Your teacher has a set of data cards. Each card represents a fish from the pond.
The cards with the word original on them represent the original fish;
the cards with GE on them represent the GE fish. On each data card, you see the length of a fish.
Every student in your class “catches” five “fish” from the “pond.”
A fish farmer raises a new species of fish he calls GE. He claims that these fish are twice as long as his original fish. One year after releasing a bunch of original fish and a smaller amount of the GE fish into a pond, students were allowed to catch some fish to check his claim. You are going to simulate this situation.
1. a. Explain how catching the “fish” in the activity is taking random samples.
b. Record the lengths of the 30 fish that were caught by you and five other students from your class, keeping track of whether the lengths belong to the original fish or the GE fish.
c. On Student Activity Sheet 2, make two different plots of the lengths: one for the original fish and one for the GE fish.
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2. a. Write at least two observations about the lengths of the two types of fish based on the plots you made with your group.
One observation should be about the mean length of the fish.
b. Compare your observations with the observations of another group. What do you notice?
The fish farmer claimed that GE fish grew twice the size of the original fish.
3. Based on your data about the length of fish in the plots, do you agree or disagree with the fish farmer’s claim about the length of the GE fish? Support your answer.
Add all the data points from every student in your class to the plots.
4. Now would you change your answer to problem 3?
5. What claim could you make about the lengths of the GE fish compared to the original fish based on the graphs of the whole class data? How would you justify your claim?
The fish farmer only wants to sell fish that are 17 centimeters (cm) or longer.
6. a. Based on the results of the simulation activity from your class, estimate the chance that a randomly caught GE fish is 17 cm or longer.
b. Estimate the chance that a randomly caught original fish is 17 cm or longer.
c. Estimate the chance that a randomly caught fish is 17 cm or longer. How did you arrive at your estimate?
Length of Original Fish
NumberofFish
Length (in cm)
80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
The fish farmer caught 343 fish from the pond and recorded the lengths. He graphed the lengths and made these histograms. The graphs are also on Student Activity Sheet 3.
Reasoning from Samples
C
Length of GE Fish
NumberofFish
Length (in cm)
80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5
0
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7. a. If you caught an original fish at random, what length (roughly) is most likely? Use the data in the histograms and give reasons for your answer.
b. If you caught a GE fish, what length would be most likely?
Remember: The fish farmer only wants to sell fish that are 17 cm or longer.
8. a. Based on the information in these graphs, estimate the chance that a randomly caught original fish will be 17 cm or longer.
b. Estimate the chance that a randomly caught GE fish will be 17 cm or longer.
c. Estimate the chance of randomly catching a fish that is 17 cm or longer.
9. a. Compare your answers to problems 6 and 8. Are they similar?
If they are very different, what might explain the difference?
b. Why is the answer to 8c closer to the answer to 8a than to the answer for 8b?
You can use a two-way table to organize the lengths of the fish that were caught.
10. a. Copy the two-way table into your notebook and fill in the correct numbers using the data from the histograms for the total of 343 fish. You already have a few of those numbers.
b. What is the chance the fish farmer will catch a GE fish?
c. Reflect How can you calculate in an easy way the chance that he will catch an original fish?
d. What is the chance that he catches an original fish that is 17 cm or longer?
e. Which type of fish do you advise the fish farmer to raise? Be sure to give good reasons for your advice.
Original GE Total
Total Up to 17 cm 17 cm or Longer
343
Too much weight in backpacks can cause shoulder pain or lower-back pain. Doctors say that you should not carry more than 15% of your own weight.
11. a. Randy weighs 40 kilograms. What weight can he carry based on the doctors’ rule?
b. Choose two other weights for students and calculate the maximum backpack weight for these weights.
Scientists decided to check the amount of weight students at an elementary school carry in their backpacks.
The scientists made a number line plot of the weights carried by a sample of students from grades 1 and 3.
Reasoning from Samples
C
0 1 2 3 4 5 6
5 10 15 20 25
Number of Students
Percentage of Student Weight