Analyzing and Displaying Data

Transcription

1 Analyzing and Displaying Data Objectives To review data concepts; to provide opportunities to find data landmarks and use graphs to draw conclusions. 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 Organize data into a tally chart. [Data and Chance Goal 1] Make a bar graph for a set of data. [Data and Chance Goal 1] Find the maimum, minimum, range, median, and mode of a class data set. [Data and Chance Goal ] Use graphs to answer simple questions. [Data and Chance Goal ] Key Activities Children predict whether first or last names are more likely to have more letters. They use data about their names to make a tally chart and bar graph, and find the maimum, minimum, range, median, and mode of the data. Key Vocabulary tally chart line plot bar graph minimum maimum range mode median Materials Math Journal 1, pp., and Student Reference Book, pp.,, and transparency of Math Masters, p. 1 Home Link 1 Class Data Pad Introducing the Math Boes Routine Math Journal 1, p. Children practice and maintain skills through Math Bo problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boes, Problem 1. [Number and Numeration Goal 1] Home Link Math Masters, p. 1 Children practice and maintain skills through Home Link activities. READINESS Making Tally Marks half-sheets of paper Children tally objects in the classroom. ENRICHMENT Finding the Total Class Data Pad Children find the total number of letters in their classmates first and last names. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 1 Children start a Math Word Bank, adding the terms maimum, minimum, and range. Advance Preparation Divide the Class Data Pad into two columns. Label the headings First Name and Last Name. Teacher s Reference Manual, Grades 1 pp. 11, 1, Lesson

2 Getting Started Mental Math and Reflees Children use slates to record answers to problems like the following: Write the number that is 10 more than 0, 9, 11, 0, 10, 191. Circle the tens digit in the numbers you just wrote. Underline the ones digit in the numbers you just wrote. 0, 10, 19 1 Write the number that is 10 less than, 55, , 5, 91. Circle the hundreds digit in the numbers you just wrote. 1, 5, 9 1 Write numbers that are 100 more than the numbers you just wrote. 1; 55; 1,01 Write the numbers: 9; 1,09; 10,09. Circle the hundreds digit in the numbers you just wrote. Underline the 10s digits. 9; 1,0 9; 10,0 9. Write numbers that are 100 less than the numbers you just wrote. 9; 99; 9,99 Math Message Use the data from problem on Math Journal 1, page. Record the number of letters in your partner s first and last names on the Class Data Pad. Which name do you think is likely to have more letters: a person s first name or last name? Home Link 1 Follow-Up Briefly go over the answers. Some children may benefit from doing the Readiness activity before you begin Part 1 of the lesson. See the Readiness activity in Part for details. Interactive whiteboard-ready epresentations are available at to help you teach the lesson. 1 Teaching the Lesson Math Message Follow-Up DISCUSSION Take a vote. How many children think that first names of children in the class have more letters than last names? How many think that last names are longer? Eplain that this lesson compares different ways to find the answer. Comparing Two Sets of Data PROBLEM SOLVING DISCUSSION Number of Children // //// ////\ / 5 ////\ // /// / Sample tally chart 5 Sample line plot Have children propose methods for checking their predictions using the class data. Suggest the following methods if no one brings them up: Method 1 Add the total number of letters in each column on the data pad. Because both columns have the same number of names listed, the larger total would mean the names in that column have more letters. Method Count the number of children whose first names are longer than their last names and the number of children whose last names are longer than their first names. Ask children with longer first names to raise their hands. Repeat with children who have longer last names. Record the totals on the board. Method Make tally charts, one for first names and one for last names. (See margin.) Unit 1 Routines, Review, and Assessment

3 Method Make line plots or bar graphs, one for first names and one for last names. (See margin and margin on preceding page.) Do Method with the class. Have children whose first names are longer than their last names raise their hands. Repeat with children whose last names are longer than their first names. Record the totals on the board. Making Tally Charts and Bar Graphs (Math Journal 1, pp. and ; Math Masters, p. 1; Student Reference Book, pp.,, and ) Before doing Methods and, ask children to turn to pages,, and in their Student Reference Books to review information about bar graphs and tally charts. Discuss what title and headings to use to make a tally chart for the class data and how to label a bar graph for these data. Then have children compare the vertical scales on the two bar graphs pictured on pages and. Ask: What differences do you notice? Sample answer: The scale on the Favorite Foods of the Class graph is labeled in intervals of and the scale for the Pull-Ups by Third Graders graph is labeled in intervals of 1. Have children discuss the bars that end halfway between the lines and those that end at the lines. Ask: What would the bars in the Favorite Foods of the Class graph look like if the scale showed intervals of 1? The bars would be longer. What would the bars in the Pull-Ups by Third Graders graph look like if the scale showed intervals of? The bars would be shorter. Display a transparency of Math Masters, page 1. You or a volunteer can write labels in the appropriate blanks. Use data from the column of the tally chart to fill in the horizontal scale. Model labeling the vertical ais with intervals of. Enter one of the values from the data set. Have children work with a partner to complete journal pages and. Half of the class may work on first names; the other half may work on last names. Date Displaying Data 1. How many first names are there? last names?. Make a tally chart for either first names or last names. Names 5 9 or more. How many letters does the longest name have? letters The number of letters in the longest name is called the maimum.. How many letters does the shortest name have? letters The number of letters in the shortest name is called the minimum. 5. What is the range of the numbers of letters? letters The range is the difference between the largest and smallest numbers.. What is the mode of the set of data? letters The number that occurs most often is called the mode.. What is the median of the set of data? letters (Hint: Look in your Student Reference Book.) Math Journal 1, p. Date Displaying Data continued. Make a bar graph for your set of data. Title: Answers vary. NOTE Children are asked to find the minimum, maimum, range, mode, and the median for the data. Although these statistical landmarks were introduced in Second Grade Everyday Mathematics, children may not remember them. Have children practice looking up this information in the Student Reference Book. Because children are just beginning to use the book as a reference tool, you may need to help them by reminding them to look for the terms in the Glossary. You can use the tally chart to find the median. With the children, count from either end of the tally chart to the number in the middle. If the data set consists of an even number of data, there are two middle values, and the median is the number halfway between those two middle values. Math Journal 1, p. Lesson 9

