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1) Core Curriculum Objective(s): 4SP1-2 Collect, organize, record, display and communicate data in charts, tables, stem-leaf graphs, and line and bar graphs with scale increments of one or greater than one. 4SP1-3 Construct, read, interpret, analyze, and write conclusions based on data (e.g., bar, line circle and stem-leaf graph: tables; charts) with or without manipulatives.
2) Overview: During this lesson the teacher should follow the teaching technique of first modeling for the students, then allowing the students to participate in the modeling demonstration, followed by allowing the students to work in small groups to complete the task and later check student mastery by allowing them to work independently. To begin this lesson students will observe as the teacher constructs a stem-leaf graph and explains what is being done. The teacher will also model for students how to interpret and analyze the data collected. Next, the teacher will pick handfuls of peanuts from a bowl as well as select several students to do the same in order to collect, record and display data on the stem-leaf graph. Following the modeling activity students will work in small groups with spinners in order to collect data for their stem-leaf graph. After completing the small group assignment, the small groups will then be instructed to interpret the data that they collected. Each small group will display their graph and discuss the findings with the large group. Once students have gained the necessary knowledge they will be placed in groups of two to create a stem-leaf graph of their choice on the computer using the table tab in Microsoft Word. Finally, the students will be assessed independently using the assessment sheet provided. Note: Rubric/Scoring Guide are provided.
3) Focus /Essential Question(s): How can data be recorded on a stem-leaf graph? Explain how data can be communicated/ read from a stem-leaf graph? What is a stem-leaf graph?
4) Time Frame: Five Forty-five minute class periods
5) Resource Materials:
* Large white chart paper for each small group to construct stem-leaf graph
* Colored markers
* Spinners for each small group (numbered 1-9)
* Pencils
* Bowl
* Peanuts (in or out of shell)
* Ruler
* Computer
* Printer
* http://www.shodor.org/interactivate/activities/data/html
6) Culminating Assessment: During the culminating assessment students will work independently to plot data by constructing a stem-leaf graph. The teacher will provide the necessary data. After plotting the given data, students will be asked to interpret data and respond to the five open response items. Note: Assessment Sheet and Scoring Chart are provided with this lesson.
PACT Note: Open response items require short answers from students that must be written in complete sentences.
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Name: ______________________________ Date:
_________________
Stem-Leaf Culminating Assessment Sheet
Construct a stem-leaf graph in the space provided below.
Then plot the data provided.
Number of minutes students watch television on Monday.
95, 88, 95, 70, 95, 30, 15, 83, 91, 26, 21, 99, 90, 65, 87, 95, 95, 78, 74, 72
1. How many students watch more than 80 minutes of television on Monday?
(2 points)
2. How many students answered the question regarding the number of minutes they watch television on Monday?
(2 points)
3. What place value do the digits on the left of the graph represent?
(2 points)
4. What place value do the digits on the right of the graph represent?
(2 points)
5. What does this stem-leaf plot tell you about this group of students?
(2 points)
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Scoring Chart
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Points
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Comprehension level
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0-2 points
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Below level
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3-5 points
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Fair level
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6-8 points
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Good level
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9-10 points
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Excellent level
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7) Instructional Activities:
Activity One:
The teacher should begin the lesson by telling students that there are several ways to record data. One way is to use a stem-leaf graph. Definition: A way to show data. Usually, the tens' digits are "stems" and the ones' digits are "leaves".
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Example:
Stem-Leaf Plot
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5
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3,7,6,2
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6
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9,0
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7
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5,5,5
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8
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7,0,4,9
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Then the teacher should draw a stem-leaf graph on the board and place the numbers 0-9 on the left of the graph. Next the teacher should reach down into a bowl of peanuts. Once the teacher has a big handful, of peanuts she should begin counting how many she has. Example: The teacher should count out loud the number of peanuts they collected, starting with one until they get to thirty-seven. Next the teacher will show the students how she is going to record 37 on the stem-leaf graph. The teacher should say I have 37 peanuts, the 3 is in the tens place so I must write the 7 to the right of the 3.
The teacher should then place the peanuts back into the bowl and grab another handful. Once she has another handful she should count out loud so that students will clearly understand the process of collecting data. Example: The second handful is 53. The teacher should again say the 5 is in the tens place so I should write the 3 next to the 5 on the stem-leaf graph. The numbers on the left are the tens place and the numbers on the right are the ones place. If necessary the teacher may grab another handful of peanuts to extend the modeling process.
Now the teacher should take the bowl around the classroom and select several students to grab a handful of peanuts. The teacher should ask the student to count out loud to collect the data. To involve more students, another student should be selected to record the data on the stem-leaf graph. The teacher should have the student who is recording data to explain where they are placing the data and why. The student should respond with the modeling that occurred at the beginning of the lesson. Example: My classmate counted twenty-seven peanuts so I must locate the two on the left side of the stem-leaf graph, which represents the tens, and write the seven on the right side of the graph, which represents the ones. The numbers on the left represent the tens place and the numbers on the right represent the one's place. As other students become involved in the process, the teacher will explain that if two, three or more students have the same data it should still be recorded. Also the teacher should explain that after each digit is written on the one's side of the stem-leaf graph, a comma should be placed after the number to represent another number. As the first part of the activity continues, the teacher should monitor student responses and assist with support as needed.
