21 st Century Math Projects

Transcription

1

2 Project Title: International Cell Phone Plan Standard Focus: Patterns, Algebra & Functions Topics of Focus: - Linear Functions - Rate of Change Time Range: 4-5 Days Supplies: Computer lab Benchmarks: Functions 8.F Interpreting Functions Expressing Geometric Properties with Equations Interpreting Categorical and Quantitative Data Interpreting Categorical and Quantitative Data Interpreting Categorical and Quantitative Data F-IF G-GPE S-ID S-ID S-ID 4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 6c. Fit a linear function for a scatter plot that suggests a linear association. 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Procedures: A.) Students will complete Cell Phone Comparison to become familiar with writing linear equations from cell phone data and using the equations. B.) Students will complete International Pre Paid Plans to continue practice writing and using linear equations. The data is from 11 different countries which can lead to interesting discussion. C. ) Student will complete Mobile Travel Guide. Students will select a country of choice and compare Roaming Costs versus Pre-Paid Phone costs in that country. This will require a computer lab. It is difficult to find data for some countries so advise students when appropriate. Students will write linear functions for voice plans and graph them on the same axes. They will be asked to write a paragraph for WikiTravel describing what they believe is the best decision.

3 Cell Phone Comparison Cell phones have become the most necessary accessories that people carry around. As you enter adulthood, one of the first decisions that you may make is how you will handle your own cell phone plan. Although costs and incentives are always changing, using critical thinking skills to decide what makes the most financial sense is important. In this assignment you will use the costs of fictional cell phone companies to create linear functions and make decisions. Voice Unlimited (per month) Text ($/text) Data ($/mb) ET&T $59.00 $0.10 $0.15 Horizon $39.00 $0.35 $0.12 Jog $49.00 $0.21 $0.08 M-Tobile $44.00 $0.18 $ ) Nadia the Texter needs to get a plan with Voice Unlimited and Texting and she is comparing the four companies above. For each plan, write an equation that represents the total monthly cost y for a voice plan and x texts per month. ET&T Horizon Jog M-Tobile Linear Function with Texting 2.) Nadia is a frequent texter and has sent an average of about 1,000 text a month. Her personal goal is to cut her texting in half to 500 texts a month. In each of these situations, what would be the total cost of her plan? ET&T Horizon Jog M-Tobile 500 texts 1,000 texts 3.) Which plan would you suggest that Nadia chooses? Explain.

4 4.) Alpha the Surfer needs to get a plan with Voice Unlimited and Data and he is comparing the four companies above. For each plan, write an equation that represents the total monthly cost y for a voice plan and x megabytes per month. Linear Function ET&T Horizon Jog M-Tobile 5.) Alpha designs webpages on the go and has been known to stream video from time to time. He uses an average of 2,000 megabytes of data per month. He may be taking on a new design project which would require a lot more data. He is estimating that it could be about 3,500 mb. In each of these situations, what would be the total cost of his plan? 2,000 mb 3,500 mb ET&T Horizon Jog M-Tobile 6.) Which plan would you suggest that Alpha chooses? Explain.

5 International Pre-Paid Plans When traveling internationally it is best to investigate options for your phone before you go. Without research and careful decision making you may receive a bill with hundreds of dollars of roaming fees. More and more, travelers are opting to purchase prepaid phones in the country they are traveling. Prepaid cell phone plans allow a buyer to purchase minutes, texts and megabytes upfront. When minutes, texts or megabytes are used up, they will need to buy more. Use the data from the table below to create linear functions and make decisions around the world. Prepaid Phone Voice ($/minute) Text ($/text) Data ($/mb) Canada $39.00 $0.38 $0.14 $0.05 Denmark $17.00 $0.17 $0.03 $0.03 Finland $25.50 $0.10 $0.10 $0.03 Hong Kong $8.50 $0.02 $0.06 $0.10 India $9.00 $0.01 $0.02 $0.01 Japan $0 $1.00 $0.01 $9.40 South Korea $4.50 $0.09 $0.02 $0.02 Sweden $10.00 $0.04 $0.04 $0.01 Taiwan $12.00 $0.12 $0.04 $0.02 United States $40.00 $0.25 $0.20 $0.08 United Kingdom $32.00 $0.36 $0.15 $0.01 Data provided by the New American Foundation

6 Voice A traveler plans to purchase a prepaid phone in each country and will purchase minutes as necessary. Construct linear functions for each country where x is the number of minutes and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Voice Function Total Cost for 100 minutes Canada Denmark Finland Hong Kong India Japan South Korea Sweden Taiwan United States United Kingdom

7 Texting A traveler plans to purchase a prepaid phone in each country and will purchase texts as necessary. Construct linear functions for each country where x is the number of texts and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Text Function Total Cost for 200 texts Canada Denmark Finland Hong Kong India Japan South Korea Sweden Taiwan United States United Kingdom

8 Data A traveler plans to purchase a prepaid phone in each country and will purchase megabytes as necessary. Construct linear functions for each country where x is the number of megabytes and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Voice Function Total Cost for 500 megabytes Canada Denmark Finland Hong Kong India Japan South Korea Sweden Taiwan United States United Kingdom

