Bridge To Algebra - Doral Academy Preparatory School
Bridge to Algebra 2008 Carnegie Learning, Inc.Assignments andSkills Practice
Pittsburgh, PAPhone 888.851.7094Fax sWe would like to thank those listed below who helpedto prepare the Cognitive Tutor Bridge to Algebra Assignments.Copyright 2008 by Carnegie Learning, Inc. All rights reserved. Carnegie Learning,Cognitive Tutor, SchoolCare, and Learning by Doing are all registered marks of CarnegieLearning, Inc. All other company and product names mentioned are used for identificationpurposes only and may be trademarks of their respective owners. This product or portionsthereof is manufactured under license from Carnegie Mellon University. Permission is grantedfor photocopying rights within licensed sites only. Any other usage or reproduction in anyform is prohibited without the express consent of the publisher.ISBN-13 978-1-934800-01-0AssignmentsPrinted in the United States of VH1-1/08 HPS 2008 Carnegie Learning, Inc.Kenneth LabuskesMarianne O’ConnorLori MartinKent Publishing, Inc.Signature DesignMichele CovattoThe Carnegie Learning Development Team
1Number Sense and Algebraic Thinking1.1Money, Money, Who Gets the Money?Introduction to Picture Algebra1.2Collection ConnectionFactors and Multiples1.3Dogs and BunsLeast Common Multiple1.4Kings and MathematiciansPrime and Composite Numbers1.5I Scream for Ice CreamPrime Factorization1.6Powers That BePowers and Exponents1.7Beads and BaublesGreatest Common Factor2 Assignmentp. 3Skills Practicep. 191 Assignmentp. 5Skills Practicep. 193 Assignmentp. 7Skills Practicep. 195 Assignment p. 11Skills Practice p. 199Assignment p. 13Skills Practice p. 201Assignmentp. 9Skills Practicep. 197Fractions2.1Comic StripsDividing a Whole into Fractional Parts2.2Dividing QuesadillasDividing More Than One Whole into Parts2.3No “I” in TeamDividing Groups into Fractional Parts2.4Fair Share of PizzaEquivalent Fractions2.5When Twelfths Are EighthsSimplifying Fractions 2008 Carnegie Learning, Inc. Assignmentp. 1Skills Practicep. 1892.6When Bigger Means SmallerComparing and Ordering Fractions p. 15 p. 203Assignment p. 17Skills Practice p. 205Assignment p. 19Skills Practice p. 207Assignment p. 21Skills Practice p. 209Assignment p. 23Skills Practice p. 211Assignment p. 25Skills Practice p. 213AssignmentSkills PracticeBridge to Algebraiii
Operations with Fractions and Mixed Numbers3.1Who Gets What?Adding and Subtracting Fractions with Like Denominators3.2Old-Fashioned GoodiesAdding and Subtracting Fractions with Unlike Denominators3.3Fun and GamesImproper Fractions and Mixed Numbers3.4Parts of PartsMultiplying Fractions3.5Parts in a PartDividing Fractions3.6All That GlittersAdding and Subtracting Mixed Numbers3.7Project DisplayMultiplying and Dividing Mixed Numbers3.8Carpenter, Baker, Mechanic, and ChefWorking with Customary Units4Decimals4.1Cents SenseDecimals as Special Fractions4.2What’s in a Place?Place Value and Expanded Form4.3My Dog Is Bigger Than Your DogDecimals as Fractions: Comparing and Rounding Decimals4.4Making Change and Changing HoursAdding and Subtracting Decimals4.5Rules Make The World Go RoundMultiplying Decimals4.6The Better BuyDividing Decimals4.7Bonjour!Working with Metric UnitsivBridge to Algebra p. 27 p. 215Assignment p. 29Skills Practice p. 217Assignment p. 31Skills Practice p. 219Assignment p. 33Skills Practice p. 221Assignment p. 35Skills Practice p. 223Assignment p. 37Skills Practice p. 225Assignment p. 39Skills Practice p. 227Assignment p. 41Skills Practice p. 229AssignmentSkills Practice p. 43 p. 231Assignment p. 45Skills Practice p. 233Assignment p. 47Skills Practice p. 235Assignment p. 49Skills Practice p. 237Assignment p. 51Skills Practice p. 239Assignment p. 53Skills Practice p. 241Assignment p. 55Skills Practice p. 243AssignmentSkills Practice 2008 Carnegie Learning, Inc.3
