The Median Objectives To review how to display a set of data with a line plot; and to review how to find the median of a set of data. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Create a line plot. [Data and Chance Goal 1] Find the maimum, minimum, range, mode, median, and mean for a set of data. [Data and Chance Goal ] Use data landmarks and representations to answer questions and draw conclusions. [Data and Chance Goal ] Key Activities Students construct a line plot to organize and summarize data about the sizes of their families. They find the minimum, maimum, range, mode, and median for the data. Ongoing Assessment: Recognizing Student Achievement Use journal page 0. [Data and Chance Goal ] Key Vocabulary line plot median Materials Math Journal 1, p. 0 Student Reference Book, p. 71 Study Link -inch-square stick-on notes tape (optional) slate 1 Playing Subtraction Top-It (Etended-Facts Version) Student Reference Book, pp. 6 and 6 Math Masters, p. 06 per partnership: each of number cards 1 10 (from the Everything Math Deck, if available) Students practice subtraction fact etensions. Math Boes 6 Math Journal 1, p. 1 Students practice and maintain skills through Math Bo problems. Study Link 6 Math Masters, p. Students practice and maintain skills through Study Link activities. Ongoing Assessment: Informing Instruction See page 117. READINESS Finding the Middle Value Math Masters, p. deck of number cards (the Everything Math Deck, if available) Students order number cards and find the median. ENRICHMENT Comparing Family-Size Data Math Masters, p. 6 Students organize and compare family-size data for two or more classes. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 10 Students add the term median to their Math Word Banks. Advance Preparation Teacher s Reference Manual, Grades 6 pp. 160 169 11 Unit Using Numbers and Organizing Data
Getting Started Mathematical Practices SMP, SMP, SMP, SMP7, SMP8 Content Standards.MD.1,.MD. Mental Math and Reflees Write the problem 0-6 on the board. Ask students to solve it mentally and write the answer on their slates. Have students share their strategies. Present the following counting-up strategy if it is not brought up during discussion: Start at 6. Add up to the net 10 and then to 0: 6 + = 0, and 0 + 0 = 0. That is + 0 =. 0 6 0 0 Pose additional problems such as the following: 0-7 = 1 0-16 = 1 60 - = 7 67-10 = 7 1-0 = 1 8-0 = 110 - = 8 180-1 = 7 0-16 = 10 Math Message Find the line plot on page 71 of your Student Reference Book. Write two things you notice about students scores on Mr. Jackson s spelling test. Study Link Follow-Up Ask partners to compare answers to Problems 6. Check to see that all students know the number of people in their families (or the number of radios, televisions, pets, or smoke detectors in their home). 1 Teaching the Lesson Math Message Follow-Up (Student Reference Book, p. 71) WHOLE-CLASS Invite volunteers to share observations about the data shown in the Scores on a -Word Spelling Test line plot. Have students stand up if they made a similar observation. Investigating the Sizes of Students Families (Math Journal 1, p. 0; Study Link ) PROBLEM SOLVING WHOLE-CLASS Tell students that in this lesson they will organize data about the number of people in their families. Then they will identify landmarks in the data. Reviewing Students Family-Size Data Remind students that in conducting their survey, all people living at home now and any siblings living elsewhere are to be included. Resolve any questions students might have. For eample: Do I count my brother who is away at college? yes We have a boarder who has rented a room for the last 10 years. We think of her as part of the family. Should I count her? yes ELL Organizing Data Once the data have been collected, it helps to organize them to make them easier to understand. Line plots and tally charts are two methods of organizing data. Number Correct In this line plot, there are Xs above the number. Four students got a score of on the test. Here are the number of hits made by 1 players in a baseball game. 1 0 1 1 0 0 0 Organize the data. 1. Make a tally chart.. Make a line plot. Check your answers on page 1. Data and Probability Mr. Jackson s class got the following scores on a five-word spelling test. Make a line plot and a tally chart to show the data below. 0 Scores on a -Word Spelling Test Number of Students 0 1 Student Page Both the line plot and the tally chart help to organize the data. They make it easier to describe the data. For eample, Five students had words correct. correct is the score that came up most often. 0 correct and correct are scores that came up least often. No student got eactly 1 correct. Student Reference Book, p. 71 In this tally chart, there are tallies to the right of. Four students got a score of on the test. Lesson 6 11