9 A little bit of Everything A traveler plans to purchase a prepaid phone in each country and will purchase minutes, texts and megabytes as necessary. Write a function (they are linear, but would be in four dimensions! Yikes!) for each country where a is the number of minutes, b is the number of texts, c is the number of megabytes and y is the total cost of the phone. Your Usage: Estimate how much you would need for a month-long trip to another country. Minutes Texts Megabytes Function Total Cost of Your Usage Canada Denmark Finland Hong Kong India Japan South Korea Sweden Taiwan United States United Kingdom Follow-Up Which country will be the cost the most for your usage? Which country would cost the least?

10 Mobile Travel Guide It s time to get your passport ready because you are about to travel around the world. On your to-do list is to research the best cell phone option for your trip. Is it best to use roaming rates with your cell phone company or purchase a prepaid phone when you land? In this assignment, you will travel to a country of your choice, research the cell phone options in that country, construct linear functions, graph them and analyze your findings. We will only be looking at the cost for voice plans and will not include any additional costs for texting or data. Please note that for some countries it may be more difficult to find this information. If you are struggling to find this information you can talk to your teacher because you may need to choose a different country. International Roaming Rates The table below shows the roaming rates for the four big American cell phone companies. Determine Voice Roaming Functions and select one of the Cell Phone Providers for this assignment. Voice Roaming Rates Voice Roaming Function AT&T $30 extra per month and $2 per minute Sprint $5 extra per month and $4 per minute T-Mobile $0.20 per minute flat rate Verizon $4 extra per month for $0.06 per minute In the space below, select a country of your choice and research the prepaid phone plans to compare the roaming costs and the prepaid phone costs. Country Prepaid Phone Voice Plan Prepaid Phone Voice Costs (to purchase the phone and cost per minute) Prepaid Voice Function Source

11 Mobile Travel On the coordinate grid graph the Voice Roaming Function of the cell phone provider of your choice and the Prepaid Voice Function for the country of your choice. Be sure to choose your scale wisely. Label your axes and label your lines. Follow-Ups 1. Do the lines intersect? What is this point and what does it mean? 2. If you planned to use 10 minutes of call time, which plan is the better option? 3. If you planned to use 250 minutes of call time, which plan is the better option?

12 Travel Guide Recommendation Wikitravel has asked researchers to determine the best cell phone options in each country. Write an informative paragraph that could be posted to the website about this topic. Wikitravel

13 Thank you for being my Math Friend! If you liked this 21 st Century Math Project You might like others. (Click the logo) Math it Up. Boomdiggy.

14 Cell Phone Comparison Cell phones have become the most necessary accessories that people carry around. As you enter adulthood, one of the first decisions that you may make is how you will handle your own cell phone plan. Although costs and incentives are always changing, using critical thinking skills to decide what makes the most financial sense is important. In this assignment you will use the costs of fictional cell phone companies to create linear functions and make decisions. Voice Unlimited (per month) Text ($/text) Data ($/mb) ET&T $59.00 $0.10 $0.15 Horizon $39.00 $0.35 $0.12 Jog $49.00 $0.21 $0.08 M-Tobile $44.00 $0.18 $ ) Nadia the Texter needs to get a plan with Voice Unlimited and Texting and she is comparing the four companies above. For each plan, write an equation that represents the total monthly cost y for a voice plan and x texts per month. Linear Function with Texting ET&T Horizon Jog M-Tobile Y= x Y= x Y= x Y= x 2.) Nadia is a frequent texter and has sent an average of about 1,000 text a month. Her personal goal is to cut her texting in half to 500 texts a month. In each of these situations, what would be the total cost of her plan? 500 texts 1,000 texts ET&T Horizon Jog M-Tobile ) Which plan would you suggest that Nadia chooses? Explain. ET&T is the cheapest.

15 4.) Alpha the Surfer needs to get a plan with Voice Unlimited and Data and he is comparing the four companies above. For each plan, write an equation that represents the total monthly cost y for a voice plan and x megabytes per month. Linear Function ET&T Y= x Horizon Y= x Jog Y= x M-Tobile Y= x 5.) Alpha designs webpages on the go and has been known to stream video from time to time. He uses an average of 2,000 megabytes of data per month. He may be taking on a new design project which would require a lot more data. He is estimating that it could be about 3,500 mb. In each of these situations, what would be the total cost of his plan? 2,000 mb 3,500 mb ET&T Horizon Jog M-Tobile ) Which plan would you suggest that Alpha chooses? Explain. M-Tobile is the cheapest option

