Activity 1: Tobacco's New Targets, TIME Magazine, July 27, 2009 (pages 50-51)
Read the text accompanying the graph and try to make sense of the information presented in different sections of pages 50-51. Then as a group, try to answer the following questions and discuss how to present your answers to others. Make sure thateverygroup member understands it completely and is able to present as the instructor will randomly select the presentation leader. If any group member has questions, try to resolve them within your group first. If nobody is able to answer and explain them, then ask the instructor. Please keep in mind that the instructor will be answeringgroup questions, not questions of individual students.
Objectives of the activity
· Discussion of the term rate in mathematics
· Reading various information from a given graph and supporting conclusions using with relevant arguments
Post-Comments
· At a certain point, you may need to emphasize the fact that we are discussing mathematical sense of the word rate. Students will be including “rating” and other meanings related to the word “rate”.
· Common students’ definitions of the rate include: “amount of something in a certain area” or “how often something occurs”. The ideas may vary considerably and the discussion should be steered so that the students realize that we usually have two quantities/measurements involved (for example the population of Mt. Pleasant is 28000 – it’s an amount in a certain area, yet, it’s not a rate) or that time is not necessarily involved (currency rate can hardly be interpreted as “how often”).
· Discuss the rate as the ratio of two measurements and the meaning of the word “per” (it appears even in “per cent”).
· The discussion might sometimes appear difficult to manage as some of the questions allow different interpretations or answers and students will look at you for the final decision on “what is the right answer?”. In such cases, you may want to explain that plurality of opinions and even answers is fine and that our focus is not as much as on finding “the right” answer as on the reasoning and argumentation to support our answers and conclusions.
The first day ended with the discussion of the problem #5.
Activities (Lines indicate “batches” in which the students are given the problems and present them before moving to the next batch):
1. Use your own words to summarize different parts of the graph. Make your descriptions short and include an example. (Suggested format: This graph here shows (…describe what the graph is about…) and you can see that (…give an example what can one see there…) )
2. Discuss the meaning of the termrate in mathematics and define it using your own words. Then use your definition to explain what smoking rate is.
3. Try to "read" the following information from the graph:
· Is it possible to tell the country with the highest smoking rate? Explain. If it is possible, what is the rate (value)?
· Is it possible to tell the country in the World with the lowest smoking rate? Explain your answer and give the rate in case it is possible.
· Does the graph show the number of tobacco use related deaths every year? Is it possible to tell if it constitutes a significant portion of all deaths? Explain.
4. What can you tell about the change in smoking rate in Indonesia since 1970. Did it increase or decrease? How much? (This information is in the text on the same page).
5. Analyze the following argument:
The cigarette graph has errors. For example Australia has only 4.1 million smokers, which is considerably less than 57.2 million U.S. smokers. Yet, Australia's cigarette is apparently longer. China has the most smokers in the world (333.7 million), yet it does not have the longest cigarette.
Is there an error in the length of some cigarettes? Or in the number of smokers quoted in the cigarettes? Or is everything fine with the graph? Provide sound mathematical arguments to support your conclusion.
6. Now look at other graphs and explain:
· Is it possible to "read" thetotal populationof Nigeria from the graph? Explain.
· Is it possible to conclude if cigarette excise tax influences smoking rates?
· How about ban of smoking in the restaurants. Does it have any effect?
· Are the observations above strong enough to formulate some recommendations to state or federal authorities?
7. The following countries have something in common: Russia, Germany, Malaysia, Italy, Pakistan, Iran. What is it?
8. Can you hypothesize how the graph may look like in the future? Explain your reasoning.
9. Generate 3 moredifferent non-trivialquestions that can be answered from the graph. Different means that if you chose to find the population of Nigeria in one question, you cannot just change the country to generate another question.Non-trivialmeans that it is not written directly in the graph and you have to engage in a certain kind of reasoning to find it.
Day 2: Continuation of Activity 1
Outline:
· Before continuing with worksheet 1, problems 6-9, a brief review and discussion of the term rate.
