Compare this to the mean of these prices which is $560,000.

 Have students review how to find the median.

    1. Write the numbers in order from smallest to largest.
    2. Find the number in the middle. If the midpoint is between two numbers then find
         the average of those two numbers.
 Have students do the guided practice on Day 2 of the student CAHSEE Math
 Problem of the Day -- Week 1 worksheet.
        Find the median of 14, 20, 12 and 10.
        Step 1: Put the numbers in order: 10, 12, 14, 20
        Step 2: There are two numbers in the middle (12, 14). Add 12 and 14 and divide by 2.
        Have the students state the ANSWER as “The median is 13”

 Have students do the CAHSEE released test item on Day 2 of the student CAHSEE
 Math Problem of the Day -- Week 1 worksheet.

        Donald priced six Compact Disc (CD) players. The prices are shown below.
        $21.00, $23.00, $21.00, $39.00, $25.00, $31.00

        What is the median price?

                                     Put the numbers in order
        A $21.00                             21, 21, 23, 25, 31, 39
        B $24.00
                                     Since the median is between 23 and 25 you will need to take
        C $27.00                     the average of those 2 numbers.
        D $30.00                             23+25=48
                                             48/2=24

                                     The median price is $24.00



Laura Westermeier, Ed.D.                                                            Fall 2007
SAUSD, Educational Services                                Week 1 – Teacher - Page 2 of 5
              CAHSEE Math Problem of the Day -- Week 1
                                     Teacher Notes

      Week        Week 1 – Day 3
Concept/Skill     Mode
   Standard       6.SP:1.1 Compute the range, mean, median, and mode of data sets.
   Materials      CAHSEE Math Released Item #37

 Review what the word mode means. Tell students that mode means the number that
 occurs most frequently in a list of numbers. In other words, the most “popular”
 number. Tell them one way they might remember mode is to think of Mode, the name
 of the magazine about popular fashion in the Ugly Betty television show.

 Have students review how to find the mode.

    1. Write the numbers in order from smallest to largest (this step is not required, but it
         does make it easier to see which number is written the most times.)
    2. Find the number the is written the most times.

 Have students do the guided practice on Day 3 of the student CAHSEE Math
 Problem of the Day -- Week 1 worksheet.

        Find the mode of 7, 8, 10, 4, 8, 5, 8, 7.

        Step 1: Put the numbers in order: 4, 5, 7, 7, 8, 8, 8, 10
        Step 2: Find the number that is written the most times which is 8.
        Have the students state the ANSWER as “The mode is 8.”

 Have students do the CAHSEE released test item on Day 3 of the student CAHSEE
 Math Problem of the Day -- Week 1 worksheet.

        The box below shows the number of kilowatt-hours of electricity used last month at
        each of the houses on Harris Street.
        620, 570, 570, 590, 560, 640, 590, 590, 580

        What is the mode of these data?

        A 560                             Put the numbers in order
                                                  560, 570, 570, 580, 590, 590, 590, 620, 640
        B 580                                     (or just count how many of each number)
        C 590
                                                    The number 590 is shown the most.
        D 640
                                          The mode is 590.




Laura Westermeier, Ed.D.                                                                Fall 2007
SAUSD, Educational Services                                   Week 1 – Teacher - Page 3 of 5
              CAHSEE Math Problem of the Day -- Week 1
                                     Teacher Notes
      Week        Week 1 – Day 4
Concept/Skill     Mean, Median, Mode
   Standard       6.SP:1.1 Compute the range, mean, median, and mode of data sets.
   Materials      SDCOE CAHSEE Prep: Mod 4 Day 6 P3 #2

 Orally quiz the students to see if they can recall the definition for mean, median, and
 mode. Tell students that today they will have a problem where they will need to find
 the mean, median, and mode.

 Have students do the SDCOE CAHSEE Prep test item on Day 4 of the student
 CAHSEE Math Problem of the Day -- Week 1 worksheet.

    Find the mean, median and mode of the following data set: 3, 3, 6, 4

    For the mean add all the numbers and divide by 4 (the number of numbers you added)
    3+3+6+4=16 then 16/4 = 4

    For the median and mode put the numbers in order from lowest to highest: 3, 3, 4, 6
    The median falls between 3 and 4 so take the average of 3 and 4 which is 3.5

    The mode is the number that occurs the most which is 3.

    ANSWER: Mean is 4         Median is 3.5 Mode is 3




Laura Westermeier, Ed.D.                                                           Fall 2007
SAUSD, Educational Services                              Week 1 – Teacher - Page 4 of 5
              CAHSEE Math Problem of the Day -- Week 1
                                    Teacher Notes
      Week        Week 1 – Day 5
Concept/Skill     Mean, Median, Mode
   Standard       6.SP:1.1 Compute the range, mean, median, and mode of data sets.
   Materials      CAHSEE Math Released Item #36

 Students will need to read a chart in order to get the data for this released test item.
  Have the students circle the data they will need to use to calculate Hector’s mean score.
  Remind students that when they take the CAHSEE it is ok and in fact they are
  encouraged to write in the CAHSEE test booklet.

 Have students do the CAHSEE released test item on Day 5 of the student CAHSEE
 Math Problem of the Day -- Week 1 worksheet.

    The chart below shows the mathematics test scores of three students.




        What is Hector’s mean score?
                                                      The mean is the same as the average.

        A 6                                           Locate the scores for Hector
                                                      Step 1 - Add up all the test scores for
        B 7                                           Hector
                                                          6+7+9+10 = 32
        C 8                                           Step 2 – Divide the total by the number of
                                                      scores added which was 4
        D 9                                               32/4=8

                                                      The correct answer is C



 At the end of the week remind students to keep the student CAHSEE
 Math Problem of the Day -- Week 1 worksheet to use as a study guide
 as they continue to prepare for the CAHSEE.




Laura Westermeier, Ed.D.                                                          Fall 2007
SAUSD, Educational Services                              Week 1 – Teacher - Page 5 of 5

								
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