Chapter 5 Resource Masters - Math Class
Chapter 5Resource Masters
Glencoe/McGraw-Hillriseruny "yx2 " x1! ##"2 " 54 " ("3)"7! #7y2 " y1m!#x2 " x1A2"2("7) ! 7(4 " r)14 ! 28 " 7r"14 ! "7r2!r4"r2"# ! #3 " 1074"r2"# ! #"77y2 " y1m!#x2 " x12slope of ! " .7458. (2, 5), (6, 2) ! "345. (14, "8), (7, "6) ! "272. ("4, "1), ("2, "5) !29. (4, 3.5), ("4, 3.5) 06. (4, "3), (8, "3) 03. ("4, "1), ("4, "5) Glencoe/McGraw-Hill2281216. (10, r), (3, 4), m ! " #71017. (10, 4), ("2, r), m ! "0.513. (7, "5), (6, r), m ! 0 !52Glencoe Algebra 1118. (r, 3), (7, r), m ! " #52315. (7, 5), (r, 9), m ! 6 "3314. (r, 4), (7, 1), m ! #41112. (2, 8), (r, "4) m ! "3 610. (6, 8), (r, "2), m ! 1 !411. ("1, "3), (7, r), m ! #343Determine the value of r so the line that passes through each pair of points hasthe given slope.7. (1, "2), (6, 2) "4. (2, 1), (8, 9) "431. (4, 9), (1, 6) 1undefinedDivide each side by "7.Subtract 28 from each side.Distributive PropertyCross multiply.Simplify.2m ! "#7 , y2 ! 4, y1 ! r, x2 ! 3, x1 ! 10Slope formulaExample 2 Find the value of r so thatthe line through (10, r) and (3, 4) has aFind the slope of the line that passes through each pair of points.ExercisesSimplify.y2 ! "2, y1 ! 5, x2 ! 4, x1 ! "3Slope formulaLet ("3, 5) ! (x1, y1) and(4, "2) ! (x2, y2).Example 1 Find the slope of theline that passes through (!3, 5)and (4, !2).of any two points on a nonvertical line21m ! # or m ! #, where (x1, y1) and (x2, y2) are the coordinatesSlopeSlope of a Line! "1PERIODStudy Guide and InterventionFind Slope5-1NAME DATE1.24 " 0.932000 " 197519501.241.481975 2000 2025*Year*Estimated0.93Source: United Nations Population Division00.51.0 0.551.52.0 20007480Source: USA TODAYWomenMen657075808590951008187*Estimated2025* 2050*Year Born7884Predicting Life ExpectancyGlencoe/McGraw-Hill282Glencoe Algebra 1decrease in rate from 2000–2025 to 2025–2050 is 0.04/yr. If the decreasein the rate remains the same, the change of rate for 2050–2075 might be0.08/yr and 25(0.08) # 2 years of increase over the 25-year span.5. Make a prediction for the life expectancy for 2050–2075. Explain how you arrived atyour prediction. Sample answer: 89 for women and 83 for men; theincreases, it does not increase at aconstant rate.4. What pattern do you see in the increase with each25-year period? While life expectancylife expectancy at the same rates.3. Explain the meaning of your results in Exercises 1and 2. Both men and women increased their2. Find the rates of change for men from 2000–2025 and2025–2050. 0.16/yr, 0.12/yr1. Find the rates of change for women from 2000–2025and 2025–2050. 0.16/yr, 0.12/yrexpectancy for men and women born in a given year.LONGEVITY The graph shows the predicted lifeExercisesc. How are the different rates of change shown on the graph?There is a greater vertical change for 1950–1975 than for 1975–2000. Therefore, thesection of the graph for 1950–1975 has a steeper slope.b. Explain the meaning of the slope in each case.From 1950–1975, the growth was 0.0152 billion per year, or 15.2 million per year.From 1975–2000, the growth was 0.0124 billion per year, or 12.4 million per year.! # or 0.01240.31251975–2000: ### ! ##change in populationchange in time! # or 0.01520.3825change in population0.93 " 0.551950–1975: ### ! ##change in time1975 " 1950Population Growth in ChinaPOPULATION The graph shows the population growth in China.a. Find the rates of change for 1950–1975 and for1975–2000.ExampleThe rate of change tells, on average, how a quantity is changing overtime. Slope describes a rate of change.Slope(continued)PERIODStudy Guide and InterventionRate of Change5-1NAME DATEPeople (billions) AgeAnswers(Lesson 5-1)Glencoe Algebra 1Lesson 5-1
