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Collecting and Describing Data Shantel Gudu – EDUC 4274 Grades A's B's C's D's 6 5 4 3 2 1 0 Yes No InBetween Table of Contents 3. Core Concepts – Data Organization 6. Curriculum Expectations Grade 1 7. Curriculum Expectations Grade 2 8. Curriculum Expectations Grade 3 9. Sorting 10. Venn Diagrams 11. Carroll Diagrams 12. Activities for Primary Grades 13. Common Errors and Misconceptions 15. Appropriate Manipulatives 18. Curriculum Expectations Juniors 21. Data Collecting 22.Common Errors and Misconceptions 24. Appropriate Manipulatives 26. Statistics 27. Core Concepts of Central Tendency 28. Activities for Junior Grades 29.Common Errors and Misconceptions 31. Appropriate Manipulatives 32. Books Used for Teaching Data Collecting 33. References 14 12 10 InBetween 8 Fail 6 Success 4 2 0 Level Level Level Level 1 2 3 4 Core Concepts - Data Organization Sorting is the physical act of grouping objects according to shared characteristics. Classifying is the process of differentiating among the groups by giving each group a category name (Small, 2013, pg 560) Step 1 Recognizing Attributes Data Organization Step 2: Attributes and Characteristics Data Organization Step 3: Describing a Sorting Rule Curriculum Expectations - Primary Data Management and Probability Grade 1 Collect and organize categorical primary data and display the data using concrete graphs and pictographs, without regard to the order of labels on the horizontal axis; Read and describe primary data presented in concrete graphs and pictographs; Describe the likelihood that everyday events will happen. Curriculum Expectations - Primary Data Management and Probability Grade 2 Collect and organize categorical or discrete primary data and display the data using tally charts, concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers, with labels ordered appropriately along horizontal areas as needed; Read and describe primary data presented in tally charts, concrete graphs, pictographs, line plots, simple bar graphs, and other graphic organizers; Describe probability in everyday situations and simple games. Curriculum Expectations - Primary Data Management and Probability Grade 3 Collect and organize categorical or discrete primary data and display the data using charts and graphs including vertical and horizontal bar graphs, with labels ordered appropriately along horizontal axes, as needed; Read, describe, and interpret primary data presented in charts and graphs, including vertical and horizontal bar graphs; Predict and investigate the frequency of a specific outcome in a simple probability. Sorting One Attribute Multiple Attributes Venn Diagrams One Attribute Carroll Diagrams Activities for Primary Grades Let’s create a sorting rule! Problem Solving: In a class of 22 students, 10 play hockey and 15 play basketball. Is it possible that there are some students who play neither sport? What is the greatest possible number of students who do not play either sport? Is it possible that all 22 students are involved in one sport or the other or even both? Explain these answers using a Venn Diagram Common Errors and Misconceptions Data Organization: Common Errors, Misconceptions, and Strategies Common Error or Misconception Using “and” and “or” Suggested Strategy Ask students to be specific when using the two interchangeably. Explain to students that using “and” in a sentence means that you want something or someone with both attributes. For example: Who is presenting their projects on Monday AND Thursday. When using “or” remind students that this is comparing two different attributes for example: Who is presenting their projects on Monday OR Thursday. Common Errors and Misconceptions Data Organization: Common Errors, Misconceptions, and Strategies Common Error or Misconception Using Venn Diagrams When students use Venn Diagrams to show a sorting, they ignore the items that do not belong inside the circles. Suggested Strategy Appropriate Manipulatives Data Organization: Examples of Manipulatives Attribute Blocks Attribute or logic blocks are ideal for sorting because of their many attributes: size, colour, shape, and thickness. Example Appropriate Manipulatives Data Organization: Examples of Manipulatives Other Sorting Materials Materials such as cards or tiles, as well as items found in the home and classroom (buttons, writing implements, footwear, etc.) can also be used to practice identifying attributes through sorting. Example Appropriate Manipulatives Data Organization: Examples of Manipulatives Geometric Shapes Shapes of different sizes are useful for sorting. Geometric shapes, both 2-D and 3-D, can be teacher-made or commercial. Attributes such as number of sides, concavity or convexity, and symmetry can be included. Example Junior – Collecting & Describing Data Opening Activity Curriculum Expectations - Junior Data Management and Probability Grade 4 Collect and organize discrete primary data and display the data using charts and graphs including stem-and-leaf plots and double bar graphs; Read, describe, and interpret primary data and secondary data presented in charts and graphs, including stem-and-leaf plots and double bar graphs; Predict the results of a simple