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Lessons

    Standards in this Lesson

    Common Core Math Standards
    6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    7.SP.B

    Draw informal comparative inferences about two populations.

    HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    CSTA Standards
    2-DA-08

    Collect data using computational tools and transform the data to make it more useful and reliable.

    3A-DA-11

    Create interactive data visualizations using software tools to help others better understand real-world phenomena.

    Alabama Standards
    AL.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    AL.7.SP.B

    Draw informal comparative inferences about two populations.

    AL.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Arkansas Standards
    AR.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    AR.7.SP.B

    Draw informal comparative inferences about two populations.

    AR.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    California Standards
    CA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    CA.7.SP.B

    Draw informal comparative inferences about two populations.

    CA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Colorado Standards
    CO.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    CO.7.SP.B

    Draw informal comparative inferences about two populations.

    CO.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Connecticut Standards
    CT.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    CT.7.SP.B

    Draw informal comparative inferences about two populations.

    CT.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Delaware Standards
    DE.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    DE.7.SP.B

    Draw informal comparative inferences about two populations.

    DE.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Delaware Standards
    GA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    GA.7.SP.B

    Draw informal comparative inferences about two populations.

    GA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Hawaii Standards
    HI.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    HI.7.SP.B

    Draw informal comparative inferences about two populations.

    HI.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Idaho Standards
    ID.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    ID.7.SP.B

    Draw informal comparative inferences about two populations.

    ID.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Illinois Standards
    IL.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    IL.7.SP.B

    Draw informal comparative inferences about two populations.

    IL.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Iowa Standards
    IA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    IA.7.SP.B

    Draw informal comparative inferences about two populations.

    IA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Kansas Standards
    KS.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    KS.7.SP.B

    Draw informal comparative inferences about two populations.

    KS.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Kentucky Standards
    KY.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    KY.7.SP.B

    Draw informal comparative inferences about two populations.

    KY.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Louisiana Standards
    LA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    LA.7.SP.B

    Draw informal comparative inferences about two populations.

    LA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Maine Standards
    ME.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    ME.7.SP.B

    Draw informal comparative inferences about two populations.

    ME.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Michigan Standards
    MI.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MI.7.SP.B

    Draw informal comparative inferences about two populations.

    MI.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Maryland Standards
    MD.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MD.7.SP.B

    Draw informal comparative inferences about two populations.

    MD.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Massachusetts Standards
    MA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MA.7.SP.B

    Draw informal comparative inferences about two populations.

    MA.9-12.CT.c.3

    Create, evaluate, and revise data visualization for communication and knowledge.

    MA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Mississippi Standards
    MS.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MS.7.SP.B

    Draw informal comparative inferences about two populations.

    MS.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Missouri Standards
    MO.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MO.7.SP.B

    Draw informal comparative inferences about two populations.

    MO.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Montana Standards
    MT.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    MT.7.SP.B

    Draw informal comparative inferences about two populations.

    MT.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    New Hampshire Standards
    NH.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NH.7.SP.B

    Draw informal comparative inferences about two populations.

    NH.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Nevada Standards
    NV.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NV.7.SP.B

    Draw informal comparative inferences about two populations.

    NV.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    New Jersey Standards
    NJ.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NJ.7.SP.B

    Draw informal comparative inferences about two populations.

    NJ.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    New Mexico Standards
    NM.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NM.7.SP.B

    Draw informal comparative inferences about two populations.

    NM.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    North Carolina Standards
    NC.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NC.7.SP.B

    Draw informal comparative inferences about two populations.

    NC.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    North Dakota Standards
    ND.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    ND.7.SP.B

    Draw informal comparative inferences about two populations.

    ND.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    New York Standards
    NY.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    NY.7.SP.B

    Draw informal comparative inferences about two populations.

    NY.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Oklahoma Standards
    OK.6.D.1.3

    Create and analyze box and whisker plots observing how each segment contains one quarter of the data.

    OK.6.DA.S.01

    Identify how the same data can be represented in multiple ways.

    OK.7.D.1.2

    Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

    OK.7.DA.S.01

    Create multiple representations of data.

    OK.8.DA.S.01

    Analyze multiple methods of representing data and choose the most appropriate method for representing data.

    Ohio Standards
    OH.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    OH.7.SP.B

    Draw informal comparative inferences about two populations.

    OH.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Oregon Standards
    OR.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    OR.7.SP.B

    Draw informal comparative inferences about two populations.

    OR.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Pennsylvania Standards
    PA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    PA.7.SP.B

    Draw informal comparative inferences about two populations.

    PA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Rhode Island Standards
    RI.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    RI.7.SP.B

    Draw informal comparative inferences about two populations.

    RI.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    South Dakota Standards
    SD.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    SD.7.SP.B

    Draw informal comparative inferences about two populations.

    SD.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Tennessee Standards
    TN.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    TN.7.SP.B

    Draw informal comparative inferences about two populations.