SlopeSkills PracticeGlencoe/McGraw-Hillx!3(1, –2)(0, 1)A3(Average)015(3, 3)1 23 3"14 Glencoe/McGraw-Hill28325. (7, r), (4, 6), m ! 0 624. (5, 3), (r, "5), m ! 4 33423. (r, 4), (7, 1), m ! # 1122. (r, 2), (6, 3), m ! # 412Glencoe Algebra 1Glencoe Algebra 1Glencoe/McGraw-HillAnswers 284Glencoe Algebra 125. SALES A daily newspaper had 12,125 subscribers when it began publication. Five yearslater it had 10,100 subscribers. What is the average yearly rate of change in the numberof subscribers for the five-year period? !405 subscribers per year2"324. ROOFING The pitch of a roof is the number of feet the roof rises for each 12 feethorizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number?20. (r, 3), (5, 9), m ! 2 221. (5, 9), (r, "3), m ! "4 823. (r, 2), (5, r), m ! 0 222. (r, 7), (11, 8), m ! " # 16Find the value of r so the line that passes through each pair of points has thegiven slope.1521. ("7, 2), ("8, r), m ! "5 719. ("5, r), (1, 3), m ! # !4769218. ("3, "4), ("5, r), m ! " # 517. ("4, 3), (r, 5), m ! # 4141216. ("2, r), (6, 7), m ! # 320. (1, 4), (r, 5), m undefined 1719. ("5, 6), (7, "8) ! "6518. ("4, 5), ("8, "5) "211917. (12, 6), (3, "5) "16. (5, "9), (3, "2) ! "7213Find the value of r so the line that passes through each pair of points has thegiven slope.x15. (2, "1), ("8, "2) "15. # , # , " # , # "! 73 34 " !13. (12, 10), (12, 5) undefined11. (3, 9), ("2, 8) "Oy14. (10, 0), ("2, 4) ! "13912. ("2, "5), (7, 8) "1710. (15, 2), ("6, 5) ! "9. (5, 9), (3, 9) 0x(–2, 3)8. ("7, 8), ("7, 5) undefined4"5(–2, –3)(3, 1)3.7. (7, "4), (4, 8) !4xOy6. (6, "2), (5, "4) 2O2.5. ("9, "3), ("7, "5) !1!3(–1, 0)(–2, 3)y4. (6, 3), (7, "4) !71.14. (0.2, "0.9), (0.5, "0.9) 0110SlopePracticePERIODFind the slope of the line that passes through each pair of points.5-1NAME DATE13. ("6, "4), (4, 1) "1211. ("3, 10), ("3, 7) undefinedLesson 5-112. (17, 18), (18, 17) !110. ("5, "8), ("8, 1) !39. (9, 8), (7, "8) 8(0, 0)Oy8. (2, 5), ("3, "5) 21"3O(3, 1)3.7. (5, 2), (5, "2) undefinedxy6. (4, 6), (4, 8) undefined(2, 5)2.5. (6, 1), ("6, 1) 02(0, 1)Oy4. (2, 5), (3, 6) 11.xPERIODFind the slope of the line that passes through each pair of points.5-1NAME DATEAnswers(Lesson 5-1)
Glencoe/McGraw-Hill3units, and the run isA4The graph is a vertical l285Glencoe Algebra 1Sample answer: If the slope is negative, choose the second pointso that its x-coordinate is less than that of the first point.3. The word rise is usually associated with going up. Sometimes going from one point onthe graph does not involve a rise and a run but a fall and a run. Describe how you couldselect points so that it is always a rise from the first point to the second point.slope used as rate of changerunSketchhow far up or down as compared to how far left or right 52,000 increase in spendingc. """"26 monthsb. "riserun21a. "difference of y-coordinates divided by difference ofcorresponding x-coordinates2. Describe how each expression is related to slope.The graph is a horizontal line.y #yx2 # x1units.The graph falls as you go from left toright.Helping You Remember Description of Graph5The graph rises as you go from left toright.zeronegativepositiveType of Slope1. Describe each type of slope and include a sketch.Reading the Lesson3 units3Thus, the slope of this line is " or " .5 units5In this graph, the rise isslope ! "riserunRead the introduction to Lesson 5-1 at the top of page 256 in yourtextbook. Then complete the definition of slope and fill in the boxeson the graph with the words rise and run.Why is slope important in architecture?SlopeyPERIODReading to Learn MathematicsPre-Activity5-1NAME DATEEnrichment Glencoe/McGraw-Hill329. "5. 11. 3Start Here1310. "6. #1142. "2863411. # "7. no slope253. # "12. 3278. "4. 0TreasureGlencoe Algebra 1PERIODUsing the definition of slope, draw lines with the slopes listedbelow. A correct solution will trace the route to the treasure.Treasure Hunt with Slopes5-1NAME DATEAnswers(Lesson 5-1)Glencoe Algebra 1Lesson 5-1
