Suggested Pacing of Lessons

Data Unit

Grade 5

Overview:

By grade 5 students have been introduced to many ways to represent data (bar graphs/double bar, circle graphs/pie charts, line graphs, line plots and many more). They are however relatively unfamiliar with stem and leaf plots which makes sense as in most cases this is a means of organizing data that is typically used in the daily work of statisticians. The following lesson suggestions should be used to review the types of graphs that children have already encountered, introduce the stem and leaf plot as a method of organizing data for representation, and the process of analyzing data for meaningful purposes. The activities should serve as a “springboard” into collecting and analyzing data all year long.

Suggested Pacing of Lessons

Wed. 9/29 / Thur. 9/30 / Fri. 10/1 / Mon. 10/2 / Tues. 10/3
Lesson 1
Reviewing Data Representation
Formulating Meaningful Questions / Lesson 2
Stem and Leaf Plots Collecting data with a purpose / Lesson 3
Collecting data for representations / Lesson 4
Representing data and formulating questions / Lesson 5
Using data to analyze questions

Lessons in the highlighted boxes could be repeated at a later date and integrated into any other content area. Examples might include:
When questions arise during literacy and children feel the need to investigate theories and collect data about a topic.
In Science when investigating any occurrence students could pose questions, collect and analyze data.
Social Studies topics may spark interest in current events. Students might collect data related to current events and determine if history is repeating itself.

Day 1: Reviewing Various Data Representations
Objective:
4.01 Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems / Students will:
Apply understanding of 4 different methods of data organization.
Vocabulary: circle graph/pie chart, double line graph, double bar graph, pictograph, range, median, mode, key, data, representation / Materials:
Large paper/poster (1 per 4 students)
Markers
Data Set Cards (see below)
Teaching Note: By 5th grade, most students have learned how to construct and interpret bar graphs, line graphs, pictographs, and pie charts/circle graphs. This lesson gives students the opportunity to quickly review these graphs, and provides time for the teacher to informally assess students and determine which graphs need additional explanation.
Before:
Graffiti Write: Give each group of 4 students a large piece of paper with the word “data” written at the top. Give students 4 minutes to quickly write everything they know/remember about data and graphing. (Each student should have his/her own marker as all students write at the same time).
Gallery Walk: Allow each group to do a quick 2-minute walk around the classroom to view all of the posters, and then return to seats. Give groups another minute to add to their original poster.
When finished, ask groups to share 1 detail they added after the gallery walk. Collect charts for posting and reference during the lesson. (Words from charts may become a part of the math word wall as they are clarified during the week’s lessons).
During:

Review the poster rubric with students being sure that students are clear of expectations.
Divide children into 8 groups of 3-4 students. Provide each group with a “Data Set” card (see below).
Double/Bar & Line data sets can changed to single sets to address the individual needs of students.
Provide each group with a sample set of data to organize and guidelines preparing them for a data presentation at the end of class.
During the lesson, make note of struggling students and/or group misconceptions and plan to address these throughout the unit as well as during re-teaching loops and the “Quick Surveys” (Investigations Ten-Minute Math Activity ) throughout the year.
Allow students to take a step back from their posters and do a silent gallery walk.
Once students have looked, have them walk around again. This time, encourage students to write a question or make a suggestion that would help the group identify critical information they may have omitted. For example; “what does your heart symbol stand for?” or “I don’t see a title.”
Give groups additional time to revise and complete their posters.

After: During the next few days, time has been provided for groups of students to share their posters.
Today, ask 2 groups with the same data set to share. Allow groups to share completed or incomplete posters. For groups who have not finished in time, determine the missing poster components as a class and allow the group additional time later to complete posters for display. Encourage a discussion about what the students notice about the similarities and differences between the two groups’ representations.
Note: Group posters should remain posted throughout the week for students to continue to view. Each day allow another set of groups to present gradually reviewing all of the representations that children will need.
Homework: Teacher Choice / Math Journal:
Each student should complete a journal write answering the two required analysis questions from the data poster on range, median, or mode.
Cut out cards, mix-up, and let each group choose one. / Graph Type:
Circle/Pie
Data Set #3
Activity / Hours spent daily (average)
Sleeping / 8
Eating / 3
Gaming / 4
Reading / 2
Homework / 3
Free Play / 4
/ Graph Type:
Double Line Graph
Data Set #4
Months / High Temperature in NC (avg)
1999 / High Temperature in NC (avg) 2009
January / 42F / 28F
March / 64F / 50F
May / 73F / 72F
July / 97F / 97F
Sept. / 74F / 75F
Nov. / 56F / 60F
Data Set #1
Creature / Heartbeats per minute
Human / 60
Cat / 150
Pig / 70
Rabbit / 205
Giraffe / 65
Elephant / 30
Graph Type:
Pictograph / Data Set #2
State / Tornadoes 1999 (average) / Tornadoes 2009 (average)
N.Carolina / 13 / 9
Iowa / 31 / 55
Texas / 124 / 130
Kansas / 47 / 45
California / 5 / 7
Florida / 46 / 36
Graph Type:
Double Bar Graph / Data Set #3
Activity / Hours spent daily (average)
Sleeping / 8
Eating / 3
Gaming / 4
Reading / 2
Homework / 3
Free Play / 4
Graph Type:
Circle/Pie
Data Set #1
Creature / Heartbeats per minute
Human / 60
Cat / 150
Pig / 70
Rabbit / 205
Giraffe / 65
Elephant / 30
Graph Type:
Pictograph / Data Set #2
State / Tornadoes 1999 (average) / Tornadoes 2009 (average)
N.Carolina / 13 / 9
Iowa / 31 / 55
Texas / 124 / 130
Kansas / 47 / 45
California / 5 / 7
Florida / 46 / 36
Graph Type:
Double Bar Graph / Graph Type:
Double Line Graph
Data Set #4
Months / High Temp. in NC (avg)
1999 / High Temp. in NC (avg) 2009
January / 42F / 28F
March / 64F / 50F
May / 73F / 72F
July / 97F / 97F
Sept. / 74F / 75F
Nov. / 56F / 60F

