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Works of the Heart. Carve your name on Hearts and not on marble. - Charles H. Spurgeon. TA-4-1a. TA-4-1b. Coordinate Graphs. Do you think taller people have wider arm spans? :. TK-3-1. Overview of Investigation 4. Goals :
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Works of the Heart Carve your name on Hearts and not on marble. - Charles H. Spurgeon TA-4-1a
Coordinate Graphs Do you think taller people have wider arm spans?: TK-3-1
Overview of Investigation 4 • Goals: • to implement the process of statistical investigation to answer questions • to review the process of measuring length, time, and distance • to analyze data by using coordinate graphs to explore relationship among variables • to explore intervals for scaling the vertical axis (y- axis) and the horizontal axis (x-axis) • Investigation 4 : Coordinate Graphs • Materials (p. 41j) • Student Handbook Pages (pp. 42 - 52) • Teaching the Investigation (pp. 52a – 52g) TK-3-2
Coordinate Graphs Is there really any relationship between a person’s height and his or her arm span?: TD-4-1
Coordinate Graphs How might we organize and display the data in a graph to help us answer this question?: TD-4-2
Relating Height to Arm Span Does the data in the double bar graph indicate any relationship between height and arm span? TD-4-3
Relating Height to Arm Span Does the data in the back-to-back stem plot indicate any relationship between height and arm span? TD-4-4
Problem 4.1 • Think about this question. If you know the measurement of a person’s arm span, do you know anything about his or her height? • To help you answer this question, you will need to collect some data. With you class, collect the height and arm span of each person in your class. Make a coordinate graph of your data. Then, use your graph to answer the question above.
Problem 4.1 follow-up • Draw a diagonal line through the points on the graph where the measures for arm span and height are the same. 1.How any of your classmates’ data are on this line? What is true about arm span compared to height for the points on this line? 2. What is true about arm span compared to height for the points below the line you drew? 3. What is true about arm span compared to height for the points above the line you drew?
Problem 4.2 • Study the graph on page 46, this graph was made using the data from Problem 3.1 • Look back at the data on page 31. On Labsheet 4.2, locate and label with initials the points for the first five students in the table. • If you know how long it takes a particular student to travel to school, can you know anything about the student’s distance from school? Use the graph to help you answer the question. Write a justification for your answer.
4.2 Follow-up • Locat the points at (17, 4.50) and (60,4.50) on the coordiante graph on Labsheet 4.2. What can you tell about the students these points represent? • Locate the points (30, 2.00),(30, 3.00) and (30, 4.75). What can you tell about the students these points represent? • What would the graph look like if the same scale were used for both axes?
Overview of Investigation 5 • Goals: • to understand the mean as a number that “evens out” or “balances” a distribution • to create distributions with a designated mean • to find the mean of a set of data • to use the mean to help describe a set of data • to reason with a model that clarifies the development of the algorithm for finding the mean • to distinguish between the mean, median, and mode as ways to describe what is typical about a set of data • Investigation 5: What Do We Mean by Mean? • Materials (p. 52h) • Student Handbook Pages (pp. 53 - 67) • Teaching the Investigation (pp. 67a – 67l) TF-4-2
Terms • Mode “the value that occurs most frequently.” • Range “the spread of data values from the lowest value to the highest value.” • Median “the value that divides the data in half.” (half of the values are below the median, and half the values are above the median) • Mean “the average of the values of the data.” TF—4-1
Evening Things Out-Inv. 5 The purpose of the Census Bureau is to count the number of people living in the United States in order to compute the number of representatives each state will have in the United States House of Representatives. The census focuses on counting the people who live in households rather than “how many people are in a family.” TG-4-1
Ollie 2 people Ruth 4 people Yarnell 3 people Paul 6 people Gary 3 people Brenda 6 people Evening Things Out-Inv. 5.1 Six students in a middle school class determined the number of people in their households using the United States census guidelines. Their data is as follows: How could we determine the average number of people in these six households? TG-4-2
5.1 Follow-up • The students had an idea for finding the average number of people in the households. They decided to rearrange the cubes to try to “even out” the number of cubes in each tower. Try this on your own and see what you find for the average number of people in the households, and then read on to see what the students did. (page 55-57)
Problem 5.2 A. Make a set of cube towers to show the size of each household. B. Make a line plot of the data. C. How many people are there in the six households altogether? Describe how you determined your answer. D. What is the mean number of people in the six households? Describe how you determined your answer.
Problem 5.2 Follow-up • How does the mean for this set of six students compare to the mean for the six students in Problem 5.1? • How does the median for this set of six students compare to the median for the six students in Problem 5.1?
The grateful heart is not only the greatest virtue but the parent of all others. - Cicero TK-4-1