PERIODSlope and Direct VariationStudy Guide and Intervention1O(0, 0)(2, 1)x111A5Simplify.(x1, y1) ! (0, 0), (x2, y2) ! (2, 1)Slope formulab. Use the direct variation equation tofind x when y # 18.y ! 6xDirect variation equation18 ! 6xReplace y with 18.3!xDivide each side by 6.Therefore, x ! 3 when y ! 18.a. Write a direct variation equationthat relates x and y.Find the value of k.y ! kxDirect variation equation30 ! k(5)Replace y with 30 and x with 5.6!kDivide each side by 5.Therefore, the equation is y ! 6x.Suppose y variesdirectly as x, and y # 30 when x # 5.Example 2O!2; !2(–1, 2)(0, 0)yy ! –2xx2.3; 3O(1, 3)(0, 0)yy ! 3xx3.3 3"; "2 2(–2, –3)(0, 0)Oyxy ! 32 x Glencoe/McGraw-Hill4. If y ! 4 when x ! 2, find y when x ! 16.28732y # 2x; 325. If y ! 9 when x ! "3, find x when y ! 6. y # !3x; !26. If y ! "4.8 when x ! "1.6, find x when y ! "24. y # 3x; !811337. If y ! #when x ! #, find x when y ! #. y # 2x; "4816Glencoe Algebra 1Write a direct variation equation that relates x to y. Assume that y varies directlyas x. Then solve.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.ExercisesThe slope is #.21!#21"0!#2"0221m!#x "xy "yFor y ! #x, the constant of variation is #.22y ! 12 xyName the constant ofvariation for the equation. Then findthe slope of the line that passesthrough the pair of points.Example 1A direct variation is described by an equation of the form y ! kx,where k 0. We say that y varies directly as x. In the equation y ! kx, k is the constantof variation.Direct Variation5-2NAME DATETRAVEL A family drove their car 225 miles in 5 hours.rise#run1V # 0.02TGlencoe Algebra 1Glencoe/McGraw-HillAnswers 5 ft32886. Find the volume of the same gas at 250 (absolute temperature).5. Graph the equation on the grid at the right.4. Write a direct variation equation that relates the variables.CHEMISTRY Charles’s Law states that, at a constantpressure, volume of a gas V varies directly as its temperatureT. A volume of 4 cubic feet of a certain gas has a temperatureof 200 (absolute temperature).3. Find the cost of #4 pound of jelly beans. 3.3732. Graph the equation on the grid at the right.C # 4.49p0901802701. Write a direct variation equation that relates the variables. 4.49 times the number of pounds p.RETAIL The total cost C of bulk jelly beans isExercisesTherefore, it will take 8 hours to drive 360 miles. CHECK (5, 225) lies on the graph.c. Estimate how many hours it would take thefamily to drive 360 miles.d ! 45tOriginal equation360 ! 45tReplace d with 360.t!8Divide each side by 45.m! #4518tV0123404.509.0013.5018.00CGlencoe Algebra 1100200TTemperature ( K)Charles’s Laww24Weight (pounds)Cost of Jelly Beans7(5, 225)(1, 45)2 3 4 5 6Time (hours)d ! 45ta. Write a direct variation equation to find the distance traveled for any numberof hours.Use given values for d and t to find r.d ! rtOriginal equation225 ! r(5) d ! 225 and t ! 545 ! rDivide each side by 5.Therefore, the direct variation equation is d ! 45t.b. Graph the equation.Automobile TripsThe graph of d ! 45t passes through the origin withdslope 45.360ExampleThe distance formula d ! rt is a direct variation equation. In theformula, distance d varies directly as time t, and the rate r is the constant of variation.Slope and Direct Variation(continued)PERIODStudy Guide and InterventionSolve Problems5-2NAME DATEDistance (miles)Glencoe/McGraw-HillCost (dollars) Volume (cubic feet)Answers(Lesson 5-2)Lesson 5-2
Slope and Direct VariationSkills PracticePERIODy ! 13 x(0, 0)Oy(3, 1)xOyy ! –2x(–1, 2)O(0, 0)y35. y ! " # x42.xOyxOy ! – 32 x(–2, 3)26. y ! # x5!2; !2 3.(0, 0)yOyxy#"x ; !24323!"2 Glencoe/McGraw-HillC # 1.80g46 8 10 12 14 gGallons289032640912151821T8T # 3c123 4 5Crates7cGlencoe Algebra 16Toys Shipped14. SHIPPING The number of delivered toys Tis 3 times the total number of crates c.1216202428CGasoline Cost13. TRAVEL The total cost C of gasolineis 1.80 times the number of gallons g.x3!";Write a direct variation equation that relates the variables. Then graph theequation.y#"x; "4212. If y ! 12 when x ! 18, find x2when y ! "16.10. If y ! "9 when x ! 3, find ywhen x ! "5. y # !3x ; 159. If y ! "4 when x ! 2, find ywhen x ! "6. y # !2x ; 1211. If y ! 4 when x ! 16, find y13when x ! 6.8. If y ! 45 when x ! 15, find xwhen y ! 15. y # 3x ; 57. If y ! "8 when x ! "2, find xwhen y ! 32. y # 4x ; 8Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.4. y ! 3xx1 1"; "3 3Graph each equation.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.5-2NAME DATECost ( )A6ToysGlencoe/McGraw-Hill(Average)Slope and Direct VariationPracticePERIOD(0, 0)Oyy ! 