Teacher Notes Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative...

Teacher Notes

Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

1

You might want to update prices at Office Max

PRACTICES: 1 Problem solving & perseverance, 3 Construct viable arguments and critique the reasoning of others, 4 Model with mathematics, 6 Attend to precision. The slides for DUPLEX laser printer and Precision at the end of the presentation are optional.

http://swwmathematics.pbworks.com/

http://creativecommons.org/licenses/by/4.0/

http://www.officemax.com/technology/printers/laser-printers/product-prod3130164?cm_sp=spb-_-laser2-_-generic


Should We Buy a Laser Printer?

Linear Functions

1/16/13 2 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015




• What could you shop for by price?

3 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015




Should We Buy a Laser Printer?• The least expensive way to make copies is

through the district Print Shop.• They charge us $0.014 for one single-sided

black and white copy.• Would it cost the math department less

money for one single sided copy if we bought a black and white laser printer?





Learning Target

5

Linear Function 2aI can represent a situation using tables, graphs, equations and in words.

What does it mean to “represent” a

function?





Should We Buy a Laser Printer?Need 1 of toner cartridgeHigh Yield Black Toner

Cartridge• Yields up to 2,600 pages• Price: $70Black Toner Cartridge• Yields up to 1,200 pages • Price: $45

Need bothDrum Cartridge• Yields up to 12,000 page• Price: $105 Multipurpose Paper• 5,000/Case• Price:$50





Present Your Solution to the Class

7

• Mr. Benson manages the district Print Shop.

• Write a letter to Mr. Benson to convince him to whether or not to buy the math department laser printers.

• Support your answer with mathematical information in your letter.

Listen to the presentations of others. - Write one complement about their mathematics.- Write one question about their mathematics.





Learning Targets

8

LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range.

LF3a I can identify the characteristics of linear functions and use function notation.

LF3b I can write equations of linear functions and linear functions them to solve problems.

LF4 I can find when a point where two equations have the same solution.


http://www.mathwarehouse.com/algebra/relation/math-function.php

http://www.onemathematicalcat.org/algebra_book/online_problems/function_notation.htm




Laser vs. Inkjet Printers

9

The graph shows the estimated cost of buying and using an inkjet printer.





Laser vs. Inkjet PrintersThe estimated cost of buying and using a home laser

printer can be found with the equation L(x) = 0.04567x + 110 where x is the number of pages.1. Use the graph to decide whether it is more cost

effective to use the laser printer or the school copier for 10, 100, 1000 or 5000 copies.

2. How many pages do you need to print for the laser printer to be more cost effective?

3. Describe the domain and range of each function.





Learning Target

11

LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range.

LF3c I can compare two functions or one function represented two different ways.• Find the inverse function

LF4 I can solve a system of equations with a table or by graphing.







Laser Printer Function of PagesThe district Print Shop charges $0.014for single-sided

white paper. • Write the equation for The Print Shop costs are

determined by the function, where the cost, d(x), is a function of the number of pages printed, x.

• Use your equation to find:a) Find d(10) b) Find d(150) C) Find d(800)6. Use your equation to solve for x.a) d(x) = 1.00 b) d(x) = 5.00d c) (x) = 100.007. Write a function to find the number of pages

printed, p(x), as a function of the cost, x. p(x) = ____________________________





Laser Printer Function of Pages

The function p(x) is the inverse function of d(x), because they undo each other. In other words, when d(a) = b, then p(b) = a.


http://www.mathwords.com/i/inverse_function.htm




Laser Printer Function of Pages8. Use p(x) = to verify your answers to #16.9. Is the function, p(x), linear? Support your answer with words, numbers and/or

diagrams.10.Find the value of x where d(x) = p(x).11.Describe the domain and range of each function.

Be Prepared to Present Your Solution to the Class

domain range d(x) p(x)





Laser Printer Function of PagesAs you already found the estimated cost as a

function of the number of pages printed is L(x) = 0.04567x + 110 .