Poster Rubric Day 1

Content/Quality:

Information neatly organized ______(5)
Components: (if incomplete students were able to state in words)
Title ______(5 pts)
Proper labels ______(5 pts)
Range statement ______(15 pts)
Median statement ______(15 pts)
Mode statement ______(15 pts)
Description of the shape of the data ______(30 pts)

Presentation:

Each group member presented an equal amount ______(5pts)

Presentation was easy to hear ______(5 pts)

Day 2 Stem-and-Leaf plots

Organize the following data set into a stem-and-leaf plot.

Basketball Points Scored
15
9
25
33
33
25
15
13
11

Day 2 Stem-and-Leaf plots

Organize the following data set into a stem-and-leaf plot.

Basketball Points Scored
15
9
25
33
33
25
15
13
11

Day 2 Stem-and-Leaf plots

Organize the following data set into a stem-and-leaf plot.

Basketball Points Scored
15
9
25
33
33
25
15
13
11
Day 2: Introducing the Stem and Leaf Plot
Objective:
4.01 Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems / Students will:
Organize data into a stem and leaf plot and determine range, median, and mode of data set.
Vocabulary: Stem-and Leaf plot, range, median, mode, organize, representation, display / Materials:
Data sets Day 2 (see below)
Teaching Note: This particular representation could be used throughout the school year with grade 5 students to set academic goals and self monitor individual progress, although a line graph would also be great. It should be no surprise to students why their grades rise and fall. They should develop the habit of predicting the outcome of this data by their comfort with mathematical material as the year progresses.
Before:
Allow 2 new groups to present their graphs from Day 1. Have a short class discussion comparing and contrasting each group’s representation. Be certain to clear up misconceptions and post graphs for students to reference when completing their final projects. Close this activity by asking students to quickly respond to this question in their journals: What is the average score that you believe you will earn in 5th grade math class this quarter?
During:

Explain to students that they will be collecting individual data throughout the year and reflecting on their progress toward reaching each individual goal throughout the quarter. Ask students to predict the score that they will earn first quarter in math and write score on post-it note. Collect scores allowing students to remain anonymous.
Explain the structure of a stem and leaf plot and that professional data collectors (statisticians) use this method to look for similarities and differences in data sets.
Allow student volunteers to help you organize the class predictive math scores into a stem and leaf plot.
Once completed have a discussion about around the following questions:
How might we determine the range of our data?
How might we determine the median piece of data in our set?
Does our data have a mode? If so, what is it?
Why do you think statisticians choose to use this method? Is it helpful?
Provide each student with a set of data to translate into a stem and leaf plot. (see master)
Allow time for students to set up a line graph with their predictive scores as the starting point. Explain that making great scores starts with the dream of great scores and that they will continue to chart their progress throughout the year.

After:
Allow another set of groups to share their data posters from yesterday and provide feedback. Solicit responses for range, median, and mode of each data set. If time permits allow more than one group to present.
Homework:
Teacher Choice / Math Journal:
What types of data might a stem-and-leaf plot be best used for? Explain.
Day 3: Collecting Data for Representations
4.01 Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems / Students will: describe and analyze a set of mystery data, generate appropriate questions to use when investigating a given topic, analyze questions for effectiveness in answering a posed question.
Vocabulary:
range, median, mode, organize, representation, display / Materials:
Mystery Data 1 (see below) Poster paper (1 per group)
Topic ideas cut and distributed
Teaching Note:
One of the most important parts of the data collection process is the forming of a question to ask. This activity is designed to help students form reasonable questions. You will spend a good portion of time clarifying questions that inform an investigation and those that do not.
Before:
Introduce children to the routine of mystery data. Place a mystery graph up on the overhead/smart board and ask student to think about where this data may have come from (the story behind the data). When students have had a minute to think this through allow time for collaboration in small groups around the story behind the data. Share group responses allowing the students to debate over each story. Each data display will be a line plot. Use this as your opportunity to review the structure of the line plot as a representation of data also.
During:

Write the topic “sports” on the board and ask students what they might want to know about 5th graders and this topic.
Propose “types of sports that most 5th graders like to play” as a topic of investigation.
Allow groups of students to brainstorm a list of 3-5 questions they could ask 5th graders that would help determine the “types of sports that most 5th graders like to play”.
After a few minutes allow groups to share their questions. Ask the class to analyze the questions to determine if they would help us to investigate the topic stated above.
Examples may include:
What sports teams are you on?
Do you like to play sports?
What’s your favorite sports team?

