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Types of Data Displays – Learning About and Deciding Which Display to Use for Data

Lesson Plan

Types of Data Displays – Learning About and Deciding Which Display to Use for Data

Grade Levels

7th Grade, 8th Grade

Course, Subject

Mathematics, Reading and Writing in Science and Technical Subjects
Related Academic Standards
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  • Big Ideas
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numerical measures describe the center and spread of numerical data.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
    Two variable quantities are proportional if their values are in a constant ratio. The relationship between proportional quantities can be represented as a linear function.
    Data can be modeled and used to make inferences.
    Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions.
    Mathematical relationships among numbers can be represented, compared, and communicated.
    Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations.
    Measurement attributes can be quantified, and estimated using customary and non-customary units of measure.
    Numerical quantities, calculations, and measurements can be estimated or analyzed by using appropriate strategies and tools.
    Patterns exhibit relationships that can be extended, described, and generalized.
  • Concepts
    Graphing on a coordinate plane
    Prediction and Inference
    Representations
    Algebraic Equations
    Categorical and Quantitative Data
    Data and Distributions
  • Competencies
    Apply a variety of strategies for proportional reasoning and use them to solve real world problems, including problems dealing with similarity and rates of change.
    Use the appropriate graphical data representation and extend understanding of the influence of scale in data interpretation.
    Analyze a set of data for a pattern, and represent the pattern with an algebraic rule and/or a graph.
    Analyze and/or interpret data displays and/or use them to make predictions (circle graph, line graph, bar graph, box-and-whisker plot, stem-and-leaf plot, scatter plot).
    Choose the appropriate measure of center and variability for a set of data.
    Construct, analyze, and interpret bivariate data displayed in scatter plots.
    Determine quantitative measures of center and variability.
    Display data in dot plots, histograms and box-and-whisker plots.
    Identify and use linear models to describe bivariate measurement data.
    Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
    Model and solve real world and mathematical problems using multiple representations such as algebraic, graphical and using tables.
    Represent and analyze quantitative relationships between Independent and dependent variables.
    Solve and interpret multi-step real life and mathematical problems posed with positive and negative rational numbers.
    Solve and interpret one variable equations or inequalities in real world and mathematical problems.
    Solve multi-step equations or inequalities with one variable.
    Summarize, represent, and interpret single-variable data and two-variable data.
    Use frequencies to analyze patterns of association seen in bivariate data.
    Use measures of dispersion to describe a set of data (range, quartiles, interquartile range).

Rationale

Different types of data lend itself to different displays. Students need to be able to look at a set of data and accurately decide which display is best for their data and why. Instructional strategies for all learners are provided throughout the lesson.

Vocabulary

Bar Graphs, Line Plot, Box & Whisker Plot, Scatter Plots, Line Graphs, Histograms, Stem & Leaf Plot, Circle Graph, Propaganda

Objectives

  1. The students will use their knowledge of data displays to decide and then create the appropriate way to display each set of data.
  2. Upon completion of this assignment, the students will be able to differentiate between different data displays and will be able to apply this knowledge when displaying data in the future.

Lesson Essential Question(s)

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
How precise do measurements and calculations need to be?
In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?

Which display is right for you?

Duration

Two 50 minute periods

Materials

Each pair (or group of 4 for larger classes) of students needs the following:

  • Data display graphic organizer
  • Materials for a project of their choice  (*see below)

Suggested Instructional Strategies

  • The students will learn a variety of skills such as how to  conduct research on a given topic, how to present information to a group, as well as which data displays are appropriate based on the data the students are collecting or given.
  • The lesson can be adapted and enhance to meet the needs of all learners.  All instructional adaptations are marked with a yellow highlighter for lower level and English as a second language learners and a green highlighter for upper level learners/enhancements.  Middle level learners are not highlighted either yellow or green but will complete all highlighted parts of this lesson.

Instructional Procedures

Pre-Assessment:  Hold up pictures of two types of graphs.  Have the students use notecards with A & B written on them to determine which graph they think is the better display.  Using these results, you will be able to determine the students’ understanding of data displays before beginning the lesson.  See below for pictures of the graphs.