• For L(x), _____________ is the input and ________________ is the out put.

• Use your equation to solve for x.a) L(x) = 110b) L(x) = 150c) L(x) = 10





Laser Printer Function of Pages14.Now find N(x), the inverse function of L(x).

15.For N(x), For L(x), _____________ is the input and ________________ is the out put.

16.Use p(x) = to verify your answers to #23.

17.Is the function, N(x), linear?

Support your answer with words, numbers and/or diagrams.





Laser Printer Function of Pages18.Find the value of x where L(x) = N(x).

19.Describe the domain and range of each function.domain range

d(x) p(x)





Laser Printer Function of Pages20. In #18 and #23, you were asked to find the value

of x where the function and its inverse function were equal to each other. What do your answers to #18 and #23 have in common?

21. In #19 and #24, you were asked to find the domain and range of function and its inverse function. What do your answers to #19 and #24 have in common?

Be Prepared to Present Your Solution to the Class





Learning TargetsLinear Functions 3a:

I can identify the characteristics of linear functions and use function notation.





Printer SpeedsMr. Aho wants to know if the laser printer is

faster than the inkjet printer he already has. He used his inkjet printer to print pages and recorded the pages and times in the table.

He looked up the specifications for the laser printer he wants to buy and made a graph to determine the time it would take to print pages.





Printer Speedsinkjet printer laser printer

24

PagesTime (sec)

4 54

6 70

10 102

18 166





Price Changes 16. Describe the input and output of the laser

printer function, L(x).7. Was the input or the output changed in #5?


8. Was the input or the output changed in #6? Support your answer with words, numbers and/or diagrams.

Be Prepared to Present Your Solution





Price Changes 29. Mr. Blake liked Mrs. Krsak’s idea of buying a laser

printer and decided to buy a laser printer for his home at the beginning of second semester. He has one Algebra 1 class fall semester, and three Algebra 1 classes next semester. How does this change the graph of the function L(x)?

10.Mrs. Doss also decided to buy a laser printer for her home at the beginning of second semester. Mrs. Doss’s schedule is changing also. She has 70 fewer students in Algebra 1 classes next semester because she’s teaching more Geometry classes. How does this change the graph of the function L(x)?





Price Changes 211. Describe the input and output of the laser

printer function, L(x).12. Was the input or the output changed in #9?


13. Was the input or the output changed in #10? Support your answer with words, numbers and/or diagrams.






Learning Targets

28

LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range.LF3c I can compare two functions or one function represented two different ways.Find the inverse functionLF4 I can solve a system of equations with a table or by graphing.







Laser Printer Function of PagesThe district Print Shop charges $0.014for single-sided

white paper. 14. Write the equation for The Print Shop costs are

determined by the function, where the cost, d(x), is a function of the number of pages printed, x.

15. Use your equation to find d(10), d(150), and d(800)

16. Use your equation to solve for x: d(x) = 1.00,

d(x) = 5.00, and d(x) = 100.0017. Write a function to find the number of pages

printed, p(x), as a function of the cost, x. 29 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a

Creative Commons Attribution 4.0 International License. 2014-2015




Laser Printer Function of PagesThe function p(x) is the inverse function of d(x),

because they undo each other. In other words, when d(a) = b, then p(b) = a.

18. Use p(x) = to verify your answers to #16.

19. Is the function, p(x), linear? • Support your answer with words, numbers

and/or diagrams.


http://www.mathwords.com/i/inverse_function.htm




Laser Printer Function of Pages20.Find the value of x where d(x) = p(x).

21.Describe the domain and range of each function.






Laser Printer Function of PagesAs you already found the estimated cost as a

function of the number of pages printed is L(x) = 0.04567x + 110 .

22. For L(x), _______ is the input and _______ is the out put.

23. Use your equation to solve for x.• L(x) = 110• L(x) = 150• L(x) = 10





Laser Printer Function of Pages24. Now find N(x), the inverse function of L(x).

