Draft last edited May 13, 2013 by Belinda Robertson

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1 Draft last edited May 13, 2013 by Belinda Robertson 97

2 98 Appendix A: Prolem Handouts Problem Title Location or Page number 1 CCA Interpreting Algebraic Expressions Map.mathshell.org high school concept dev. Lesson or Alg 1 dropbox Unit 2 2 Create a word problem for 58=153-5x Page 99 3 Create a word problem for 7a + 5b = 106 Page 99 4 Seating people at tables Page Riley s Baseball cards Page Conference Tables Pages CCA Modeling Situations with Linear Equations Map.mathshell.org high school concept dev. Lesson or Alg 1 dropbox Unit 2 8 Square Patterns Pages Lawson Feeding Dog Page Sarah s Water Tank Page Parker s Water Tank Page Printing Tickets Pages Algebraic Representations of Linear Functions Folder in Appendix A Folder named algebraic RepresentationsofLinear 14 CCA: Classifying Solutions to Systems of Equations Runctions Map.mathshell.org high school concept dev. Lesson or Alg 1 dropbox Unit 2 15 Buying Chips and Candy Pages Jake and Lawson Tee Shirts Page Road Rage Pages Measure and Linear Regression Page 127 Student handout pages Relationship Representation Pages Translation of Inequality Statements Page Inequality Exploration (Plotting Activity) Page Kim s Pledges Page Marsha s Garden Page Eilene s Workweek Page Unit Assessment Pages Last edited by Belinda on May 13, 2013

3 99 Problem 2: Write a story problem that will describe this equation. 58 = 153 5x Problem 3: Write a story problem that will describe this equation. 7a + 5b = 106 Draft last edited May 13, 2013 by Belinda Robertson

4 100 Problem 4: A square table seats 4 people. Two square tables pushed together seats 6 people. Three square tables pushed together seats 8 people. If we add another table, how many people can be seated? 1. What would be a rule that determines how many people can be seated if we add another table? (Recursive rule) 2. How many people can 10 tables pushed together seat? Show your work. 3. How many tables would need to be put together to seat 32 people? Show your work. 4. What is a rule we could write to determine how many people can be seated at 50 tables? N number of people? Last edited by Belinda on May 13, 2013

5 Problem 4 (with the first 3 tables) A square table seats 4 people. Two square tables pushed together seats 6 people. Three square tables pushed together seats 8 people If we add another table, how many people can be seated? 2. What would be a rule that determines how many people can be seated if we add another table? (This is a recursive rule.) 3. How many people can 10 tables pushed together seat? Show your work. 4. How many tables would need to be put together to seat 32 people? Show your work. 5. What is a rule we could write to determine how many people can be seated at 50 tables? N number of people? Draft last edited May 13, 2013 by Belinda Robertson

6 102 Problem 5: Riley has 24,000 baseball trading cards. She has agreed to sell 75 cards each Monday to a friend that has a sports memorabilia shop. How many cards will she have after Show your work or your reasoning. 1 week? 2 weeks? 3 weeks? What is a recursive rule for this problem? 10 weeks? 50 weeks? n weeks? What is a rule to find the amount of cards Riley has after n weeks? After how many weeks will she have 23,125 cards? How many weeks until she has no cards? What are the variables in this problem? What is the domain and range of this function? Explain your thinking. Would a graph of this data be a line? Why? Last edited by Belinda on May 13, 2013

7 103 Problem 6: Conference Tables Draft last edited May 13, 2013 by Belinda Robertson

8 104 Conference Tables continued Last edited by Belinda on May 13, 2013

9 105 Problem 6 conference Tables Rubric Draft last edited May 13, 2013 by Belinda Robertson

10 106 Problem 8 Rubric: Last edited by Belinda on May 13, 2013

11 107 Problem 8: Draft last edited May 13, 2013 by Belinda Robertson

12 108 Last edited by Belinda on May 13, 2013

13 109 Problem 9: Lawson has $720. He pays Kathy $18 each week to feed his dogs. 1. How much money does each have after 1 week? 2 weeks? 3 weeks? 10 weeks? n weeks? 2. Make a table to show the amount of money each have. 3. Make a graph of these relationships: two graphs on the same grid. 4. State rules (equations) for each person s amount of money over time. 5. How does Kathy s and Lawson s funds relate? 6. Can you see this relationship in the tables, graphs, equations? Where? Explain. Draft last edited May 13, 2013 by Belinda Robertson