probability experiment then conduct the experiment and compare the prediction to the results. Curriculum Expectations - Junior Data Management and Probability Grade 5 Collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs; Read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs; Represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic list and area models. Curriculum Expectations - Junior Data Management and Probability Grade 6 Collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including continuous line graphs; Read, describe, and interpret data, and explain relationships between the sets of data; Determine the theoretical probability of an outcome in a probability experiment, and use it to predict the frequency of the outcome. Data Collection Common Errors and Misconceptions Data Collection: Common Errors, Misconceptions and Strategies Common Errors or Misconceptions Using or Vague Survey Questions Suggested Strategy Have students try out their questions on a variety of different audiences to see the kinds of responses they get. Encourage students to ask questions that will result in responses that are unambiguous because they ask for specific information. Common Errors and Misconceptions Data Collection: Common Errors, Misconceptions and Strategies Common Errors or Misconceptions Non-Discrete Categories When students ask survey questions, they include choices that are not exclusive or discrete. Ex) What is your favourite type of game? a) Monopoly b) Sorry c) Board Games d) Game of Chance Suggested Strategy It is important to remind students that, if they were to compare the sizes of the groups who chose each answer, or determine the total number of people who were surveyed, then they cannot choose more than one answer. Encourage students to review the list of categories to see how they can refine it so that categories do not overlap. Appropriate Manipulatives Data Collection: Examples of Manipulatives Concrete Graphing Materials Younger students may prefer to use concrete materials to keep track of survey results. Example Hanging clothespins on a string Linking cubes to make a “tower” for each response Making rows of stickers Stacking paper cups Using magnetic pictures or name tags Placing craft sticks in labeled cups Appropriate Manipulatives Data Collection: Examples of Manipulatives Clipboards Many students using clipboards when they are surveying others. Examples Clipboards make it easy for students to conduct surveys anywhere. Statistics Statistics involves using numerical values to describe a set of data. Measures of Central Tendency Mean Median Mode Range Core Concepts of Central Tendency The purpose of a measure of central tendency is to assign a value, to a set of data that is a good representation of the data. Three measures of central tendency are mean, median, and mode. The mean indicates the value that would result from putting all the values together and distributing them evenly. The median is the middle number when pieces of the data are listed in order. If there are two middle values, the median is the mean of these values. Sometimes a combination of range and mean, median, or mode gives a better picture of the data than one measure alone. Activities for Junior Grades Create 2 data sets that are quite different but have the same mean Create 4 data sets so that the mean is 42 and the median is 12 Create a set of data with a mean of 10, a median of 5, and a range of 33 Common Errors and Misconceptions Statistics: Common Errors, Misconceptions and Strategies Common Error or Misconception Incorrectly Counting the Mean Students forget to put the numbers in order and simply right down the middle number. Students take half of the number of values and use that value incorrectly to identify the mean. Suggested Strategy Remind students that once the median is located, there should be just as many number set above and below the median. Provide students with the opportunity to check their work for possible errors when calculating the mean. Common Errors and Misconceptions Statistics: Common Errors, Misconceptions and Strategies Common Error or Misconception Incorrectly Reporting the Range Ex) 4,4,5,7,7,7,8,9 students may describe the range of the set of data as “from 4 to 9” rather than “5”. Suggested Strategy Remind students that like the mean or median the range is a single value. The range is a single value used to describe the spread of data. Appropriate Manipulatives Statistics: Example of Manipulatives Linking Cubes and Grid Paper Linking cubes and grid paper are good tools to use when you first introduce the concepts of mean, median, and mode. Example To determine the mean, students adjust the cubes the cubes until they are all the same length. To determine the median students line up the cubes in order from least to greatest when identifying the middle cube. To determine the mode, students line up the cubes in order to identify the most frequent length. Books Used for Teaching Data Collecting Books for Teaching Data Collection References Ministry of Education. (2005). The Ontario Curriculum Grades 1-8, Mathematics. Government of Ontario. Small, M. (2013). Making Math Meaningful to Canadian Students, K-8. (2nd Edition). Nelson Education Ltd.