5Ratio and Proportion5.1Heard It and Read ItRatios and Fractions5.2Equal or Not, That Is the QuestionWriting and Solving Proportions5.3The Survey SaysUsing Ratios and Rates5.4Who’s Got Game?Using Proportions to Solve Problems6Percents6.1One in a HundredPercents6.2Brain WavesMaking Sense of Percents6.3Commissions, Taxes, and TipsFinding the Percent of a Number6.4Find It on the Fifth FloorFinding One Whole, or 100%6.5It’s Your MoneyFinding Percents Given Two Numbers6.6So You Want to Buy a CarPercent Increase and Percent Decrease7 p. 65 p. 253Assignment p. 67Skills Practice p. 255Assignment p. 69Skills Practice p. 257Assignment p. 71Skills Practice p. 259Assignment p. 73Skills Practice p. 261Assignment p. 75Skills Practice p. 263AssignmentSkills PracticeIntegers7.1I Love New YorkNegative Numbers in the Real World7.2 2008 Carnegie Learning, Inc. p. 57 p. 245Assignment p. 59Skills Practice p. 247Assignment p. 61Skills Practice p. 249Assignment p. 63Skills Practice p. 251AssignmentSkills PracticeGoing Up?Adding Integers7.3Test Scores, Grades, and MoreSubtracting Integers7.4Checks and BalancesMultiplying and Dividing Integers7.5Weight of a PennyAbsolute Value and Additive Inverse7.6Exploring the MoonPowers of Ten7.7Expanding Our PerspectiveScientific Notation p. 77 p. 265Assignment p. 79Skills Practice p. 267Assignment p. 81Skills Practice p. 269Assignment p. 83Skills Practice p. 271Assignment p. 85Skills Practice p. 273Assignment p. 87Skills Practice p. 275Assignment p. 89Skills Practice p. 277AssignmentSkills PracticeBridge to Algebrav
Algebraic Problem Solving8.1Life in a Small TownPicture Algebra8.2Computer Games, CDs, and DVDsWriting, Evaluating, and Simplifying Expressions8.3Selling CarsSolving One-Step Equations8.4A Park Ranger’s Work Is Never DoneSolving Two-Step Equations8.5Where’s the Point?Plotting Points in the Coordinate Plane8.6Get Growing!Using Tables and Graphs8.7Saving EnergySolving Problems Using Multiple Representations9Geometric Figures and Their Properties9.1Figuring All of the AnglesAngles and Angle Pairs9.2A Collection of TrianglesClassifying Triangles9.3The Signs Are EverywhereQuadrilaterals and Other Polygons9.4How Does Your Garden Grow?Similar Polygons9.5Shadows and MirrorsIndirect Measurement9.6A Geometry GameCongruent Polygons10 p. 91 p. 279Assignment p. 93Skills Practice p. 281Assignment p. 95Skills Practice p. 283Assignment p. 97Skills Practice p. 285Assignment p. 99Skills Practice p. 287Assignment p. 101Skills Practice p. 289Assignment p. 103Skills Practice p. 291AssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practice p. 105p. 293 p. 117p. 305 p. 121p. 309p. 107p. 295p. 109p. 297p. 111p. 299p. 113p. 301p. 115p. 303Area and the Pythagorean Theorem10.1 All Skate!Perimeter and Area10.2 Round Food Around the WorldCircumference and Area of a CircleAssignmentSkills PracticeAssignmentSkills Practicep. 119p. 30710.3 City PlanningAreas of Parallelograms, Triangles, Trapezoids,and Composite Figures10.4 Sports Fair and SquareSquares and Square Roots10.5 Are You Sure It’s Square?The Pythagorean Theorem10.6 A Week at Summer CampUsing the Pythagorean TheoremviBridge to AlgebraAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practicep. 123p. 311p. 125p. 313p. 127p. 315 2008 Carnegie Learning, Inc.8
11Probability and Statistics11.1 Sometimes You’re Just Rained OutFinding Simple Probabilities11.2 Socks and MarblesFinding Probabilities of Compound Events11.3 What Do You Want to Be?Mean, Median, Mode, and Range11.4 Get the Message?Histograms11.5 Go for the Gold!Stem-and-Leaf Plots11.6 All About Roller CoastersBox-and-Whisker Plots11.7 What’s Your Favorite Flavor?Circle Graphs12AssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practice p. 129p. 317 p. 143p. 331p. 131p. 319p. 133p. 321p. 135p. 323p. 137p. 325p. 139p. 327p. 141p. 329Volume and Surface Area12.1 Your Friendly Neighborhood GrocerThree-Dimensional Figures12.2 Carnegie Candy CompanyVolumes and Surface Areas of Prisms12.3 The Playground OlympicsVolumes and Surface Areas of Cylinders12.4 The Rainforest PyramidVolumes of Pyramids and Cones12.5 What on Earth?Volumes and Surface Areas of Spheres 2008 Carnegie Learning, Inc.AssignmentSkills Practice12.6 Engineers and ArchitectsNets and Views12.7 Double TakeSimilar SolidsAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeBridge to Algebrap. 145p. 333p. 147p. 335p. 149p. 337p. 151p. 339p. 153p. 341p. 155p. 343vii