25. For N(x), _______ is the input and _______ is the out put.

26. Use p(x) = to verify your answers to #23.





Laser Printer Function of Pages27. Is the function, N(x), linear? • Support your answer with words, numbers

and/or diagrams.

28.Find the value of x where L(x) = N(x).

29.Describe the domain and range of each function.





Laser Printer Function of Pages30. In #18 and #23, you were asked to find the value of

x where the function and its inverse function were equal to each other. What do your answers to #18 and #23 have in common?

31. In #19 and #24, you were asked to find the domain and range of function and its inverse function. What do your answers to #19 and #24 have in common?






Learning Target

36






Printer SpeedsMr. Aho wants to know if the laser printer is faster than

the inkjet printer he already has. He used his inkjet printer to print pages and recorded the pages and times in the table. He looked up the specifications for the laser printer he wants to buy and made a graph to determine the time it would take to print pages.

32. Use the laser printer table and the inkjet printer graph to answer Mr. Aho’s question.

33. Is Mr. Aho’s inkjet printer function, represented by a table, linear? Support your answer with words, numbers and/or diagrams.

Be Prepared to Present Your Solution37 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a





Learning Target

38






Printing BudgetThe school district is trying to save money. They put all

teachers on a $900 budget for what they order from the Print Shop. At the end of first semester Mr. Kaden had ordered 48,963 copies (both one-sided and two-sided, and white and color paper) from the Print Shop and was charged $485.14.





Printing Budget34. Write a function Mr. Kaden can use to determine what is

left in his budget from the number of copies he has made. Be sure to define the variables you use.

35. Is the budget function linear? Support your answer with words, numbers and/or diagrams.

36. Make a graph that Mr. Kaden can refer to and find out how much of his budget remains. Be sure to show in your graph when Mr. Kaden has no money left in his budget.

37. Find the maximum number of copies Mr. Kaden can make. Support your answer with information from your graph.

Be Prepared to Present Your Solution40 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a





Learning Target

41






Laser Printer Detailed CostsIf we buy paper, toner and drum cartridges, as we need

them would the graph really look like this?• If you think this is the graph, support your answer

with words, numbers and/or diagrams.• If you think the graph would be different, describe or

sketch the new graph.





Laser Printer Detailed CostsThroughout this lesson, we have used the function

L(x) = 0.04567x + 110 to estimate the printer costs.





Laser Printer Detailed Costs





Laser Printer Detailed CostsMr. Aho made a detailed graph of the costs of the laser

printer.Support all of your answers with information from the

diagram.38. Is the graph a function?39. Is the graph a linear function?40. Describe the domain and range of the values shown

on the graph.41. Find the start up cost of the printer. What is

included in that cost?





Laser Printer Detailed CostsSupport all of your answers with information from the

diagram.38. Is the graph a function?39. Is the graph a linear function?40. Describe the domain and range of the values shown

on the graph.41. Find the start up cost of the printer. What is

included in that cost?42. Pick two different intervals. Describe what is

happening in each of the intervals.Be Prepared to Present Your Solution





Should We Buy a Duplex Laser Printer?

• The least expensive way to make copies is through the district Print Shop.

• They charge us $0.02 for one single-sided black and white copy.

• Would it cost the math department less money for one single sided copy if we bought a black and white laser printer?





Precision• How many decimal places did you use when

you calculated the cost of toner for 1 page?LIST ANSWERS:

• How many places are necessary?• How can you find a more accurate answer?





PrecisionHOW TO USE THE MEMORY OF A GRAPHING

CALCULATOR• Find cost of toner for 1 page. Store this cost in your

calculator as “T” STO> T• Find cost of the drum for 1 page. Store this cost in your

calculator as “D” STO> D• Find cost of 1 piece of paper. Store this cost in your

calculator as “P” • The cost of 1 page T + D + P• Find cost of toner for 1 page. Store this cost in your

calculator as “T” STO> C





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