Integrated Algebra Statue of Liberty Activity

Transcription

1 Name mods Date Integrated Algebra Statue of Liberty Activity Consider this problem: The Statue of Liberty in New York City has a nose that is 4 feet 6 inches long. What is the approximate length of one of her arms? 1. Solve the problem. (Hint: Think about your own nose and arms.) 2. Pick two other body parts and find the approximate length that these parts should be on the Statue of Liberty. 3. Compare your results with another group s results. Did you get the same answers? Why or why not?

2 4. When officials want to count the number of animals in a given region, they use a technique called capture-recapture, since it would be almost impossible count the actual number of animals. In this process, a small number of animals are captured and marked in some way. For example, horses are often branded on an easily-seen part of the body. Then the marked animals are released. After they have had time to mix with the rest of the animals in a region, a second group is captured. Finding the number of marked animals in this group makes it possible to make an estimate of the entire population. Suppose in a large grassland, 20 horses are captured and marked. Then they are released into the grassland. After a week, 80 horses are captured. Five of those horses are found to be marked. a. Write a proportion that models the situation. b. Use your proportion to estimate the population of horses in this region. 5. How is the horse problem similar to the Statue of Liberty problem? Explain.

3 Integrated Algebra Name: 1.2 Proportions as Models

4 4. Walking at a fast pace burns 5.6 calories per minute. How many minutes of walking at a fast pace are needed to burn the 500 calories consumed by eating a dish of ice cream? 5. A plan for an office building uses a scale of 1 inch to 1 foot. How long would a 35 foot 16 wall appear on the plan? 6. Given: ABCDE ~ RSTUV. Find the value of x

5 Integrated Algebra Name: 1.2 Homework No Work = No Credit

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7 Integrated Algebra Name: 1.3 R.A.P.

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9 Integrated Algebra Name: 1.4 Patterns and Explanations 1. Does the line graph below show hourly daytime temperatures (8:00 am 7:00 pm) or hourly nighttime temperatures (8:00 pm 7:00 am)? Explain. 2. Which of the tables below better models the height of a plant over time? Explain.

10 3. The height of a person over his or her lifetime. A context and a figure showing three graphs are given above. a. Which graph (a, b, or c) best models the given situation? b. What features made you choose that particular graph? c. What features made you discount the other graphs? d. What are the two quantities or variables in the given situation? 4. The circumference of a circle as its radius changes. A context and a figure showing three graphs are given above. a. Which graph (a, b, or c) best models the given situation? b. What features made you choose that particular graph? c. What features made you discount the other graphs? d. What are the two quantities or variables in the given situation?

11 5. The height of a ball as it is thrown in the air. A context and a figure showing three graphs are given above. a. Which graph (a, b, or c) best models the given situation? b. What features made you choose that particular graph? c. What features made you discount the other graphs? d. What are the two quantities or variables in the given situation? 6. The daily average low temperature in degrees Fahrenheit over the course of one year in Fairbanks, Alaska. A context and a figure showing three graphs are given above. a. Which graph (a, b, or c) best models the given situation? b. What features made you choose that particular graph? c. What features made you discount the other graphs? d. What are the two quantities or variables in the given situation?

12 Integrated Algebra Name: 1.4 Homework No Work = No Credit

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14 Name mods Date Integrated Algebra Activity Matching Graphs with Scenarios (20 points) Your goal is to match your scenario or graph to the graph or scenario that best matches it. Once you have found your partner, write his or her name here: Then explain in the space below how you knew that the scenario matched the graph (what aspects of the graph led you to pick it?). (4 points) Once everyone has found his or her partner, we will go over all of the scenarios as a class. The scenarios are listed below. Sketch a graph for each scenario. Make sure you label the axes! (1 point each) 1. This graph shows the relationship between kilometers and miles. 8 kilometers = 5 miles 2. The water boiled at 100 C then cooled to the room temperature of 20 C after 1 hour.

15 3. The journey was 100 miles long. We traveled at a steady 50 mph and arrived after 2 hours. 4. When we took the bread from the freezer, its temperature was 20 C. It took about 30 minutes to thaw. 5. When full, the tank held 100 liters of oil. We used 20 liters every day. After 5 days it was all gone. 6. This graph shows the relationship between Fahrenheit and Celsius. For water, freezing point is 0 C or 32 F boiling point is 100 C or 212 F.

16 7. I was driving at a steady 50 mph when I had to do an emergency stop. 8. The plant grew slowly at first, then more quickly. It reached a height of 50 cm after 10 weeks. 9. My bath took 5 minutes including the time taken to fill it and let out the water. The depth of the water rose to 50 cm when I got in. 10. My heart rate rose quickly to 100 beats per minute during exercise. It took longer to fall when I stopped. My heart rate was back to normal 50 minutes after I started exercising.

17 11. After setting off from the intersection I sped up to 50 mph in 10 seconds. 12. This container holds 200 ml of water. The water was poured in steadily until it was full after 50 seconds. Closing Questions 13. When interpreting a graph, which key features are useful? 14. Describe a real situation that would give a linear graph (other than the ones we ve already discussed). 15. Describe a real situation that would give a curved graph (other than the ones we ve already discussed). 16. Describe a real situation that would give a graph with more than one section (straight or curved).