Linear Functions13.1 Running a Tree FarmRelations and Functions13.2 Scaling a CliffLinear Functions13.3 Biking AlongSlope and Rates of Change13.4 Let’s Have a Pool Party!Finding Slope and y-Intercepts13.5 What’s for Lunch?Using Slope and Intercepts to Graph Lines13.6 Healthy RelationshipsFinding Lines of Best Fit1414.1 Is It a Bird or a Plane?14.2 How Many Times?Powers of Rational Numbers14.3 Sew What?Irrational Numbers14.4 Worth 1000 WordsReal Numbers and Their Properties14.5 The House That Math BuiltThe Distributive Property15.115.2Worms and AntsMaps and ModelsScale Drawings and Scale Models15.3Designer MathematicsSliding and Spinning15.4Secret CodesFlipping, Stretching, and Shrinking15.5A Stitch in TimeMultiple TransformationsBridge to AlgebraAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practicep. 157p. 345 p. 169p. 357 p. 179p. 367p. 159p. 347p. 161p. 349p. 163p. 351p. 165p. 353p. 167p. 355AssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practicep. 171p. 359p. 173p. 361p. 175p. 363p. 177p. 365TransformationsGraphing in Four QuadrantsviiiAssignmentSkills Practice Number SystemsRational Numbers15AssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills PracticeAssignmentSkills Practicep. 181p. 369p. 183p. 371p. 185p. 373p. 187p. 375 2008 Carnegie Learning, Inc.13
AssignmentNameAssignment for Lesson 1.1DateMoney, Money, Who Gets the Money?Introduction to Picture AlgebraYou and your friend Jamal go to lunch. You each order a cheeseburger and a large soft drink.Jamal also orders a small salad, which costs 1.09. The total for both of you is 6.27.How much does each of you owe?1. Draw and label two “boards” that represent the amounts that you and Jamal owe.2. Use the picture that you drew to help you solve the problem. What amount does each ofyou owe? Write your answer using a complete sentence.Jamal and Carla mow a lawn together to earn some more money for the summer. Carla beginsmowing 30 minutes before Jamal. Then they mow together for 75 minutes until they finish.How much time did Jamal and Carla each spend mowing?3. Draw and label two “boards” that represent the amount of time that Jamal andCarla mowed. 2008 Carnegie Learning, Inc.4. Use the picture that you drew to determine the amount of time spent mowing. How muchtime did Jamal and Carla spend mowing? Write your answer using a complete sentence.5. What was the total time spent mowing? Write your answer using a complete sentence.6. Suppose that Jamal and Carla together are paid 15.00. How much were they paid foreach hour of work? Remember that 1 hour is equal to 60 minutes. Write your answerusing a complete sentence.7. Because he worked for 75 minutes, Jamal should receive 6.25 of the 15.00. How muchshould Carla receive? Use complete sentences to explain how you found the answer.Chapter 1 Assignments11
2008 Carnegie Learning, Inc.12Chapter 1 Assignments
