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Model The Data Using Mathematical Representations


What are various ways to represent numerical data?

Develop a clear enough understanding of numerical data and how it is presented to be able to identify and explain various ways sets of numbers are presented visually and how visual representations are used to tell a story about the numbers. 

Time To Complete 

3-4 Hours

Content Areas 

  • Math

Common Core Standards 

  • CCSS.MP.5
  • CCSS.MP.6
  • CCSS.MP.4
  • CCSS.MP.2

I Can Statements 

I can:

  • Choose a format for presenting data that aids understanding
  • Present data accurately

I will know my representation of data is of high quality when it:

  • Aids understanding by clarifying, organizing, or using other presentation techniques

Suggestions for Assessing Student Readiness to Move Forward:

  • Confer with students, reviewing their data representations to ensure they meet the requirements of the assignment, purpose, and audience.
  • Ask students to use rubrics or checklists to self-assess their work and develop a plan for revision.
Possible Activities 
  1. Introduce students to possible representations, including graphic, tabular, algebraic, and infographic. Ask students to consider the question “How can you figure out what you want to present, and present it in the most compelling, comprehensive, and memorable way possible?” 

  2. Conduct a mini-lesson on the definition and purpose of using and presenting data to answer questions about the world around us focusing on real-world examples such as:

    • Do women make the same amount of money as men around the world? (comparing salaries worldwide)
    • In what country is a child most likely to be undernourished or illiterate? (comparing global statistical data)
    • What is the average level of education for various ethnic groups? (average educational attainment)
    • What is the likelihood the world will be hit by an asteroid? (measuring probability outcomes)
    • Have students work in groups to brainstorm other questions that can be answered by using numbers. (available data) 
  3. Matching:  Using two colors of card stock, give students two piles, one containing sets of data and one containing various ways of presenting numerical data (for example, bar graphs, pie charts, dot plots, line graphs, scatter plots, pictographs, histograms, frequency distribution, stem-and-leaf plots, and cumulative tables and graphs). Ask students to work in teams to match the numerical data to a graph well suited to tell a story about the data and have groups come up with a story or sentence that the data reveals or a question the data answers. Have groups present and justify their responses. 

  4. Comparing Presentations of Data:  Give students two visual representations of the same data and have them evaluate which better tells a particular story.  For example, ask, “Which foods have more chemicals added: foods from McDonald’s or foods from Subway?”  Present the data in two pie charts and in one bar chart and ask students to analyze which is easier to comprehend and why.  Have students discuss in teams and present their responses to the class.

  5. Students should brainstorm about the benefits and drawbacks of different types of representations.  Offer students a chance to look at exemplars.

  6. Model planning the right design for presentation through think-alouds, revealing how you organize your notes and then begin to create your draft. You might want to try multiple organizations, graphs, and visuals and ask students to evaluate that they find most effective and why.

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