    TN.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Utah Standards
    UT.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    UT.7.SP.B

    Draw informal comparative inferences about two populations.

    UT.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Vermont Standards
    VT.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    VT.7.SP.B

    Draw informal comparative inferences about two populations.

    VT.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Washington Standards
    WA.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    WA.7.SP.B

    Draw informal comparative inferences about two populations.

    WA.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    West Virginia Standards
    WV.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    WV.7.SP.B

    Draw informal comparative inferences about two populations.

    WV.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Wisconsin Standards
    WI.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    WI.7.SP.B

    Draw informal comparative inferences about two populations.

    WI.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Wyoming Standards
    WY.6.RP.A

    Understand ratio concepts and use ratio reasoning to solve problems.

    WY.7.SP.B

    Draw informal comparative inferences about two populations.

    WY.HSS.ID.A

    Summarize, represent, and interpret data on a single count or measurement variable.

    Textbook Alignment

    IM Algebra 1
    IM.Alg1.1.3

    A Gallery of Data

    IM.Alg1.1.2

    Data Representations

    IM 8 Math™
    IM.8.6.2

    Plotting Data

    IM.8.6.1

    Organizing Data

    Practices in this Lesson

    Math
    MP.5

    Use appropriate tools strategically

    MP.6

    Attend to precision

    Science and Engineering
    SEP.3

    Planning and Carrying Out Investigations

    Social Justice
    SJ.2

    Students will develop language and historical and cultural knowledge that affirm and accurately describe their membership in multiple identity groups

    SJ.4

    Students will express pride, confidence and healthy self-esteem without denying the value and dignity of other people.

    SJ.7

    Students will develop language and knowledge to accurately and respectfully describe how people (including themselves) are both similar to and different from each other and others in their identity groups.

    Students learn to generate and compare pie charts & bar charts, explore other plotting & display functions, and (optionally) design an infographic.

    Lesson Goals

    Students will be able to:

    • Read pie and bar charts

    • Explain the difference between pie and bar charts

    • Generate pie and bar charts (among others) from the Animals Dataset

    Student-facing Lesson Goals

    • Let’s use functions to create pie charts, bar graphs and other data displays from Tables.

    Materials

    Preparation

    Supplemental Resources
    Glossary
    bar chart

    a display of categorical data that uses bars positioned over category values; each bar’s height reflects the count or percentage of data values in that category

    categorical data

    data whose values are qualities that are not subject to the laws of arithmetic

    contract

    a statement of the name, domain, and range of a function

    domain

    the type or set of inputs that a function expects

    percentage

    a ratio showing the parts per hundred

    pie chart

    a display that uses areas of a circular pie’s slices to show percentages in each category

    🔗Pie and Bar Charts 30 minutes

    Overview

    Students extend their understanding of Contracts and function application, learning new functions that consume Tables and produce displays and plots.

    Launch

    • Where have you seen infographics and graphs used to display data in the real world?

    Here is the Contract for a function that makes pie charts:

    # pie-chart :: Table, String ‑> Image

    And here is an example of using the function:

    pie-chart(animals-table, "legs")

    • What is the Name of this function?

      • pie-chart

    • How many inputs are in its Domain?

      • two

    • In the Interactions Area, type pie-chart(animals-table, "legs") and hit "Enter". What happens?

      • An interactive pie chart appears.

    A pie chart showing how many animals have each number of legs🖼Show image

    Hovering over a pie slice reveals the label, as well as the count and the percentage of the whole. In this example we see that there is 1 animal with 0 legs, representing 3.1% of the population.

    We can also resize the window by dragging its borders. This allows us to experiment with the data before closing the window and generating the final, non-interactive image.

    The function pie-chart consumes a Table of data, along with the name of a categorical column you want to display. The computer goes through the column, counting the number of times that each value appears. Then it draws a pie slice for each value, with the size of the slice being the percentage of times it appears. In this example, we used our animals-table table as our dataset, and made a pie chart showing the distribution of the number of legs across the shelter.

    People aren’t Hermaphrodite? When students make a display of the sex of the animals, they will see that some animals are male, some are female and some are hermaphrodites. We use the descriptor sex rather than gender because sex refers to biology, whereas gender refers to identity. Hermaphrodite is the biological term for animals that carry eggs & produce sperm (nearly 1/3 of the non-insect animal species on the planet!). Plants that produce pollen & ovules are also hermaphrodites. While the term was previously used by the medical community to describe intersex people or people who identify as transgender or gender non-binary, it is not biologically accurate. Humans are not able to produce both viable eggs and sperm, so "hermaphrodite" is no longer considered an acceptable term to apply to people.

    Investigate

    Here is the Contract for another function, which makes bar charts:

    # bar-chart :: Table, String ‑> Image

    • Which column of the animals table tells us which species the animal is?

      • The second column, "species"

    • Use bar-chart to make a display showing how many animals there are of each species.

    • Experiment with pie and bar charts, passing in different column names. If you get an error message, read it carefully!

