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Grade: elementary
Subject: Mathematics

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#3. A Concrete Approach to Relative Frequency

Mathematics, level: elementary
Posted by David Spangler ().
ActiveMath Workshops
ActiveMath Workshops, US
Materials Required: paper, pencil, sidewalk with cracks
Activity Time: 20 minutes
Concepts Taught: mathematics, probability

Did, you ever wonder what the probability is of stepping on a crack when you walk on a sidewalk? This activity is designed to help cement this probability in your mind.

Work with a partner, at your own pace.

1a. How many steps do you think it will take for you to walk from ____________ to

_____________ ? Estimate:

1b. About what percent of the time do you think you will step on a crack? (We define a crack to be an original line in the sidewalk that separates the squares.)

2. With your partner, walk the distance three times. Each time keep track of the number of steps you take. Do not look at the cracks! Your partner will keep track of the number of times you step on a crack. Record your results for each of your trips in the table below.

Trip 1 # of steps # of cracks

Trip 2 # of steps # of cracks

Trip 3 # of steps # of cracks

3. Repeat the activity, this time keeping track of the cracks for your partner.

4a. How many total steps did you take during the three trips?

4b. How many times did you step on a crack?

4c. Find your relative frequency for stepping on a crack.

5. How do you think your relative frequency compares with those of your classmates? How does it compare with your estimate in 1b above?

6. List some factors that could have affected your data. Why do you think you were asked to make three trips? Hopefully this activity did not curb your appetite for probability. Rather, it should pave the way for you to be in-step with the NCTM Standards. (I'm sure you expected some bad cracks.)

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