Secondary Mathematics I: An Integrated Approach Module 3 Arithmetic and Geometric Sequences PDF
Preview Secondary Mathematics I: An Integrated Approach Module 3 Arithmetic and Geometric Sequences
1 Secondary Mathematics I: An Integrated Approach Module 3 Arithmetic and Geometric Sequences By The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius www.mathematicsvisionproject.org In partnership with the Utah State Office of Education V © 2012 Mathematics Vision Project | M P In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license. Sequences 1 Math 1: Intro to Arithmetic Sequences Name:_____________________________ Pd:_____ Congratulations, you have just won The Fillmore High School lottery! You are given the option of receiving your payments in one of two ways for the next 16 days: Would you rather Receive $20 a day for 16 days Or For the next 16 days, double 1 penny on Day 1 for a total of 2 pennies and receive 2 more pennies on Day 2, 4 more pennies on Day 3, 8 more on Day 4, etc.? 1.) Which payment would you choose? Why? 2.) How much money would each one give you after 5 days? $20 a day (start with 0) Pennies a day (start with 1) Day $ added Total $ Day $ added Total $ 1 20 20 1 .01 .02 2 20 40 2 .02 .04 3 20 60 3 .04 .08 4 20 80 4 .08 .16 5 5 3.) How much money after 10 days? 15 days? 4.) If the contest went for 16 days, which option would you choose? How much money would you make? Check the other option at 16 days. Did you make a good choice? Why? 5.) Plot your point (Days, $ Total) on the graph. DAYS 6) Look at the $20 a day, what is the amount changing by each day? (i.e., what is the slope?) 7) Look at the pennies a day, what happens to the amount each day? 8) Try to create an equation for the $20 a day. (hint: it is a line) 9) Try to create an equation for the pennies a day. (hint: it doubles each time, 2 * 2 * 2 * …* 2) 10) What would the difference in the total dollars between the two be after 20 days? Bonus: Each $20 dollar bill weighs .002 lbs. What would the weight be of your $20 dollar bills be after 15 days of receiving them? Each penny weighs .006 lbs. What would the weight be of your pennies after 15 days of receiving them? Homework Math 1: Introduction to Arithmetic and Geometric Sequence 3 e mit o c 3.1Growing Dots de s/f o A Develop Understanding Task hot p m/ o c kr. w.flic w w 2 1 20 © 1. Describe the pattern that you see in the sequence of figures above. 2. Assuming the sequence continues in the same way, how many dots are there at 3 minutes? 3. How many dots are there at 100 minutes? 4. How many dots are there at t minutes? Solve the problems by your preferred method. Your solution should indicate how many dots will be in the pattern at 3 minutes, 100 minutes, and t minutes. Be sure to show how your solution relates to the picture and how you arrived at your solution. V © 2012 Mathematics Vision Project | M P In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license. Sequences 3 4 Name: Sequences 3.1 Ready, Set, Go! © 2012 www.flickr.com/photos/fdecomite Ready Topic: Exponents, Substitution, and Function Notation Find each value. 1. 3! 2. 3! 3. 3! 4. 3! For each of the following, find f (1), f (2) and f (3) 5. 𝑓 𝑥 = 2! 6. 𝑓 𝑥 = 3! 7. 𝑓 𝑥 = 2 𝑥−1 +3 Complete each table. 8. Term 1st 2nd 3rd 4th 5th 6th 7th 8th Value 2 4 8 16 32 9. Term 1st 2nd 3rd 4th 5th 6th 7th 8th Value 66 50 34 18 10. Term 1st 2nd 3rd 4th 5th 6th 7th 8th Value -‐3 9 -‐27 81 11. Term 1st 2nd 3rd 4th 5th 6th 7th 8th Value 160 80 40 20 12. Term 1st 2nd 3rd 4th 5th 6th 7th 8th Value -‐9 -‐2 5 12 V © 2012 Mathematics Vision Project | M P In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported license Sequences 4 5 Name: Sequences 3.1 Set Topic: Completing a table Fill in the table. Then write a sentence explaining how you figured out the values to put in each cell. Explain how to figure out what will be in cell #8. 13. You run a business making birdhouses. You spend $600 to start your business, and it costs you $5.00 to make each birdhouse. # of birdhouses 1 2 3 4 5 6 7 Total cost to build Explanation: 14. You borrow $500 from a relative, and you agree to pay back the debt at a rate of $15 per month. # of months 1 2 3 4 5 6 7 Amount of money owed Explanation: 15. You earn $10 per week. # of weeks 1 2 3 4 5 6 7 Amount of money earned Explanation: 16. You are saving for a bike and can save $10 per week. You have $25 already saved. # of weeks 1 2 3 4 5 6 7 Amount of money saved Explanation: V © 2012 Mathematics Vision Project | M P In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported license Sequences 5 6 Name: Sequences 3.1 Go Topic: Good viewing window 1 When sketching a graph of a Example: g (x) = x – 6 function, it is important that 3 we see important points. For Window: [ -‐10, 10] by [ -‐10,10] Window: [-‐10, 25] by [ -‐10, 5] linear functions, we want a x-‐ scale: 1 y-‐scale: 1 x-‐scale: 5 y-‐scale: 5 window that shows important information related to the story. Often, this means including both the x-‐ and y-‐ intercepts. Good window NOT a good window 1 17. f(x) = -‐ x + 1 18. 7 x – 3 y = 14 10 x: [ , ] by y: [ , ] x: [ , ] by y: [ , ] x-‐scale: y-‐scale: x-‐scale: y-‐scale: 19. y = 3(x – 5) +12 20. f (x) = -‐15 (x + 10) – 45 x: [ , ] by y: [ , ] x: [ , ] by y: [ , ] x-‐scale: y-‐scale: x-‐scale: y-‐scale: V © 2012 Mathematics Vision Project | M P In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported license Sequences 6
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