**Written by Lisa Parsons Rockdale County

Title:  Data Interpretation                     Subject:  Algebra Concepts

Topic:  Statistics and Probability           Grade:  8th      Designer(s):  Lisa Parsons

Algebra Concepts (Variables - Grade 5)

 

Stage 1 – Desired Results

Established Goals:

(QCC 43)  Students will collect and organize data, determine appropriate method and scale to display data, and construct frequency distributions; bar, line, and circle graphs; tables and charts; line plots, stem-and-leaf plots, box-and-whisker plots, and scatter plots.

 

Understandings:

Students will understand that…

  • Collected data can be organized and displayed utilizing a variety of methods and must be presented in an appropriate method.
  • Collected data can be presented in a method that can be “misleading” in order to sway public opinion.

 

Essential Questions:

 

  • How do you collect, organize and display a set of data utilizing an appropriate method of presentation?
  • How can “misleading statistics” be used by advertising companies to sway public opinion?

Knowledge:

Students will know…

  • The measures of central tendency (mean, median, mode and range) for a set of data.
  • Various types of statistical graphs:  frequency tables, bar graphs, line graphs, circle graphs, stem-and-leaf plots, box-and-whisker plots, and scatter plots.

 

Skills:

Students will be able to…   (VERBS)

  • Calculate the measures of central tendency (mean, median, mode and range) for a set of data.
  • Read and interpret statistical graphs.
  • Display data by constructing frequency tables, bar graphs (histograms), line graphs, circle graphs, stem-and-leaf plots, box-and-whisker plots, and scatter plots.
  • Display data utilizing an appropriate method of presentation.

 

 

Stage 2 – Assessment Evidence

Performance Tasks:

 

1.  Students complete Outer Space Middle School Project by determining the measures of central tendency for the height and weight of the middle school students at Outer Space Middle School.

 

2.  Students construct stem-and-leaf plot, frequency table, histogram and box-and-whisker plots for each set of data involving height and weight.

 

3.  Students construct a scatter plot for height and weight of the middle school students to look for a correlation between height and age and weight and age.

 

4.  Students will answer questions about the hair and eye color of the students at Outer Space Middle School.

 

5.  Students will construct bar graphs to show how the eye colors of the students from each grade level at Outer Space Middle School compare.

 

6.  Students will construct circle graphs to show the percentages of the student from Outer Space Middle School who have various hair colors.

Other Evidence:

 

·   Students will complete various assignments from the text.

·   Students will complete several worksheet puzzles from Pre-algebra With Pizzazz!

·   Teacher observation of students working on tasks.

·   Assessment of student work.

·   Orally review vocabulary words.

·    Oral discussion and written response to Essential Questions. 

·   Performance task rubric for Outer Space Middle School Project.  (Attachment 3)

 

Stage 3 – Learning Plan

1.  Begin with the Warm-Up Activity using the overhead (Attachment 1) to introduce the measures of central tendency.

 

2.  Use the results of the Warm-Up Activity to define:  mean, median, mode and range and explain how the mean, median, mode and range can be used look for trends in the population. 

 

3.  Ask students to anonymously write down their test score and the amount of time they studied.  Define:  scatter plot and use the data to show what type of correlation exists (if any) between study time and test score.

 

4.  Have students determine the mean, median, mode and range for the following sets of data:

a.  (12, 12, 11, 9, 10, 20, 18, 11, 9)  b. (2, 2, 1, 9, 1, 2, 8, 1, 9, 2, 1, 7, 5, 6)  c.  (127, 312, 191, 99, 160, 210, 178, 116, 119, 172). 

 

5.  Have students answer the following question about measures of central tendency.  Biology:  A biologist studying bald-eagles counts eggs in several nests.  Five nests have 1 egg, 63 nests had 2 eggs, and 4 nests had 3 eggs.  She concludes that bald-eagles usually have 2 eggs at a time in a nest.  What measure of central tendency did the biologist most likely use?

 

6.  Have students determine the measures of central tendency for the height of the 6th graders at Outer Space Middle School using the data tables in Attachment 2.

 

7.  Define:  Stem-and-Leaf Plot, Frequency Table, Histogram, and Box-and-Whisker Plot and have students construct one of each for the weight of the 7th graders at Outer Space Middle School using the data tables found in Attachment 2.

 

8.  Define:  Line graph, bar graph and circle graph.  Review the definition of scatter plot and have students construct a line graph to show how the average height and weight of the students at Outer Space Middle School Changes over time.  Have students construct a bar graph to show how the hair color of the 8th graders at Outer Space Middle School compares.  Have students construct a circle graph to show how the eye color of the 8th graders at Outer Space Middle School compares.