4 Date Math Boes 1. Write the numbers that are 10 less and 10 more ,5 1,5 1,59. Write 5 names in the 5-bo. 5 Sample answers: 50 5; ; 5Â ////\ ////\ ////\ ////\ ////\. Put these numbers in order from smallest to largest. 0 9 (smallest) (largest). Draw hands on the clock to show : Bring the class together and compare results. What are the advantages of displaying data in a tally chart or in a bar graph? Tally charts and bar graphs provide a way to see and compare the data. Using these displays, it is easy to find the maimum, minimum, range, mode, and median of a set of data. Which names in the class have more letters: first names or last names? Check the data your class gathered. Ongoing Learning & Practice Lara brought 1 candies to school. She gave away during recess. How many candies does she have now? candies. Add. 0 + = = + = 11 = + 15 = 9 + Unit Introducing the Math Boes Routine (Math Journal 1, p. ) Math Journal 1, p Mied Practice Eplain that Math Boes refer to practice problems children will complete on a regular basis. These pages are designed for independent work, but children may work in partnerships if appropriate. Some cells on the Math Boes page will contain a page number that will refer children to a specific page in the Student Reference Book that will help them with the Math Boes problem. Math Boes in this lesson are paired with Math Boes in Lesson 1-. The skill in Problem previews Unit content. NOTE Make sure the children have easy access to their tool kits, a number grid, and Student Reference Books as they work through the Math Boes. Name Date HOME LINK 1 5 Family Note How Much TV Did They Watch? You can find information about tally charts on pages in the Student Reference Book. You can find information about the minimum, maimum, range, mode, and median of a set of data on pages 9 and Please return this Home Link to school tomorrow. Paul asked some of his classmates how many hours they watched television over the weekend. His classmates reported the following number of hours: 1 hour hours 1 hour 5 hours 0 hours hours hours hours hours hours hours 1. Make a tally chart for the data. Spent Watching TV Hours Home Link Master 0 / 1 // // //// / 5 /. What was the least (minimum) number of hours watched? hours. What was the greatest (maimum) number of hours watched? 5 hours. What is the range for the data? 5 hours (Remember that range is the difference between the greatest number and the least number.) 5. What is the mode for the data? hours (Remember that the mode is the number that occurs most often.). What is the median for the data? hours (Remember that the median is the number in the middle.) Math Masters, p. 1 0 Ongoing Assessment: Recognizing Student Achievement Math Boes Problem 1 Use Math Boes, Problem 1 to assess children s progress toward writing whole numbers using standard base-10 notation. Children are making adequate progress if they write the numbers that are 10 more and 10 less than the given - and -digit numbers. Some children may be able to write the number that is 10 more or less than the given -digit number. [Number and Numeration Goal 1] Writing/Reasoning Have children write a response to the following: Eplain the meaning of the equals sign (=) in the sentence 0 + =, in Problem. The equals sign means that the sum of 0 + is the same as. 0 + and are equivalent names. Home Link (Math Masters, p. 1) INDEPENDENT Home Connection Children make a tally chart for a set of data and use the chart to find the maimum, minimum, range, mode, and median for the data. 0 Unit 1 Routines, Review, and Assessment

5 Differentiation Options READINESS Making Tally Marks 5 15 Min To provide eperience making tally marks, give each child or partnership a tally assignment such as the following: Tally the number of children wearing gym shoes; the number of children wearing sandals; the number of Ms on the bulletin board; the number of steps the teacher (or a child) takes in one minute; or the number of objects in the Numbers All Around Museum. Children record tally marks on half-sheets of paper and then write the number represented by the tallies. ENRICHMENT Finding the Total Number of Letters 5 15 Min PROBLEM SOLVING To further eplore working with data, have children predict the median for total letters in a name (including first and last names). Have children share their prediction strategies. Children count the total number of letters in each column of the Class Data Pad. Ask them to compare their results to those of their partner. If there is a discrepancy, both partners should do the addition again until they get the same answer. Children find the median for their total and discuss the results. ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 1) SMALL-GROUP 15 0 Min To provide language support for data landmarks, have children use the Word Bank template found on Differentiation Handbook, page 1. Ask children to write the terms maimum, minimum, and range, draw a picture representing the terms, and write other related words. See the Differentiation Handbook for more information. Planning Ahead For Lesson 1-, you will need items for a Chance Museum. Some items may be found in newspapers and magazines and would use the language of chance, such as weather reports. A jar filled with beads of several colors suggests random drawing with different chances for different colors. Collect devices that generate random outcomes, such as coins, dice, dreidels, spinners, and so on. Lesson 1