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High School — Mathematics
Data Analysis and Probability

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    Data Analysis and Probability

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      Strategies: Help with Fundamentals

      The following activities are suggestions for working with students who need help with fundamentals. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Difficulty 1

      In mathematical situations that use the terms "and" or "or", students may have trouble deciding whether to add probabilities or multiply them.

      • Give each student two groups of different colored items. Make sure the number of items in each group is small. For instance, Group 1 might have one red, one white, and one blue tile. Group 2 might have one green, one yellow, and one purple tile. Have students answer such questions as:

        • What is the probability of randomly drawing a red tile from Group 1?
        • What is the probability of randomly drawing a green tile from Group 2?
        • List all the pairs possible by randomly drawing one tile from Group 1 and one tile from Group 2.
        • Look at the list of possible pairs and determine the probability of drawing one red tile and then one green tile.

        Have students complete several sets of similar activities. Then ask them to decide how they can use the probabilities of the independent events (answers to the first two questions) to find the probability of a compound event using "and" (answer to the last bullet point.)

        When students have figured out how to find the probability of a compound event using "and," create similar activities with an "or" situation. Students are more likely to remember the algorithms when they understand the mathematical processes behind them.

      Difficulty 2

      If students have trouble identifying the median, minimum, maximum, and upper and lower quartile, help them understand these terms by using manipulatives.

      • Give students or pairs of students an odd number of linking cubes, colored tiles or other manipulatives. If possible make sure that each student or group receives more than 10 different items. Have students arrange their manipulatives in a horizontal line. Tell them to imagine that they have arranged the manipulatives in order with the smallest item on the left and the largest item on the right.

        Now remind students that the median is the middle object, and ask students to find the object that is the median of their arrangement. Have them push it up so it is slightly out of line. Repeat this process with the minimum (smallest item), maximum (largest item), lower quartile (the object that is halfway between the median and the smallest item), and the upper quartile (the object that is halfway between the median and the largest item.) Note: Since the students are working with an odd number of objects, they should include the median when finding the lower quartile and when finding the upper quartile. For example, if students are working with one red, one orange, one yellow, one blue and one green tile in that order, then the yellow tile is the median. When finding the quartiles, students should consider the set {red, orange, yellow} and the set {yellow, blue, green}.

        Finally, have students write a number under each of their manipulatives. Make sure that they write the numbers in order from smallest to largest, moving left to right across the page. Now have students identify the numbers that are the median, lower quartile, upper quartile, minimum and maximum.

        Once students can accurately identify these terms using manipulatives, pose a grade level problem that requires them to know these terms without the use of manipulatives.

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