AssignmentNameAssignment for Lesson 1.2DateCollection ConnectionFactors and Multiples1. What factor of 24 is paired with 8? Write all of the factor pairs of 24.2. What factor of 42 is paired with 6? Write all of the factors of 42.3. What factor of 35 is paired with 5? Write all of the factors of 35.4. A collection of 24 marbles is divided into equal-sized groups. What group sizesare possible?5. Our number system is based on the number 10. The Babylonians based their numbersystem on the number 60. Write all of the factors of 60.6. Why do you think the Babylonians chose the number 60 as the base of their system?Write your answer using a complete sentence. 2008 Carnegie Learning, Inc.7. Lilly listed 1, 2, 3, 4, 8, 12, 24, 32, 48, and 96 as factors of 96. Is her list complete?8. Caitlin has a collection of CDs. The number of CDs that she has is divisible by 2, 3, 4, 5,and 6. What is the least number of CDs that Caitlin can have in her collection?9. Write four number sentences using the numbers 3, 6, and 18. Then completethe statements.The number 3 is a of 18.The number 18 is a of 6.The numbers 3 and 6 are a of 18.Chapter 1 Assignments31
2008 Carnegie Learning, Inc.14Chapter 1 Assignments
AssignmentAssignment for Lesson 1.3NameDateDogs and BunsLeast Common MultipleYour club is packing bag lunches for an upcoming trip and wants to include at least onehard-boiled egg in each lunch. There are 8 students going on the trip. Eggs are sold in cartonsof one dozen, or 12 eggs. The club wants to put an equal number of eggs in each lunch andhave no eggs left over. How many dozens of eggs do they need to buy?1. List the first ten multiples of 8.2. List the first ten multiples of 12.3. What numbers are in both sets of multiples?4. Of the numbers that are in both sets, which is the smallest?5. How many dozens of eggs does the club need to buy?In a video game, a character needs to shine a light through two spinning wheels that haveholes in them. The first wheel makes a complete rotation in 7 seconds. The second wheelmakes a complete rotation in 9 seconds. The holes are lined up at 0 seconds. How manyseconds will pass before they are lined up again? 2008 Carnegie Learning, Inc.6. List the first ten multiples of 7.7. List the first ten multiples of 9.8. What is the least common multiple of 7 and 9? Write a complete sentence to explainyour answer.9. How many seconds will pass before the holes are again lined up?10. Find the least common multiple of each pair of numbers.3 and 54 and 68 and 1610 and 15Chapter 1 Assignments51
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AssignmentNameAssignment for Lesson 1.4DateKings and MathematiciansPrime and Composite NumbersUse the divisibility rules on page 18 in your text to decide whether each numberis prime or composite. Use a complete sentence to explain your reasoning.1. 512. 713. 454. 875. 41All of the prime numbers up to 50 are listed below.2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 2008 Carnegie Learning, Inc.6. List all of the even prime numbers.7. Explain your answer to Question 6 using divisibility rules.In each list, identify the number that is not prime. Then write a completesentence that explains why it is not prime.8. 59, 63, 71, 799. 101, 103, 105, 107Name the property that is illustrated.10. 27 1 2711. 2 3 3 2Chapter 1 Assignments71
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AssignmentAssignment for Lesson 1.5NameDateI Scream for Ice CreamPrime FactorizationDesmond’s class invents a game that they call “Factor It.” For each round, the teacher turnsover a card with a number on it and the students write a factorization for the number. Studentsreceive 1 point for each factor in their factorization. For example, suppose that the teacherturned over a card with 36 on it.Desmond writes down 3 12 and receives 2 points.Cynthia writes down 2 2 9 and receives 3 points.Juan writes down 2 2 3 3 and receives 4 points.Juan wins the round because he has the most points. 2008 Carnegie Learning, Inc.For each number on the cards that the teacher turns over, write a factorization that will get youthe greatest number of points in the game. Construct a factor tree to check your answer.1. 482. 723. 544. 1285. 6406. 10007. Suppose that the teacher turns over a card that has a 60 on it. Desmond writes(2 2) 5 3 4 5 3. Juan writes 2 2 (5 3) 2 2 15.Whose answer is correct? How do you know? Write a complete sentence toexplain your reasoning.Chapter 1 Assignments91