14 110 Problem 10 Sarah is filling a large rectangular water tank. When she started filling the tank there was already 3 inches of water in the tank. After 1 hour there was 5 inches of water in the tank. She checked the tank again after another hour passed and there was 7 inches of water in the tank. When she checked the 3rd hour, there was 9 inches of water in the tank. 1. How many inchers of water were in the tank after 4 hours? 7 hours? 7.5 hours? 10.8 hours? h hours? Use various representations to show this relationship. 2. If the water level is at 41 inches, how much time has passed? Show your work or explain how you came up with your solution. 3. Is it possible for the water level to be 84 in? Explain. If it can, how much time will pass? 4. Is this relationship a function? Explain. If it is a function, describe using function notation. Define all the variables. Last edited by Belinda on May 13, 2013

15 Problem 11 Parker was emptying a 9 (108 inches) foot tall water tank for his dad. After the first hour he saw that the water level was at 8ft. 6 inches. When he checked again in another hour, the water level was 8 ft. He didn t check again at after the 3 rd hour, but at the 4 th hour the water level was 7ft. Remember to show your work. 1. At this rate, what will be the water level after 5 hours? after 9 ¼ hours? When will the water lever be only 2 feet? 3. If the water level is 75 in. (6ft. 3 in.), how much time has passed? Explain. 4. Compare and contrast this problem to problem 6. Like number 6 Different from number 6 Draft last edited May 13, 2013 by Belinda Robertson

16 112 Problem 12 Last edited by Belinda on May 13, 2013

17 Draft last edited May 13, 2013 by Belinda Robertson 113

18 114 Problem 8 rubric Last edited by Belinda on May 13, 2013

19 115 Problem 13: Multiple Representations of Linear Relations Problem 14 : MDC CCA Classifying Solutions to Systems of Equations Draft last edited May 13, 2013 by Belinda Robertson

20 116 Problem 15: Last edited by Belinda on May 13, 2013

21 Draft last edited May 13, 2013 by Belinda Robertson 117

22 118 Last edited by Belinda on May 13, 2013

23 119 Problem 15 summary Draft last edited May 13, 2013 by Belinda Robertson

24 120 Problem 15 rubric Last edited by Belinda on May 13, 2013

25 Draft last edited May 13, 2013 by Belinda Robertson 121

26 122 Problem 16 Jake has a screen print tee shirt business. For a custom designed shirt he charges $25 for the screen design plus $7 per shirt. In another town, Jessie also has a screen print tee shirt business. She sells her shirts for $9 each. At what point will Jessie make more money than Jake for the same size order? Use tables, graphs, words and equations to explain your reasoning.. Lawson paid $250 for his print machine and ink supplies. He has to pay $2.50 for his plain tee shirts and sells the printed shirts for $8 each. Parker lives in another town and also sells printed tee shirts. He pays $3.75 for his plain tee shirts and sells them for $9.25. He also paid $250 for his print machine and ink supplies. Who is going to make more profit based on the number of shirts sold? Use tables, graphs, words and equations to explain your reasoning. Last edited by Belinda on May 13, 2013

27 Problem 17: 123 Draft last edited May 13, 2013 by Belinda Robertson

28 124 Last edited by Belinda on May 13, 2013

29 Draft last edited May 13, 2013 by Belinda Robertson 125

30 126 Problem 18: Measurement and Linear Regression (graphing calculator will be needed) Last edited by Belinda on May 13, 2013

31 Measurement and Linear Regression Teacher Notes I. Collect the data 1. Be sure students realize that each line is to be measure twice. Once using the inches side of the ruler and once using the centimeters side of the ruler. Data should be similar to the following: Line # Inches Centimeters II. Analyze the data 1. If L 1 and L 2 already contain data, then students should clear out the data. They can do they by arrowing to the top of L 1 and highlighting it, then pressing Clear, then Enter. Should students accidentally delete a list completely, it can be resent by pressing 2 nd Stat, then choosing option 5: Set up Editor and pressing enter. In this step it is also very important that students correctly pair the x and y coordinates together. 2. Be sure that only one plot is turned on. 3. Setting the window is extremely important. If students skip this step they may not be able to see the scatterplot. 4. If students have trouble, be sure to check that there is nothing stored in Y=. 5. In this menu, there is another LinReg (Option #8). We use number 4 in this activity because it gives us our linear regression in slope-intercept form. 6. If students only enter LinReg(ax+b) then press enter, the calculator will automatically do a regression on L 1 vs. L 2. The Y 1 at the end will paste the equation into Y= for you. III. Analyze the results (Sample results are included below.) 1. What is the equation, in slope-intercept form, of the line passing through your points? y 2.53 x 0 2. What is the slope of the line passing through your points? What is the y-intercept of the line passing through you points? 0 4. Remembering that slope is change in y over change in x, what would be the units for the slope?centimeters/inch 5. What does the slope indicate in this situation? The number of centimeters in one inch 6. What does the y-intercept indicate in this situation? The number of centimeters in zero inches 7. Is the y-intercept what you would expect it to be? Explain. Yes. I would expect the y-intercept to be zero since the y-intercept is the number of centimeters when a line measures zero inches. 127 Draft last edited May 13, 2013 by Belinda Robertson

