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K–12 teaching and learning · from the UNC School of Education

Sticks and stones

http://illuminations.nctm.org/LessonDetail.aspx?ID=L585

A lesson plan for grades 3–8 Mathematics

Provider: National Council of Teachers of Mathematics


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While playing “Sticks and Stones,” a game based on an Apache game, students collect data, investigate the probability of various moves, and determine the average number of turns necessary to win the game. Working in small groups, students develop an understanding of the place-value system. Illuminations provides a demonstration of the game and transparencies that can be used by the teacher for the lesson.

Students will:

  • Collect and display data regarding the moves in a game.
  • Use probability to estimate the average number of turns needed to win a game.
  • Modify the rules to create a different game.

NCTM Standards and Expectations that are covered in this lesson include:

  • Collecting data using observations, surveys, and experiments.
  • Representing data using tables and graphs such as line plots, bar graphs, and line graphs.
  • Proposing and justifying conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.
  • Computing probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.
  • Selecting, creating, and using appropriate graphical representations of data, including histograms, box plots, and scatterplots.
  • Discussing and understanding the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, 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 4.03: Solve probability problems using permutations and combinations.

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 4.03: 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.

Grade 6

  • Goal 4: Data Analysis and Probability - The learner will understand and determine probabilities.
    • Objective 4.01: Develop fluency with counting strategies to determine the sample space for an event. Include lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle.
    • Objective 4.02: Use a sample space to determine the probability of an event.
    • 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.
    • Objective 4.02: Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.