16 International Pre-Paid Plans When traveling internationally it is best to investigate options for your phone before you go. Without research and careful decision making you may receive a bill with hundreds of dollars of roaming fees. More and more, travelers are opting to purchase prepaid phones in the country they are traveling. Prepaid cell phone plans allow a buyer to purchase minutes, texts and megabytes upfront. When minutes, texts or megabytes are used up, they will need to buy more. Use the data from the table below to create linear functions and make decisions around the world. Prepaid Phone Voice ($/minute) Text ($/text) Data ($/mb) Canada $39.00 $0.38 $0.14 $0.05 Denmark $17.00 $0.17 $0.03 $0.03 Finland $25.50 $0.10 $0.10 $0.03 Hong Kong $8.50 $0.02 $0.06 $0.10 India $9.00 $0.01 $0.02 $0.01 Japan $0 $1.00 $0.01 $9.40 South Korea $4.50 $0.09 $0.02 $0.02 Sweden $10.00 $0.04 $0.04 $0.01 Taiwan $12.00 $0.12 $0.04 $0.02 United States $40.00 $0.25 $0.20 $0.08 United Kingdom $32.00 $0.36 $0.15 $0.01 Data provided by the New American Foundation

17 Voice A traveler plans to purchase a prepaid phone in each country and will purchase minutes as necessary. Construct linear functions for each country where x is the number of minutes and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Voice Function Total Cost for 100 minutes Canada Y=$ x 77 Denmark Y=$ x 34 Finland Y=$ x 35.5 Hong Kong Y=$ x 10.5 India Y=$ x 10 Japan Y=$0+1.00x 100 South Korea Y=$ x 13.5 Sweden Y=$ x 14 Taiwan Y=$ x 24 United States Y=$ x 65 United Kingdom Y=$ x 68

18 Texting A traveler plans to purchase a prepaid phone in each country and will purchase texts as necessary. Construct linear functions for each country where x is the number of texts and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Text Function Total Cost for 200 texts Canada Y=$ x 67 Denmark Y=$ x 23 Finland Y=$ x 45.5 Hong Kong Y=$ x 20.5 India Y=$ x 13 Japan Y=$0+0.01x 2 South Korea Y=$ x 8.5 Sweden Y=$ x 18 Taiwan Y=$ x 20 United States Y=$ x 80 United Kingdom Y=$ x 62

19 Data A traveler plans to purchase a prepaid phone in each country and will purchase megabytes as necessary. Construct linear functions for each country where x is the number of megabytes and y is the total cost of the phone. Choose four of the countries to graph on the grid below. Be sure to choose your scale wisely. Label your axes and label your lines. Voice Function Total Cost for 500 megabytes Canada Y=$ x 64 Denmark Y=$ x 32 Finland Y=$ x 40.5 Hong Kong Y=$ x 58.5 India Y=$ x 14 Japan Y=$0+9.40x 4700 South Korea Y=$ x 14.5 Sweden Y=$ x 15 Taiwan Y=$ x 22 United States Y=$ x 80 United Kingdom Y=$ x 37

20 A little bit of Everything A traveler plans to purchase a prepaid phone in each country and will purchase minutes, texts and megabytes as necessary. Write a function (they are linear, but would be in four dimensions! Yikes!) for each country where a is the number of minutes, b is the number of texts, c is the number of megabytes and y is the total cost of the phone. Your Usage: Estimate how much you would need for a month-long trip to another country. Minutes Texts Megabytes Canada Denmark Finland Hong Kong India Japan South Korea Sweden Taiwan United States United Kingdom Function Y=$ a+0.14b+0.05c Y=$ a+0.03b+0.03c Y=$ a+0.10b+0.03c Y=$ a+0.06b+0.10c Y=$ a+0.02b+0.01c Y=$0+1.00a+0.01b+9.40c Y=$ a+0.02b+0.02c Y=$ a+0.04b+0.01c Y=$ a+0.04b+0.02c Y=$ a+0.20b+0.08c Y=$ a+0.15b+0.01c Total Cost of Your Usage Follow-Up Which country will be the cost the most for your usage? Which country would cost the least?

21 Mobile Travel Guide It s time to get your passport ready because you are about to travel around the world. On your to-do list is to research the best cell phone option for your trip. Is it best to use roaming rates with your cell phone company or purchase a prepaid phone when you land? In this assignment, you will travel to a country of your choice, research the cell phone options in that country, construct linear functions, graph them and analyze your findings. We will only be looking at the cost for voice plans and will not include any additional costs for texting or data. Please note that for some countries it may be more difficult to find this information. If you are struggling to find this information you can talk to your teacher because you may need to choose a different country. International Roaming Rates The table below shows the roaming rates for the four big American cell phone companies. Determine Voice Roaming Functions and select one of the Cell Phone Providers for this assignment. Voice Roaming Rates Voice Roaming Function AT&T $30 extra per month and $2 per minute Y=2x+30 Sprint $5 extra per month and $4 per minute Y=4x+5 T-Mobile $0.20 per minute flat rate Y=0.20x Verizon $4 extra per month for $0.06 per minute Y=0.06x+4 In the space below, select a country of your choice and research the prepaid phone plans to compare the roaming costs and the prepaid phone costs. Country Prepaid Phone Voice Plan Prepaid Phone Voice Costs (to purchase the phone and cost per minute) Prepaid Voice Function Source