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AssignmentAssignment for Lesson 1.6NameDatePowers That BePowers and Exponents1. How can divisibility rules help you to find the prime factorization of 513? Use completesentences to explain.For each power, identify the base and the exponent. Then evaluate the power.2. 65 3. 112 Base:Base:Exponent:Exponent:4. 302 5. 104 Base:Base:Exponent:Exponent:Use a factor tree to find the prime factorization of each number. Then useexponents to write the prime factorization. 2008 Carnegie Learning, Inc.6. 40Prime factorization 8. 72Prime factorization 7. 98Prime factorization 9. 128Prime factorization Chapter 1 Assignments111
2008 Carnegie Learning, Inc.112Chapter 1 Assignments
AssignmentAssignment for Lesson 1.7NameDateBeads and BaublesGreatest Common Factor1. Your aunt’s club is planning to sell small bags of different types of beads to people whowant to make their own bead jewelry. The table below lists the different types of beadsand how many they have.Type of BeadQuantityOval bead24Metal bead18The club wants to divide these beads into bags so that each bag has exactly the samenumber of oval beads and metal beads. What is the greatest number of bags that theycan make so that all of the beads are used and there is the same number of each bead ineach bag? Write your answer using a complete sentence.2. Complete the table to find the greatest common factor of 100 and 64.NumberUnique Factor PairsUnique FactorsCommon Factors10064 2008 Carnegie Learning, Inc.The greatest common factor of 100 and 64 is .3. Complete the table to find the greatest common factor of 36 and 48.NumberUnique Factor PairsUnique FactorsCommon Factors3648The greatest common factor of 36 and 48 is .Find the greatest common factor of each set of numbers.4. 72 and 305. 25 and 506. 27 and 807. 30 and 548. 22, 55, and 1109. 96, 48, and 80Chapter 1 Assignments131
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AssignmentAssignment for Lesson 2.1NameDateComic StripsDividing a Whole into Fractional PartsWrite the fraction that is represented by the fraction model.1.22.3. 2008 Carnegie Learning, Inc.Divide and shade each rectangle to represent the fraction.4.235.356.187.71238. Divide and shade the circle to represent .8Chapter 2 Assignments15
2008 Carnegie Learning, Inc.216Chapter 2 Assignments
AssignmentNameAssignment for Lesson 2.2DateDividing QuesadillasDividing More than One Whole into PartsSix friends are sharing 4 quesadillas equally for lunch at a table in the cafeteria.1. Show one way that you can divide the quesadillas equally. How many pieces would eachperson get? Use complete sentences to explain your reasoning.22. Juanita divided all of the quesadillas into thirds. How many pieces would each personget? Write your answer using a complete sentence. 2008 Carnegie Learning, Inc.3. Dwayne said he would divide each quesadilla into six pieces. How many pieces wouldeach person get? Is that the same amount of quesadillas that Juanita got? Use acomplete sentence to explain your reasoning.4. Gretchen made 3 pans of lasagna for her 5 friends. Show one way that she can cut upthe pans so that her friends all have an equal amount of lasagna. Draw a picture andexplain your solution.Chapter 2 Assignments17
Introduction to Picture Algebra Skills Practice p. 189 1.2 Collection Connection Assignment p. 3 Factors and Multiples Skills Practice p. 191 1.3 Dogs and Buns Assignment p. 5 Least Common Multiple Skills Practice p. 193 1.4 Kings and Mathematicians Assignment p. 7 Prime and Composite Numbers Skills Practice p. 195 1.5 I .
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