 

 

***EXTENSION:

Intermath connection:

1.  COCA-COLA POPULARITY

A pie graph has four unequal slices representing a sample of n people taste testing their favorite soft drink. Eight more people join the sample and three-fourths of them choose Coca-Cola as their favorite soft drink. This result makes the Coca-Cola slice increase to exactly 54% of the total graph. How many people were initially in the sample? Explain your solution.

2.  JOHN’S WAY OF FINDING AVERAGES

John claims he has found an easier way of finding the average (mean) of a set of numbers when you only need an estimate. It's easier because you work with smaller numbers. To illustrate his method, let's use these numbers:

31,25,35,18,14

John first takes the smallest number in the set and subtracts it from the other numbers in the set.

(31-14)=17, (25-14)=11, (35-14)=21, (18-14)=4.

Then he uses the "standard" procedure to average those numbers.

(17+11+21+4 + 0)/5 = ~10.6 (approximately 10.6)

He then adds the smallest number from the original set to this average (mean).

14 + 10.6 = 24.6

This average (mean) is the average (mean) of the original set of numbers (24.6).

Does John's way of finding the average (mean) of a set of numbers always work? Why or why not? Would his method work if you did the first step AGAIN with the smallest number in the new set (4), found the average (mean) of this new set of numbers, and then added this average (mean) with 14 and 4? Why or why not?

 

 

 

 

Attachment 1

 

The following is the set of test scores for 4th Period’s Unit 2 Test Scores.  Examine the scores and answer the questions that follow.

 

85

85

90

75

65

90

60

75

100

90

70

70

75

55

75

95

95

80

80

80

85

90

70

90

65

 

QUESTIONS:

 

1.   What was the class average? 

2.   Which score was scored most often?

3.   What was the lowest score?

4.   What was the highest score?

5.   Are there more A’s, B’s, C’s, D’s or F’s?

Created by Lisa Parsons

 

 

Attachment 2

OUTER SPACE MIDDLE SHOOL DATA –Created by Lisa Parsons

 

HEIGHT IN INCHES

 

6TH GRADERS

 

102

105

99

98

97

99

90

89

84

90

97

98

97

101

97

97

85

86

100

104

 

 

 

7TH GRADERS

 

90

90

87

86

82

82

85

85

79

75

77

92

93

67

88

88

89

84

86

87

 

8TH GRADERS

 

60

59

55

65

67

78

78

79

69

67

57

57

58

65

65

63

64

67

70

70

 

 

WEIGHT IN POUNDS

 

6TH GRADERS

 

60

65

63

80

77

59

70

83

65

67

65

68

64

65

65

65

67

67

68

70

 

 

 

7TH GRADERS

 

100

98

95

90

96

89

88

100

100

87

83

80

91

87

84

83

87

87

87

86

 

8TH GRADERS

 

115

105

105

128

127

110

111

110

109

107

106

129

130

100

100

135

130

104

103

112

 

 

HAIR COLOR

 

6TH GRADERS

 

GREEN

7

ORANGE

2

PURPLE

9

BLUE

2

 

 

 

7TH GRADERS

 

GREEN

4

ORANGE

5

PURPLE

4

BLUE

7

 

8TH GRADERS

 

GREEN

2

ORANGE

11

PURPLE

6

BLUE

1

 

 

EYE COLOR

 

6TH GRADERS

 

GREEN

2

PINK

6

YELLOW

10

 

 

 

7TH GRADERS

 

GREEN

5

PINK

11

YELLOW

4

 

8TH GRADERS

 

GREEN

9

PINK

5

YELLOW

6

 

Attachment 3

OUTER SPACE MIDDLE SCHOOL PROJECT RUBRIC TABLE OF CONTENTS

Created by Lisa Parsons

ITEM

COMPONENT

POINTS POSSIBLE

POINTS RECEIVED

1

Title Page

2

 

2

Table of Contents

1

 

3

Measures of Central Tendency (Data Sheet 1)

Height and Weight for 6th, 7th and 8th Grade Students

24

 

4

Stem-and-Leaf Plots (Data Sheet 2)

Height and Weight for 6th, 7th and 8th Grade Students

18

 

5

Frequency Tables(Data Sheet 3)

Height and Weight for 6th, 7th and 8th Grade Students

18

 

6

Histograms (Data Sheet 4)

Height and Weight for 6th, 7th and 8th Grade Students

18

 

7

Box and Whisker Plot (Data Sheet 5)

Height and Weight for 6th, 7th and 8th Grade Students

18

 

8

Written Description and Picture of the Average 6th Grader at OSMS

3

 

9

Written Description and Picture of the Average 7th Grader at OSMS

3

 

10

Written Description and Picture of the Average 8th Grader at OSMS

3

 

11

DATA ANALYZATION

4

 

 

TOTAL

112