· List some of the commonly used rates and see how they relate to our “definition” of the rate as a ratio of two quantities (descriptions will vary).
o Smoking rate from activity one; # of smokers/total population over 15. It was expressed as %: 25% means that 25 people older than 15 out of 100 (or 1 out of 4) smoke.
o Exchange rate, 1.4 Dollars per one Euro
o Birth rate: # of the nativity (childbirths) per 1000 people per year
o Speed: distance per hour
o Heart rate: beats per minute
o Inflation rate: Price (price index) increase per year
o Tax rate: ratio of amount taxed to total income; tax dollars per 100 dollars, etc.
o Interest rate: price paid for borrowing money per $100 borrowed
o Is fuel efficiency and consumption also a rate? MPG vs. liters per 100 kilometers.
o Etc.
· Do the problems on the worksheet on the next page.
· Finish the Activity 1 worksheet (problems #6 – 9).
To solve and explain:
- From the “cigarette graph”, find the population older than 15 in Nigeria.
- Today’s exchange rate is 1.4 USD per EUR. Explain how much you would get for one Dollar.
- Birth rate in the New York City is about 14 and the total population is 8.4 million. As a member of NYC Planning Department, try to come up with a projection of how many children will be born in the upcoming 4 months.
- Fuel economy (MPG) vs. fuel consumption (l/100km). Your car gives you 30 MPG on highway. Imagine that you will live for some time in Europe or Australia that uses metric system and you want to buy a car with the same fuel economy or better. What consumption values (in l/100km) will you be looking for? What is the fuel consumption in l/100km of a car of one of your group members?
- One argument for using fuel consumption over fuel economy (l/100km over MPG) says that using MPG complicates finding the average fuel efficiency. Try to examine the argument using the following pictorial hints and formulate your conclusion.
6. Another argument in favor of fuel consumption (l/100km) comes from the following comparison.
a. Compare the fuel cost if you ride a car with 35MPG and 33 MPG. How much are you saving?
b. Compare the fuel cost if you ride a car with 15 MPG and 17 MPG. How much are you saving now?
c. Do a similar comparison with fuel consumption (l/100km). (For example, compare a car with 4 l/100km and 6 l/100km and then do the same comparison for 11 l/100km and 13 l/100km).
d. Use your own words to explain why the fuel consumption numbers (l/100km) may work better for savings estimation than fuel economy numbers (MPG).
Activity 4: Solar Energy and Electricity, NG Sept 2009pg 40-41 & 52-53
1. Read the text accompanying the graph. Summarize its major points.
2. All units appearing in the graph relate to Wh or Watthours. What is a Watthour? Describe it using simple, understandable terms.
a. Although all the units relate to Watthours, they have various prefixes: tera- (TWh), giga- (GWh) and kilo- (kWh). Explain what the prefixes mean.
b. How much is 1 TWh of energy? Describe it using easily understandable terms, for example how long (in years) would 1 TWh power a 100 W bulb.
c. Tera obviously represents a very large multiple of an original unit. Have you ever heard of other "Tera units"?
d. There is one prefix missing in the sequence kilo-, Giga-, Tera-. Do you know which one it is? What is its value?
3. Look at the graph showing how much electricity could be generated worldwide from renewable sources.
a. How much energy (in TWh) can be generated from land-based wind turbines?
b. And how much energy from the wind total?
c. How does it compare to electricity generated worldwide in 2006?
4. Which three countries produce the most electricity generated from solar energy?
a. How much each country produces?
b. What portion of all electricity generated from solar energy during 2006 did these countries generate? (Assume that if there is no reading for a country, it generated 0 GWh).
c. What portion of electricity generated worldwide do these three countries generate (combined)? Compare your numbers in b and c and describe what these numbers tell you.
d. What are different numerical forms to represent this portion? Give at least 2 forms and compare their advantages/ disadvantages.
5. Identify the regions (down to countries if you can) of the World that receive the most of solar energy.
a. By how much does the largest producer of solar electricity receives less solar energy than these countries?
b. If the amount solar energy received does not seem to be a major factor in solar electricity production, what is the major factor in your opinion?
c. How about the future outlook?
6. Generate 3 moredifferent non-trivialquestions that can be answered from the graph.