32 128 Measurement and Linear Regression Name: Hour: I. Collect the Data. Measure one dimension of 10 objects in both inches and in centimeters. Record the data in the table below. II. Analyze the Data. 1. Enter your data into L 1 and L 2. Press STAT then ENTER to enter inches data into L 1 and centimeters data into L 2. (Figure 1) Object Line # Inches Centimeters Figure 1 2. Press 2nd Y= to plot the data. Press 1. Make sure the settings are the same as those in Figure 2. Figure 2 Last edited by Belinda on May 13, 2013

33 Set the window. Remember that the x-variable represents inches and the y-variable represents centimeters. Press WINDOW and choose settings that resemble the ones in Figure Press GRAPH. Does the data appear to be linear? 5. Perform a linear regression on the data. Press STAT, arrow over to CALC, then choose 4:LinReg(ax+b). 6. Press 2nd 1, 2nd 2, VARS, then arrow over to Y-VARS, choose 1:Function, then choose 1:Y 1. See Figure Press ENTER. Enter the values for a and b below. a = b = 8. Press GRAPH. Does the line go through your data points? Does it seem to fit your line well? Figure 3 Figure 4 Draft last edited May 13, 2013 by Belinda Robertson

34 130 III. Analyze your results. 8. What is the equation, in slope-intercept form, of the line passing through your points? 9. What is the slope of the line passing through your points? 10. What is the y-intercept of the line passing through you points? 11. Remembering that slope is change in y over change in x, what would be the units for the slope? 12. What does the slope indicate in this situation? 13. What does the y-intercept indicate in this situation? 14. Is the y-intercept what you would expect it to be? Explain. Last edited by Belinda on May 13, 2013

35 131 Problem 19. Below are some representations of relations. Identify each relation that is also a function. For each function, identify its domain and range. For each relations that is not a function, explain why. A. C. D. E. { (5, 0) (2,0) (8,0) (12,5) } F. { (5, 0) (4, 5) (5,5) (12,12) G. H Draft Last edited May 13, 2013 by Belinda Robertson

36 132 Problem 20: Write other sentences that are equivalent to the sentences below and write inequalities to represent these sentences: You have to be at least 36 inches tall to ride this amusement park ride. You can make at most 100 points on this exam. You may not exceed 55 miles per hour while driving on state highways. The salary is between $7.50 per hour and $12 per hour (inclusive). To ride this amusement park ride, you have to weigh less than 100 pounds. To bake a cake, the oven temperature has to be between F and F. The cage at the zoo will hold no more than 50 spiders. There has to be more than 10 students enrolled in the class. Write a sentence for these inequalities. You can use any variable (noun) for these. x< 5 5> x y < 9-2 X > 12 Last edited by Belinda on May 13, 2013

