Breaking the Stick

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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

G 1 4 Worksheets G14* and ** are available for individual work to provide practice determining successful choices of points. On the ** worksheet, explain that the open dots in the example are used only to indicate that certain points cannot be breaking points, whereas every point between the open dots could be a second breaking point. G-64 IG-VI
G15 BREAKING A STICK #3 G 1 5 Capsule Lesson Summary Establish the one-to-one correspondence between a point in a triangle and two breaking points on a stick. Use this correspondence to provide a means for randomly choosing two breaking points. Materials Teacher • Colored chalk • Meter stick • Grid board Student • Worksheets G15* and** Advance Preparation: Use Blackline G15 to make a grid, or prepare your grid board as indicated on this Blackline. On the board, draw a line segment about 1 m long, and refer to this as a “stick” in the following discussion. T: What is the “breaking a stick” problem? S: If you break a stick in two places to make three pieces, sometimes the three pieces can be used to form a triangle, and sometimes they cannot. We want to know the probability of forming a triangle if the breaking points are chosen at random. T: When will the three pieces form a triangle? S: When the shorter two pieces together are longer than the longest piece. T: With our 20-cm stick, could one of the pieces be 10 cm long? S: No, because together the other two pieces would be 10 cm long. When we try to make a triangle, the two shorter pieces collapse to a line segment 10 cm long. Students often use their hands in describing this situation. T: Could one of the pieces be longer than 10 cm? S: No, there would be even less of the stick left for the other two pieces. T: So what can we say about the length of each of three pieces that will form a triangle? S: Each is shorter than 10 cm. Write this requirement on the board for emphasis. Mark the midpoint of the line segment on the board and label it 10 cm. T: The problem involves a question about probability. If we choose the breaking points at random, what is the probability that the three pieces will make a triangle? How can we choose two breaking points at random? IG-VI G-65
Page 1 and 2: G13 BREAKING A STICK #1 G 1 3 Capsu
Page 3 and 4: G 1 3 Distribute copies of Workshee
Page 7: Your table should resemble this one
Page 11 and 12: Choose a student to come to the boa
Page 13 and 14: Shade the interior of the (red) tri
Page 17 and 18: When the class is convinced that no
Page 19 and 20: G 1 6 By now the class should suspe

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