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http://illuminations.nctm.org/LessonDetail.aspx?ID=L579

A lesson plan for grades 3–8 Mathematics

Provider: National Council of Teachers of Mathematics


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Using multiple representations, students analyze the frequency of letters that occur in the names of all 50 states. After students predict which letters will appear most often in the names of the 50 states, they use the activity sheet to identify the frequency of each letter. Students determine the most effective method for collecting data and then create graphs. Illuminations provides an activity sheet, detailed instructions, and a link to an online bar graphing tool.

Students will:

  • Determine the number of times that each letter of the alphabet is used when writing the names of all 50 states.
  • Understand how various representations, including steam-and-leaf plots, box-and-whisker plots, and histograms, can be used to organize the data.

NCTM Standards and Expectations:

Grades 3-5:

  • Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  • Collect data using observations, surveys, and experiments.
  • Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.
  • Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.
  • Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.

Grades 6-8:

  • Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 3

  • Goal 4: Data Analysis and Probability - The learner will understand and use data and simple probability concepts.
    • Objective 4.01: Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems.

Grade 4

  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs, probability, and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including line graphs and bar graphs) to solve problems.
    • Objective 4.02: Describe the distribution of data using median, range and mode.
    • Objective 4.03: Solve problems by comparing two sets of related data.
    • Objective 4.04: Design experiments and list all possible outcomes and probabilities for an event.

Grade 5

  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems.
    • Objective 4.02: Compare and contrast different representations of the same data; discuss the effectiveness of each representation.
    • Objective 4.03: Solve problems with data from a single set or multiple sets of data using median, range, and mode.

Grade 6

  • Goal 4: Data Analysis and Probability - The learner will understand and determine probabilities.
    • Objective 4.06: Design and conduct experiments or surveys to solve problems; report and analyze results

Grade 7

  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.

Grade 8

  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including scatterplots) to solve problems.