Note: Every stem-leaf graph will look different with this activity. Once the teacher feels students have mastered the concepts, the teacher is ready to model how students can read data on a stem-leaf plot.
Concepts:
(1) Tens place on left, ones place on right
(2) Comma's are used to separate the data on the one's side of the graph
(3) Ones place must correspond with the tens place.
The teacher will model the reading process by actually pointing to the number with a ruler or hand. The teacher should start with the number of ones digits on the right side of the chart. She will say to the students this is how you will know the number of students that participated in getting a handful of peanuts. The teacher may choose to have the students count along with her to communicate the number of students that participated in the activity. Each digit plotted represents a person's handful of peanuts.
At this point the teacher should read the data on the chart to be sure students understand how to read the data. Once that process is completed, the teacher should select several digits on the graph one at a time and have students read the number. The teacher should monitor and assist as necessary.
The teacher should now ask questions such as how many people grabbed a handful of 20, 30, 40 or more peanuts? Students should look at the stem-leaf plot and count the numbers that appear higher than 20, 30 or 40 in order to respond correctly. Several students should be questioned. After a student gives an answer the teacher should select several other students to see if they agree. The student should not respond with a yes or no answer but explain why or why not.
The teacher can also allow students to come to the board so that they may point to the stem-leaf graph and then respond to questions to increase mastery and large group participation. The teacher should monitor and assist as necessary.
Finally, the teacher should ask the large group what this stem-leaf plot tells them or how would they interpret these numbers. The teacher should accept all reasonable answers. Possible responses: (1). The majority of people that participated have small hands because only two people grabbed 50 or more peanuts. (2). Five people that participated may have hands about the same size because five people picked up the same number of peanuts. The teacher should assist students with responses during this time as they interpret/read data for the first time.
Activity Two:
Students are now ready to be placed into small groups of 3 no more than four to create their own stem-leaf graph. The teacher will explain that earlier in the lesson they collected data using peanuts. With this activity they will collect data using spinners. Note: It is significant that the teacher explains to students how they are collecting data for their stem-leaf graph. Each student in the group will spin the spinner ten times to collect 5 two-digit numbers. Students should record their number at the top of the large white paper. Next they will take turns as they construct the stem-leaf graph. As the teacher goes around to monitor and assist, she should hear groups say such things as, we must draw a line to separate the tens place and the ones place. She should also hear students explain why they are placing a certain number in a certain place. The most important rule during this activity is that every one in the group should have a chance to plot data and no one in the group can write on the stem-leaf graph without explaining what they are doing.
After all directions have been given the teacher should hand out one colored marker to each group, one large piece of white chart paper and one spinner with the numbers 1-9.
As students work in small groups, the teacher should monitor and assists small groups for correct responses. Also as the teacher monitors groups, she should question students.
Possible questions:
How many times did someone spin a number greater than 50?
What do the numbers on the left of the graph represent?
What do the numbers on the right represent?
Did the same number appear more than once?
Why did your group place a 4 to the right of this 3?
Activity Three:
Note:
Prior to beginning activity three, each small group should be told that during the large group sharing time each person from the group must communicate one thought from the stem-leaf graph to the class. During this time, the teacher will also question the small groups to assist them in interpreting and analyzing their information further. Students in the audience may also ask questions of the small groups. Note: This is a great way to increase mastery and student success.
Possible questions:
What are the highest and lowest numbers on the graph?
How many times did a particular group spin the spinner?
How do you know?
Did anyone in this group spin the number 66?
How do you know?
Did any number appear more than once?
Activity Four:
Prior to this activity students should have knowledge of how to create a table in Microsoft word. Prior to activity four, the teacher should also provide pairs of students with possible topics for stem-leaf graphs.
Examples:
(1) Number of videos each student has at home.
(2) How many times it takes to lick a lollypop before it breaks or cracks.
(3) How many minutes they play outside on Saturday.
(4) How many times they go shopping each month.
(5) How often they eat sweets per month.
Students will now work in pairs to create a stem-leaf graph of their choice on the computer using the table tab in Microsoft word. They must type how or what they used to collect the data, construct the graph as well as create four questions of their own and answer them regarding their stem-leaf graph, using the computer. Pairs of students can do this during computer time in class or the entire class could be scheduled to complete this task during Computer Lab Time. Note: How activity four is completed is up to the teacher because of limited access to computers in a self-contained classroom.
Extension: As an enrichment activity students should be provided with the website
http://www.shodor.org/interactivate/activities/data/html which will provide students with enrichment activities and content related to stem-leaf graphs.
Activity Five:
Students will be assessed using the Stem-Leaf Culminating Assessment sheet provided and Scoring chart provided.
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