Teacher Note: While the questions above are interesting, they may not provide information that would help students draw conclusions about the types of sports that most 5th graders play. If students don’t mention the questions above offer them to the class for discussion.

Explain that a question like “What’s your favorite sports team?”, only informs us about the teams that students watch, and that this may have nothing to do with playing sports at all.
Explain that selecting the right question when collecting data is a very important process and that each group is going to have a chance to brainstorm good questions and poor questions for a topic.
Their task will be to generate three good examples of questions that a student might ask and two non-examples for each topic. Examples should be written on a poster. When students feel that they have good examples allow table groups to trade posters and encourage a discussion about the posters.
Choose 1 example from the poster that agree with
Choose 1 example that you have a question about (questions should be written on the poster for groups to consider when they get their poster back)
The teacher should circulate to support this process.

After:
Discuss the questions that came up on group posters and any thoughts that students may have about these questions.
Homework: How much time does the television stay on in your house? Collect data tonight about this question and organize data into a pie chart. * Do not worry about time after you are sleep. / Math Journal:Why is it important to ask the right question when collecting data?
Day 4:Organizing Data Presentations/Formulating Meaningful Questions
Objective:
4.01 Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems
4.02 Compare and contrast different representations of the same data; discuss the effectiveness of each
representation. / Students will: Collect data and determine the best way to organize the data for display.
Vocabulary:
range, median, mode, organize, representation, display / Materials:
Mystery Data 2
Presentation guidelines
List of topics to be cut and distributed
Teaching Note:
Some students will need support to organize data. Refer them to the posters that were done on day one for clarification. Students should be allowed to choose the form of data representations that they find most useful for displaying their data. A large part of this exercise is allowing students to assess various types of data displays and determining the most effective display for a given set of data. If they do not choose wisely, it will come out at presentation time.
Before:
Place a mystery graph up on the overhead/smart board and follow the Mystery data directions.
During:

Pair students up and distribute the topics and have students generate 2 questions that they wish to investigate.
When students are ready send them to another grade 5 class to poll 10-15 students for responses to questions.(10 minutes max)
Students will return with their data, determine the set with the most interesting results, organize the set of data, and create a representation using the data presentation guidelines.
Provide each student pair with presentation guidelines.
Circulate throughout student groups to answer questions as needed and to provide clarification of misconceptions that children may have.
Schedule a time with your neighboring teacher to conduct a gallery walk of their class posters on day 5.

After
Select a few groups to share which question and data set they chose to represent and to explain why. Briefly explain the events of next day and what students can expect. Invite students to raise any questions that they may have lingering before tomorrow’s presentation.
Homework:
Teacher Choice / Math Journal:
Teacher Choice
Day 5: Analyzing Data and Determining the Most Effective Representation
Objective:
4.01 Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems
4.02 Compare and contrast different representations of the same data; discuss the effectiveness of each
representation.
4.03 Solve problems with data from a single set or multiple sets of data using median, range, and mode / Students will:
Analyze different data representations for effectiveness and accuracy.
Materials:
*Mystery Graph: Title Match *Post-it notes *Presentations Rubrics
Teaching Note:
You will want posters to have at least 1 statement or question for the range, median, and mode. Students should not have all statements or all questions.
Before:
Students will solve the mystery graph title match as a warm up.
During:

Provide all groups with 10 minutes to ensure that their charts are ready for viewing and have all required components.
Take students to another classroom to view data representations.
Students should study the poster that has the same topic that they investigated.
While viewing posters students should ask questions if they don’t understand something on the charts writing comments on sticky notes and placing them on the charts. They should also answer a range, median, or mode question from at least two posters in their math journals.
Students should determine if the poster that they are visiting displays the data in a more clear way than their own and explain why or why not. (this information need not go on the charts)
After visiting return to the classroom to review student posters and visitor comments.
In small groups allow students to discuss the outcome of the activity, their feelings, or any new ideas that they have after viewing posters.
Circulate around the room being careful to listen for students who have gained new insight from the poster comments or any other part of the experience.

After:
Solicit responses to the following questions:

If you could change your poster would you and why?
What did you learn from your data experiment?

Homework:
Teacher Choice / Math Journal:
What new questions do you have as a result of the data you collected?

Possible Scoring Rubric: Feel free to modify as a grade level