My parents are divorced. I live with my mother during the school year and with my father during summer vacations. How should I count them? Count only those people living in your present household. I have a cousin who lives in France. Should he be counted? no After questions have been resolved, students may need to revise their family lists. Then have students record their family size in Problem 1 on journal page 0 and on a stick-on note. Constructing a Line Plot Draw a number line on the board. Ask students to attach their stick-on notes in the appropriate places above the number line, creating a line plot. To support English language learners, discuss the everyday as well as the mathematical meaning of the word plot. NOTE A line plot is a quick and easy way to organize and display data. You can think of it as a rough sketch of a bar graph. If graphing software is available, have students create their line plots using the software. 6 6 9 6 7 8 9 10 11 1 Number of People in Family After everyone s stick-on note has been posted on the board, students copy the line plot on their journal pages. Have them use Xs in place of the stick-on notes. Analyzing the Data Ask students to complete Problem on journal page 0 on their own. Then have students share their observations about the data. In discussing the data landmarks, students can use informal terms, but you should refer to these terms as maimum, minimum, range, and mode. Adjusting the Activity ELL As you discuss each landmark, have a volunteer label the number on the class line plot. Consider having students do the same on journal page 0. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 11 Unit Using Numbers and Organizing Data
Here are some other questions for discussion: How are the landmarks reflected in the shape and distribution of the data in the line plot? Sample answers: The mode is the family size that occurs most frequently. The number with the most stick-on notes is the mode. If two or more family sizes have the tallest columns of stick-on notes, they are all modes. Where are the clusters, bumps, holes, and far-out numbers? Ongoing Assessment: Recognizing Student Achievement Journal page 0 Problem Use journal page 0, Problem to assess students understanding of data landmarks. Students are making adequate progress if they are able to identify the maimum, minimum, range, and mode of the data set. Some students may be able to identify the mean. [Data and Chance Goal ] Date 6 Follow your teacher s directions and complete each step. 1. How many people are in your family? people Write the number on a stick-on note.. Make a line plot of the family-size data for the class. Use Xs in place of stick-on notes. Family Size Number of Families Student Page. Find the following landmarks for the class data: Time Class Data on Family Size a. What is the maimum () number of people in a family? people b. What is the minimum () number of people in a family? people c. What is the range? (Subtract the minimum from the maimum.) people d. What is the mode (most frequent family size)? people. What is the median family size for the class? people 6 7 8 9 10 11 1 1 Number of People in Family 71 7 7 Finding the Median of the Class Data Review ways of finding a middle value for family size; that is, about half the families should be smaller and half should be larger than this middle number. Remind students that the middle number is called the median. Here is one way to find the median: 1. List all the data from to (or to ).. Count from each end to the number (or pair of numbers) in the middle.. If two numbers are in the middle, the median number is the average of the two numbers. This happens when there is an even number of data. Math Journal 1, p. 0 NOTE Stem-and-leaf plots are covered in Grade. If your curriculum requires that this concept be covered in Grade, see www.everydaymathonline.com. Ages of boys: 9 10 11 11 1 The median age of the boys is 11. Ages of 6 girls: 9 10 10 11 11 1 The median age of the girls is 10 1_ the value halfway between the two middle numbers. Lesson 6 11
To find the median family size for the class, you can remove the stick-on notes from the line plot and line them up single file in ascending order on the board. (Have tape available to secure stickon notes that fall off.) Then have two students remove the stick-on notes two at a time, one from each end, until only one or two notes are left on the board. Students then record the median on journal page 0, Problem. last note remaining 6 6 9 Adjusting the Activity ELL Instead of lining up stick-on notes on the board, have each student take a stick-on note and line up in order. Model finding the median by asking one student from each end of the line to come together as a pair and then sit down. Repeat this until one or two students are left standing and identify the median. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L After finding the median family size for your class, ask the following questions: Are the median and the mode for family size the same? How does your own family size compare with the median size? Is your family size equal to the median size? Less than the median size? Greater than the median size? Eplain that the median is the most useful landmark for describing the middle point of a data set, and it is often called a typical value. Adjusting the Activity Ask students to find the mean of the data set and eplain how the mean is similar to or different from the median. Then ask them to eplain which landmark they think better represents the data. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 116 Unit Using Numbers and Organizing Data