34 xx(4, 3)3 3"; "4 4Oyx65(0, 0)Oy5. y ! # x2.Oyxy ! 43 x(3, 4)x4 4"; "3 3(–2, 5)53O(0, 0)y ! " 52 xy6. y ! " # x3.x348. If y ! 80 when x ! 32, find x when y ! 100.328120246810246 8 10 12 !LengthRectangle DimensionsWC # 4.50t0510152025C123 4 5Tickets6Cost of Tickets x2Glencoe/McGraw-Hill290to their weight. Then find the cost of 4 # pounds of bananas.14Glencoe Algebra 1C # 0.32p ; 1.363 # pounds of bananas for 1.12. Write an equation that relates the cost of the bananast11. TICKETS The total cost C of tickets is 4.50 times the number of tickets t.12. PRODUCE The cost of bananas varies directly with their weight. Miguel bought32W#"!10. MEASURE The width W of arectangle is two thirds of the length !.Write a direct variation equation that relates the variables. Then graph theequation.9. If y ! # when x ! 24, find y when x ! 12.y # 15x; !4.5y # 2.5x; 4031y#"x; "7. If y ! 7.5 when x ! 0.5, find y when x ! "0.3.Oy255!";! "Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.4. y ! "2xGraph each equation.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.5-2NAME DATEWidth Cost ( )Answers(Lesson 5-2)Glencoe Algebra 1Lesson 5-2
Glencoe/McGraw-HillA7Sample answer: For each minute the shower runs, 6 gallonsof water come out. So, if the shower ran 10 minutes, thatwould be 60 gallons. Think about the first sentence. What does it mean to say that a standardshowerhead uses about 6 gallons of water per minute?They are the coordinates of the points on the graph. How do the numbers in the table relate to the graph shown?Read the introduction to Lesson 5-2 at the top of page 264 in your textbook.How is slope related to your shower?Slope and Direct VariationGlencoe/McGraw-Hill291Glencoe Algebra 1of variation relates x and y in the same value every time, and thatrelationship never changes.5. Look up the word constant in a dictionary. How does this definition relate to the termconstant of variation? Sample answer: Something unchanging; the constantHelping You Rememberc. The wages W earned by an employee vary directly with the number of hours h thatare worked. Enrique earned 172.50 for 23 hours of work. W ! 7.50hb. The perimeter p of a pentagon with all sides of equal length varies directly as thelength s of a side of the pentagon. A pentagon has 5 sides. p ! 5sd ! 88ta. The distance d varies directly as time t, and a cheetah can travel 88 feet in 1 second.4. For each situation, write an equation with the proper constant of variation.3. The expression “y varies directly as x” can be written as the equation y ! kx. How wouldyou write an equation for “w varies directly as the square of t”? w ! kt 2the same value as the slope of the graph of the equation.2. How is the constant of variation related to slope? The constant of variation has1. What is the form of a direct variation equation? y ! kxReading the Lesson PERIODReading to Learn MathematicsPre-Activity5-2NAME DATEEnrichmentPERIODGlencoe Algebra 1Glencoe/McGraw-HillAnswers 292Glencoe Algebra 1Answers will vary. For example, bone strength limits the size humanscan attain.9. What can you conclude from Exercises 7 and 8?only 2224 pounds8. According to the adult equation for weight supported (Exercise 5), howmuch weight could a 20-foot tall giant’s legs actually support?7440 pounds7. According to the adult equation you found (Exercise 1), how muchwould an imaginary giant 20 feet tall weigh?35k ! 2.16 for h ! "ft6. For a baby who is 20 inches long and weighs 6 pounds, find an “infantvalue” for k in the equation s ! kh2.k ! 5.565. For a person 6 feet tall who weighs 200 pounds, find a value for k in theequation s ! kh2.k has a greater value.4. How does your answer to Exercise 3 demonstrate that a baby issignificantly fatter in proportion to its height than an adult?35k ! 1.296 for h ! "ft3. Find the value for k in the equation w ! kh3 for a baby who is 20 incheslong and weighs 6 pounds.2. Use your answer from Exercise 1 to predict the weight of a person whois 5 feet tall. about 116 poundsk ! 