37 Problem 21: 133 (-5,5) (-4,5) (-3,5) (-2,5) (-1,5) (0,5) (1,5) (2,5) (3,5) (4,5) (5,5) (-5,4) (-4,4) (-3,4) (-2,4) (-1,4) (0,4) (1,4) (2,4) (3,4) (4,4) (5,4) (-5,3) (-4,3) (-3,3) (-2,3) (-1,3) (0,3) (1,3) (2,3) (3,3) (4,3) (5,3) (-5,2) (-4,2) (-3,2) (-2,2) (-1,2) (0,2) (1,2) (2,2) (3,2) (4,2) (5,2) (-5,1) (-4,1) (-3,1) (-2,1) (-1,1) (0,1) (1,1) (2,1) (3,1) (4,1) (5,1) (-5,0) (-4,0) (-3,0) (-2,0) (-1,0) (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (-5,-1) (-4,-1) (-3,-1) (-2,-1) (-1,-1) (0,-1) (1,-1) (2,-1) (3,-1) (4,-1) (5,-1) (-5,-2) (-4,-2) (-3,-2) (-2,-2) (-1,-2) (0,-2) (1,-2) (2,-2) (3,-2) (4,-2) (5,-2) (-5,-3) (-4,-3) (-3,-3) (-2,-3) (-1,-3) (0,-3) (1,-3) (2,-3) (3,-3) (4,-3) (5,-3) (-5,-4) (-4,-4) (-3,-4) (-2,-4) (-1,-4) (0,-4) (1,-4) (2,-4) (3,-4) (4,-4) (5,-4) (-5,-5) (-4,-5) (-3,-5) (-2,-5) (-1,-5) (0,-5) (1,-5) (2,-5) (3,-5) (4,-5) (5,-5) Teachers note for directions to students: Print off and cut out sets of ordered pairs for groups of 2-3 students. Have 4 pieces of graph paper for each group. Glue sticks or tape and a straight edge will be needed for each group. Student directions: Choose a set of ordered pairs from your envelope. Decide if your ordered pair is a solution to the inequality that is displayed. If it is attach it to the appropriate place on the graph. Are these the only solutions to the inequality? How would we show all the solutions on the graph? On your graph paper, graph one inequality per sheet. Randomly choose 10 ordered pairs. Decide if they are solutions to each ordered pair. Graph all the points that are solutions to the inequalities. Graph all the solutions to the inequalities. Possible inequalities: Draft Last edited May 13, 2013 by Belinda Robertson

38 134 Problem 22 Kim s pledge for raising funds in a walk-a-thon is $10 plus $2 per mile for each mile walked. She needs to know how many miles that she needs to walk to earn at least $40. Write an inequality for this situation and solve. Explain what the solution means in the context. Last edited by Belinda on May 13, 2013

39 135 Problem 23 Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants to buy at least 5 plants and can spend no more than $100. Write a system of linear inequalities to model the situation. Sketch a graph of the solutions. Can Marsha buy 6 plants and 12 bags of soil? How do you know? Is (6, 10) a solution for this situation? What does (6, 10) mean in the context? Draft Last edited May 13, 2013 by Belinda Robertson

40 136 Problem 24 Problem 25 Unit 2 Linear Functions Assessment Last edited by Belinda on May 13, 2013

41 137 Kim, Linda and Nancy are participating in a walk-a-thon. They each have a different plan. Kim has received pledges that will net her $2 a mile. Linda s pledges were a $5.00 donation plus $0.50 a mile walked. Nancy received a donation of $ What if everyone walked 2 miles what would each receive? 10 miles? 20 miles? m miles? Show your work. 2. Will the amount of money be the same for each walker? Explain. 3. Who will make the most money for the charity? Explain. 4. In Linda s plan, how would the $5 be represented in a table, graph or equation? 5. What would the point or ordered pair (12, 11) represent in this problem? Whose plan would the ordered pair (12, 11) be associated with? Explain. Draft Last edited May 13, 2013 by Belinda Robertson

42 Axis Title Axis Title Axis Title Identify which table corresponds with which walker. What are the labels for the tables? A. B. C Identify which graph corresponds with which walker. What are the axis titles? A Axis Title B Axis Title C Axis Title Last edited by Belinda on May 13, 2013

43 Are there a number of miles where any two walkers raise the same amount of money? Show your work or explain. 9. There are several representation of relationships below. Circle the ones that are functions? For each that are not functions, explain why they are not functions. If they are functions, list their domains and ranges. { (2, 5) (7, 5) (8, 9) (0, 12) } { ( apples, red) (oranges, orange) (apples, yellow) (lemons, yellow) } Robert James Lindsey Ray Susan Male Female Y 2 = 2X Y= 2(5 2X) + 4 X Domain is the zip code and the range is the name of the cities. The height (range) of a person (domain) on their 15 th birthday. Draft Last edited May 13, 2013 by Belinda Robertson

44 Translate the inequalities below and graph the solutions. State whether the solutions are discrete or continuous. a) You have to be at least 16 years old to use the exercise machines in the gym. b) The oven s temperature has to be between and c) The golfer s scores range between -5 and 5 for a tournament. d) Romon needs to earn at least $250 at his job to pay his weekly expenses. His job at the Bob s Grocery, pays $15 per hour. Show all solutions on a graph for this situation. Last edited by Belinda on May 13, 2013