    • What do you think are the rules for what kinds of columns can be used by bar-chart and pie-chart?

    • When would you want to use one chart instead of another?

    To dig deeper into pie charts and bar charts, have students complete Bar & Pie Chart - Notice and Wonder. They can also focus on one display at a time using Pie Chart - Notice and Wonder or Bar Chart - Notice and Wonder.

    Complete Matching Bar Charts to Pie Charts.

    Common Misconceptions

    • Pie charts and bar charts can show counts or percentages of categorical data. If there are more people with brown hair than blond hair, for example, a pie chart of hair color will have a larger slice or longer bar for "brown" than for "blond". In Pyret, pie charts show percentages, and bar charts show counts.

    • A pie chart can only display one categorical variable, but a bar chart might be used to display two or more. Pie charts have a wedge for each represented category. Unlike in bar charts, empty categories will not be included in a pie chart. When comparing bar charts, it is important to read the scales on the y-axes. If the scales do not match, a taller bar may not represent a larger value.

    • Bar charts look a lot like another kind of chart - called a "histogram" - which are actually quite different because they display quantitative data, not categorical. This lesson focuses entirely on pie- and bar charts.

    Synthesize

    Confirm that students have correctly matched the displays on Matching Bar Charts to Pie Charts.

    • What strategies did you use to match the bar charts to the pie charts?

    • Which displays do you find it easier to interpret? Why?

    • What information is provided in bar charts that is hidden in pie charts?

      • In a bar chart, categories with no values are shown as empty categories, but there are no wedges for categories with 0% on a pie chart.

    • Why might this sometimes be problematic?

      • Sample Answer: If a service isn’t reaching a sector of the population, it’s easier to ignore the issue if that population doesn’t get represented in the display.

    Bar Charts and Pie Charts display how much of the sample belongs to each category. If they are based on sample data from a larger population, we use them to infer the proportion of a whole population that might belong to each category.

    Bar Charts and Pie Charts are mostly used to display categorical columns.

    While bars in some bar charts should follow some logical order (alphabetical, small-medium-large, etc), the pie slices and bars can technically be placed in any order, without changing the meaning of the chart.

    Mini Project: Making Infographics Infographics are a powerful tool for communicating information, especially when made by people who actually understand how to connect visuals to data in meaningful ways. Making an Infographic is an opportunity for students to become more flexible math thinkers while tapping into their creativity. This project can be made on the computer or with pencil and paper. There’s also an Infographics Rubric to highlight for you and your students what an excellent infographic includes.

    🔗Exploring other Displays 25 minutes

    Overview

    Students freely explore the Data Science display library. In doing so, they experiment with new charts, practice reading Contracts and error messages, and develop better intuition for the programming constructs they’ve seen before.

    Launch

    There are lots of other functions, for all different kinds of charts and plots. Even if you don’t know what these plots are for yet, see if you can use your knowledge of Contracts to figure out how to use them.

    Investigate

    Have students share their answers and discuss.

    Common Misconceptions

    There are many possible misconceptions about displays that students may encounter here. But that’s ok! Understanding all those other plots is not a learning goal for this lesson. Rather, the goal is to have them develop some loose familiarity, and to get more practice reading Contracts.

    Synthesize

    • What displays did you find that work with just one column of data?

      • pie and bar charts, histograms and box plots

    • What displays did you find that work with more than one column of data?

      • scatter plots and lr-plots

    • What displays did you find that work with categorical data?

      • pie and bar charts

    • What displays did you find that work with quantitative data?

      • histograms, box plots, scatterplots, and lr-plots

    Today you’ve added more functions to your toolbox. Functions like pie-chart and bar-chart can be used to visually display data, and even transform entire tables!

    You will have many opportunities to use these concepts in this course, by writing programs to answer data science questions.

    Extension Activity

    Sometimes we want to summarize a categorical column in a Table, rather than a pie chart. For example, it might be handy to have a table that has a row for dogs, cats, lizards, and rabbits, and then the count of how many of each type there are. Pyret has a function that does exactly this! Try typing this code into the Interactions Area: count(animals-table, "species")

    What did we get back? count is a function that consumes a table and the name of a categorical column, and produces a new table with exactly the columns we want: the name of the category and the number of times that category occurs in the dataset. What are the names of the columns in this new table?

    • Use the count function to make a table showing the number of animals that are fixed (or not) from the shelter.

    • Use the count function to make a table showing the number of animals of each sex from the shelter.

    Sometimes the dataset we have is already summarized in a table like this, and we want to make a chart from that. In this situation, we want to base our display on the summary table: the size of the pie slice or bar is taken directly from the count column, and the label is taken directly from the value column. When we want to use summarized data to produce a pie chart, we have the contract for another function:

    # pie-chart-summarized :: Table, String, String ‑> Image

    And an example of using that function (applying count to the animals-table to force it into the shape pie-chart-summarized needs):

    pie-chart-summarized(count(animals-table, "species"), "value", "count")

    🔗Additional Exercises

    These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.