Ongoing Learning & Practice Playing Subtraction Top-It (Etended-Facts Version) (Student Reference Book, pp. 6 and 6; Math Masters, p. 06) PARTNER Students play an etended-facts version of Subtraction Top-It to develop automaticity with subtraction fact etensions. See Lesson 1- for additional information. Consider having students record several rounds of play on Math Masters, page 06. Math Boes 6 (Math Journal 1, p. 1) INDEPENDENT Mied Practice Math Boes in this lesson are paired with Math Boes in Lesson -8. The skills in Problems and 6 preview Unit content. Writing/Reasoning Have students write a response to the following: Suppose the data set in Problem represents the number of hours each volunteer at an animal shelter worked during the month of July. What was the median number of minutes worked? 780 minutes Eplain how you found your answer. Sample answer: There are 60 minutes in an hour, so 60 1 = 780. Do you think it makes more sense to report data like this in hours or in minutes? Why? Sample answer: It makes more sense to report it in hours. I understand what 1 hours feels like, but 780 minutes doesn t mean as much to me. The larger unit makes more sense. Study Link 6 (Math Masters, p. ) INDEPENDENT Home Connection Students construct a line plot from data given in a tally chart. Then they find landmarks of the data set. Ongoing Assessment: Informing Instruction Watch for students who think that the median number of hours spent watching television is 19.. Students need to order the actual numbers of hours reported by Sylvia s class to find the median of the data set. Date 6 Math Boes 1. Add mentally. a. + 7 = 9 b. 0 + 70 = 90 c. 00 + 700 = 900 d. 1 = 8 + e. 10 = 80 + 0 f. 1,00 = 800 + 00. Subtract mentally or with a paper-andpencil algorithm. a. b. 17-6 91 Name Date Time STUDY LINK 6 Line Plots The students in Sylvia s class estimated 1. Construct a line plot for the data. how much time they spend watching television each week. The tally chart Student Data on Television Time below shows the data they collected. Number of Hours per Week Spent Watching TV 16 /// 17 /// 18 Study Link Master Number of Students 19 ////\ / 0 ////\ //// 1 / ////\ //. Find the following landmarks for the data: Number of Students 16 17 18 19 0 1 Number of Hours Spent Watching Television Each Week a. The maimum number of hours spent watching television each week. hours 16 0 1-6 8 10 11 1 1. A royal python can be feet long. An anaconda can be 8 feet long. What would be their combined length, end-to-end? 6 feet Math Journal 1, p. 1 Student Page Time. Write,007,9 in words. 7 0 b. minimum hours c. range hours d. mode hours e. median hours. Find the median of the data set.,, 1, 1,, 7, 19 Fill in the circle net to the best answer. A B 1 C 1 D four million, seven thousand, three hundred ninety-two 6. Tell whether each number sentence is true or false. a. 1 + 7 = false b. 6 = 1 + false c. - 1 = true d. 7 = 0-1 true. Estimate the amount of time that you watch television each week. hours 71 7 18 Try This. Calculate the mean number of hours Sylvia and her classmates spent watching TV each week. 19.7 hours Practice 110 180. 80 0 6. 90 90 7. 10 8. 0 10 70 60 10 Math Masters, p. Lesson 6 117
Name Date Time 6 Find the Median Number The number in the middle of an ordered set of data is called the middle value, or median. For Problems 1, Draw nine cards from a deck of number cards. Arrange the cards in order from to. Record the numbers in the boes below. Circle the number in the middle. Eample: 1... 0 Teaching Master 0. Describe how you found the middle number in the problems above. Sample answer: With 9 cards total, the middle card has cards on each side of it. So the fifth card is the middle one.. If you arranged the cards in Problem 1 in order from to, would the middle number stay the same? Eplain. The order of the numbers would be reversed, but the middle number would remain the same. Math Masters, p. 7 7 8 yes 8 9 9 The median of my nine cards is. The median of my nine cards is. The median of my nine cards is. 1 1 18 18 7 Differentiation Options READINESS Finding the Middle Value (Math Masters, p. ) PARTNER 1 0 Min To provide eperience with finding the median of a data set using a concrete model, have students order number cards and find the middle value. ENRICHMENT Comparing Family-Size Data (Math Masters, p. 6) PARTNER 0+ Min To further investigate organizing and summarizing data, have students compare the family-size data of their class with those of other fourth-grade classes. If graphing software is available, encourage students to use it to create their displays. Teaching Master Name Date Time Building a Math Word Bank 1 Min (Differentiation Handbook, p. 10) To provide language support for data landmarks, have students use the Word Bank Template found on Differentiation Handbook, page 10. Ask students to write the term median, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information. ELL SUPPORT SMALL-GROUP 6 Comparing Family-Size Data 1. Create a display that compares the family-size data from your class with those of other fourth-grade classes.. Compare the maimum, minimum, range, mode, and median for family size for each class. Write about the similarities and differences. Use the back of this page if you need more space. 70 7 Combine and organize the data from all of the classes. Then answer the following questions.. What is the median family size for all of the classes? people. How does your class median compare with the larger sample?. What is the mean family size for all of the classes? people 6. If you had to predict the family size of a student from your school that you did not know, what would you predict? Eplain your answer. Math Masters, p. 6 118 Unit Using Numbers and Organizing Data