The Calvin Cycle and Summary of Photosynthesis

Class: Eighth Grade Mathematics Instructor: Marc Vogel Unit: Probability and Statistics Time: 1 Period (68 Minutes)

Grab Bag Cuisenaire Rods Lesson

Behavioral Objectives SWBAT:  Determine the mean, median, and mode for a data set.  Draw conclusions about a data set.  Recognize patterns in data.  Make and test hypotheses.

Timeline

Time Activity and Description 5 - 10 min.  Anticipatory Set/Do Now o How do you calculate the mean, median, and mode for a set of numbers? o What is the mean, the median, and the mode for the set of the following girl’s shoe sizes: {4, 5, 5, 5, 5, 5, 5, 6, 6.5, 6.5, 7, 8, 9}? 15 min.  Grab Bag Activity o Distribute paper bags with Cuisenaire Rods in them. o Distribute Activity Masters. o Prompt: Hector insisted that anytime he picked rods out of the class storage box, there would always be a blue rod in his pick. He therefore thought that blue must be the average length for a rod. What do you think? Suppose you reach into a bag and grab a handful of Cuisenaire Rods. What is the typical length of a rod in your handful? . Divide the students into groups of two. . Have the students read and follow the directions on the activity master.  Player 1 should grab a handful of rods without looking and place them on the desktop, recording the number of each color of rod in the handful.  The students must then find and record the median length, the mode length, and the mean length of the handful.  Then, the students must put the rods back into the bag, and Player 2 must grab a handful of Cuisenaire Rods without looking.  Then, the students must calculate the mean length, the median length, and the mode length for this handful of Cuisenaire Rods.  Then, the students must combine the data from Class: Eighth Grade Mathematics Instructor: Marc Vogel Unit: Probability and Statistics Time: 1 Period (68 Minutes)

both handfuls of Cuisenaire Rods and determine the mean length, the median length, and the mode length of the combined handfuls.  The students must be prepared to explain what the three measures of central tendency (the mean, the median, and the mode) tell you about the typical lengths of rods in a handful. 15 min.  Interactive Discussion o Which measure (median, mode, or mean) best represents the typical length of a rod from a handful of Cuisenaire Rods? Explain your reasoning. o What does the mode tell you about the handful? Why is the mode sometimes very different from the mean and median? o What does the median tell you about the handful of rods? o How is the mean useful in describing the typical length of a rod? o Which set of data (Player 1, Player 2, or the combined trials) is most useful in describing the typical length of a rod? Why? o Have the teams share their work with the class. Have them add their results to a chart on the board. Ask the students if they can see a pattern. 15 min.  Grab Bag Activity Extension o Prompt: What if the contents of the bag were changed? Suppose two orange, two blue, and two brown Cuisenaire Rods were removed from the bag. How would this affect the typical length in a handful of Cuisenaire Rods? . The students must first predict the median, the mode, and the mean of a handful of Cuisenaire Rods in this experiment. . Then, the students must follow the same procedures as in the original Grab Bag Activity. . The students must be prepared to explain the results of this experiment and their predictions. 10 min.  Interactive Discussion o How did you go about making your predications? o How did the data you collected compare to your predications? o Compare your data to that gathered during the first activity. Which measure—the mean, the median, or the mode—was affected most by the removal of the Cuisenaire Rods? Why? 5 min.  Closure/Informal Assessment o What did you learn from this lesson? 2 min.  Homework Assignment o Complete the Mean, Median, and Mode Worksheet Class: Eighth Grade Mathematics Instructor: Marc Vogel Unit: Probability and Statistics Time: 1 Period (68 Minutes)

Materials: Cuisenaire Rods, Paper Bags, Activity Masters

Reflection: Did the learners meet the objectives? What went well during the lesson? What could be added or changed to make the lesson more effective?