0.931. For a person 6 feet tall who weighs 200 pounds, find a value for k in theequation w ! kh3.Answer each question.The weight that a person’s legs will support is proportional to thecross-sectional area of the leg bones. This area varies directly as the squareof the person’s height. The equation of variation has the form s ! kh2.Assume that the weight of a person of average build varies directly as thecube of that person’s height. The equation of variation has the formw ! kh3.An equation of the form y ! kxn, where k " 0, describes an nth powervariation. The variable n can be replaced by 2 to indicate the second powerof x (the square of x) or by 3 to indicate the third power of x (the cube of x).nth Power Variation5-2NAME DATEAnswers(Lesson 5-2)Lesson 5-2
PERIODSlope-Intercept FormStudy Guide and Interventiony ! mx # b, where m is the given slope and b is the y-intercept3Simplify.Divide each side by 4.Subtract 3x from each side.3O(0, –2)yx3x 4y ! 8(4, 1)A8y ! #2x # 12. slope: 2, y-intercept 1(0, –2)(1, 0)y ! 2x # 2Oyx Glencoe/McGraw-HillOy7. y ! 2x # 1xGraph each equation.4.(3, 0)y ! #x 3O(0, 3)yO293y8. y ! 3x # 25.xxWrite an equation of the line shown in each graph.y ! 8x # 31. slope: 8, y-intercept 3(0, –5)(4, –2)43y! "x#5OyOyxxGlencoe Algebra 19. y ! x 16.y ! #x # 73. slope: 1, y-intercept 7Write an equation of the line with the given slope and y-intercept.ExercisesThe y-intercept of y ! %x 2 is 2 and the slope is %. So graph the point (0, 2). From44this point, move up 3 units and right 4 units. Draw a line passing through both points. 3x # 8 4y% ! %% 4 43y!%x 24Original equationGraph 3x # 4y ! 8.3x 4y ! 8 4y ! 3x # 8Example 2Example 1 Write an equation of the line whose slope is #4 and whosey-intercept is 3.y ! mx # bSlope-intercept formy ! 4x # 3Replace m with 4 and b with 3.Slope-Intercept FormSlope-Intercept Form5-3NAME DATESlope-Intercept Form1. Write an equation to find the percent P of households thatsubscribed to cable TV for any year x between 1995 and 1999. Glencoe/McGraw-Hill2946. Find the population in 2050. about 400,000,0005. Graph the equation on the grid at the right.4. Write an equation to find the population P in any year xbetween 2010 and 2050. P !2,500,000x 300,000,000POPULATION The population of the United States isprojected to be 300 million by the year 2010. Between2010 and 2050, the population is expected to increase byabout 2.5 million per year.3. Find the percent that subscribed to cable TV in 1999. 68.1%2. Graph the equation on the grid at the right.P ! 0.6x 65.7010,50010,60010,70010,80010,900N12 3 4 5 6Years Since 1997Cable TV Systemsx1 2 3 4 5 xYears Since 1995Glencoe Algebra 10x2040Years Since 2010Source: The World Almanac300320340360380400Projected UnitedStates PopulationPSource
Glencoe/McGraw-Hill A3 Glencoe Algebra 1 Answers NAME _ DATE _ PERIOD _ Skills Practice Slope 5-1 Glencoe/McGraw-Hill
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 1 Resource Masters includes the core materials needed for Chapter 1. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 6 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 6 Resource Masters includes the core materials needed for Chapter 6. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 7 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 7 Resource Masters includes the core materials needed for Chapter 7. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Algebra 2 Teacher’s Guide to Using the Chapter 3 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 3 Resource Masters includes the core materials needed for Chapter 3. These materials include worksheets, extensions, and assessment options.
Glencoe/McGraw-Hill iv Glencoe Geometry Teacher’s Guide to Using the Chapter 9 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 9 Resource Masters includes the core materials needed for Chapter 9. These materials include worksheets, extensions, and assessment options.
Chapter 11 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 11 Resource Masters includes the core materials needed for Chapter 11. These materials include worksheets, extensions, and assessment options. The an