Instructional Procedures:

  1.  You work for a company called Coca Classic.  Your boss just landed a big project and wants you to help him set up all of the data for the upcoming meeting.  Did you know that there are several types of data displays?  Which one would you choose?  Like shoes, you want the one that fits the data you have.  After all, you wouldn’t want to put on the wrong pair of shoes or shoes that are too big or too small!! Today, you’re each going to learn about different data displays and then create a presentation to teach the rest of the class what you learned.
  2. As the students work through this project they are to be using group members for help to guide them through the project; however, give each group of students a red cup and a green cup.  Tell the students that if they get really stuck they are to put the red cup on top to signal they need help.  If the green cup is on top, then they’re good to go! The teacher should circulate the room throughout the entire lesson checking on the students to make sure they are on task and working the entire time.  This is also a check to make sure they are not stuck regardless of the cup color.
  3. Hand each student a graphic organizer that has all of the data displays on it.  Then assign each pair or group of 4 a different display to research.For learning support students, have the list of websites to help them find the information on their specific data display.  See below.  For gifted and upper level learners, do not give them a list of the types of displays and have them write down all of the displays they know of as a class then take charge to assign the different displays to research in groups.  They can have more than one if needed.
  4.  Have each pair/group of students research their data display.  As the students finish their research, introduce the “Sell Your Data Display” project.  Then they should complete their presentation on their data display.  (It needs to include a visual and all important information.  See student handout below with rubric).  This should take roughly 60 minutes.  Learning support students may need more time than this to complete this task.
  5.  Have students present their data display to the class.  The students not in that group will need to take notes to complete their graphic organizer on the different data displays.
  6.  After all presentations are completed have students look at the different data displays again.  Tell students that companies often want to make their products look good so they will pick the best data display to represent their product or they might use a certain display for their data that makes a similar product look bad.  This is an example of propaganda.   That is information, ideas, or rumors deliberately spread widely to help or harm a person, group, movement, institution, nation, etc.
  7. Have the students complete a two minute quick-write using the information they gathered about data displays to describe how a company could use a display to help their product look good or another company’s product look bad.  What other types of propaganda have they seen on TV or advertised in a newspaper or learned about?

Responses should be graded according to the students’ response to the question citing a specific example of a data display that can make a company look good or bad as well as give one other example of a type of propaganda they have seen or heard of (maybe in history class?? Hitler?)  Grading of responses can be done at the teacher’s discretion. 

Formative Assessment

  • The students will be assessed based on the information that they gathered on their data display as well as on their presentation as a class based on the rubric below.
  • Ticket out the door – Use the “Which would you use?” worksheet below as a ticket out the door and an assessment for the students to apply what they learned.  These should be graded according to the student responses and will determine if further instruction is needed on this concept and can also be used as a summative assessment tool.

Learning support students may use their graphic organizer if deemed appropriate.

To enhance the learning of gifted students and upper level students, add this question to the worksheet below:

With the help of computers, mathematicians have computed and analyzed billions of digits of the irrational number π.  One of the things the analyze is the frequency of each of the numbers 0 through 9.  The table shows the frequency of each number in the first 100,000 digits of π.

Number

0

1

2

3

4

5

6

7

8

9

Frequency

9999

10,137

9908

10,025

9971

10,026

10,029

10,025

9978

9902

  1.  Display the data in a bar graph.
  2. Display the data in a circle graph.
  3. Which data display is more appropriate.  Explain.
  4. Describe the distriubution.

Related Materials & Resources

Please see attachments below for pre-assessment, assignment, rubric, weblinks, graphic organizers and the post-test/ticket out the door.

Pre-Assessment Graphs - Data Displays.docx
Sell Your Data Displays Assignment and Rubric.docx
Web Links and Graphic Organizer for Data Displays.docx
Which Would You Use - Post Test & Ticket Out the Door.docx

Author

Tina Warfel, TIU11

Date Published

June 09, 2014
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