Hot-Air Balloon

HOT-AIR BALLOON

Enduring Understanding: Develop a better understanding of how to develop a table and how to represent slope in a graph.

Essential Questions:

Original Lesson Design Suggestions for English Language Learners  What is an informative title for a graph? Enhance Vocabulary:  What is an appropriate interval for the x- and y-axes? Altitude  How can a graph be used to make Equation predictions? Descent  What is meant by the term “constant” Dependent/independent variables when describing elements of a problem? Function  How are the dependent and independent Conclusion variables determined? Intersects  What decisions must be made when Steady rate developing a table for a function? Scatterplot Fitted line  How can a conclusion be supported using mathematical information and calculations?

Lesson Overview:

Original Lesson Design Suggestions for English Language Learners  Before allowing the students the  Use a website such as: opportunity to start the activity: access http://travel.howstuffworks.com/hot-air- their prior knowledge with regards to balloon2.htm having seen a hot-air balloon, having to illustrate the working of a hot air balloon. ridden in a hot-air balloon. Have them read an article that you supply regarding the hot-air balloon event in Boise or Arizona or elsewhere.  What is meant when a graph intersects an axis?  How can you support a conclusion that  Have students work in pairs to develop you make? What evidence from graphs and support a conclusion. Provide an can be used to support/justify your opportunity for students to present their conclusion? solutions to the class.  Use resources from your building. EALRs/GLEs:

1.1.6 1.4.4 1.5.2 1.5.6 2.2.2 3.3.2 5.1.2 5.2.1

Item Specifications: NS02; PS03; AS03; SR02; SR05; MC01 Assessment:  Use WASL format items that link to what is being covered by the classroom activity  Include multiple choice items

Hot-Air Balloon

At the Boise, Idaho Balloon Festival, a hot-air balloon is sighted at an altitude of 800 feet and appears to be descending at a steady rate of 20 feet per minute. Spectators are wondering how the altitude of the balloon is changing as time passes.

1. Make a table of values to show the balloon’s altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.

2. Write the equation that best describes this situation and define the variables that you use.

The equation ______

3. Graph the values from the table you completed in #1.

4. What was the height of the balloon 5 minutes before it was sighted? ______

5. Explain how you determined the height of the balloon 5 minutes before it was sighted.

______

6. How long does it take the balloon to reach an altitude of 20 feet? Support your answer using words, numbers and/or diagrams. 7. How long does it take the balloon to reach land? ______Support your conclusion using words, numbers or diagrams.

______

8. A second balloon is first sighted at an altitude of 1200 feet and is descending at a steady rate of 20 feet per minute. Make a table of values to show the balloon’s altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.

9. How does the descent and landing time of the second balloon compare with that of the first balloon? What information allows you to reach that conclusion? What does this mean graphically?

______

10. A third balloon is first sighted at an altitude of 800 feet but is descending at 30 feet per minute. Make a table of values to show the balloon’s altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.

11. How does the descent and landing time of the third balloon compare with that of the first balloon? What does this mean graphically? ______

______

12. At the instant the first balloon is sighted, a fourth balloon is launched from the ground rising at a rate of 30 feet per minute. Make a table of values to show the balloon’s altitude every 5 minutes beginning at the time the balloon was first sighted until the balloon reaches an altitude of 1000 feet. 13. When will the first and fourth balloon be at the same altitude? ______Support your answers using words, numbers or diagrams.

14. What is that altitude? ______Support your answers using words, numbers or diagrams.

15. What does this mean graphically? ______

______

16. The equation of a fifth balloon is y = 700 – 20x. How would the movement of the balloon have been different than the first balloon? ______

______

17. Would the fifth balloon have landed sooner or later than the first balloon? Support your answer using words, numbers or diagrams.

______

18. The scatter plot below shows the number of job offers and grade point averages for the students in an economics class. Which of the following would describe the best-fitted line for the given data points?

A. a horizontal line B. a vertical line C. a line with a negative slope D. a line with a positive slope

19. Anti-Fungal Spray Results

m 8 o s f s

l r 6 e B

d 5 e m t u c 4 e N f 3 n i

U 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Day

Based on the fitted lines for the scatterplot, how many uninfected blossoms would he expect to find on day 12?

A. 4 B. 6 C. 8 D. 10