Arithmetic for College Readiness Student Workbook

526 Pages·2016·5.85 MB·English

Scottsdale Community College

Arithmetic for College Readiness
Student Workbook

Development Team
Amy Volpe
Jenifer Bohart
Judy Sutor
Donna Slaughter
Martha Gould

First Edition
2016

This work is licensed (CC-BY) under a
Creative Commons Attribution 4.0 International License
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ATTRIBUTIONS

This work, “Arithmetic for College Readiness”, is an adaptation of the following.
1. “Basic Arithmetic” by Dr. Donna Slaughter (formerly Gaudet) under CC BY-SA 4.0.
2. “MCCCD Number Sense 1” by The Maricopa Modules for College Readiness Number Sense 1 Team
under CC BY-SA 4.0.
3. “MCCCD Number Sense 2” by The Maricopa Modules for College Readiness Number Sense 2 Team
under CC BY-SA 4.0.
4. “MCCCD Multiplicative Reasoning” by The Maricopa Modules for College Readiness Multiplicative
Reasoning Team under CC BY-SA 4.0.
Web tools and images utilized with permission.
1. Math Aids: http://www.math-aids.com/
2. National Library of Virtual Manipulatives: http://nlvm.usu.edu/

“Arithmetic for College Readiness” is licensed under CC BY-SA 4.0

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ABOUT THIS WORKBOOK
Mathematics instructors at Scottsdale Community College in Scottsdale, Arizona created this workbook. The
included content is designed to lead students through arithmetic, from a multiple representations approach, and
to develop a deep understanding of the concepts associated with number and operations. The included curriculum
is broken into fourteen units. Each unit includes the following components:
MEDIA LESSON
 The Media Lesson is the main instructional component for each lesson.
 Media Examples can be worked by watching online videos and taking notes/writing down the problem as
written by the instructor. Video links can be found at http://sccmath.wordpress.com or may be located within
the MathAS Online Homework Assessment System.
 You Try problems reinforce Lesson concepts and should be worked in the order they appear showing as much
work as possible. Answers can be checked in Appendix A.

PRACTICE PROBLEMS
 This section follows the Lesson. If you are working through this material on your own, the recommendation
is to work all practice problems. If you are using this material as part of a formal class, your instructor will
provide guidance on which problems to complete. Your instructor will also provide information on accessing
answers/solutions for these problems.

END OF UNIT ASSESSMENT
 The last part of each Unit is a short end of lesson assessment. If you are working through this material on your
own, use these assessments to test your understanding of the unit concepts. Take the assessments without the
use of the book or your notes and then check your answers. If you are using this material as part of a formal
class, your instructor will provide instructions for completing these problems and for obtaining solutions to
the practice problems.

MATHAS ONLINE HOMEWORK ASSESSMENT SYSTEM
If you are using these materials as part of a formal class and your class utilizes an online homework/assessment
system, your instructor will provide information as to how to access and use that system in conjunction with this
workbook.

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Table of Contents
UNIT 1 – PLACE VALUE AND WHOLE NUMBERS ............................................................................. 1
UNIT 1 − MEDIA LESSON ....................................................................................................................... 2
SECTION 1.1: USING BASE BLOCKS TO REPRESENT WHOLE NUMBERS ...............................................2
SECTION 1.2: DECOMPOSING AND REGROUPING NUMBERS ..................................................................3
SECTION 1.3: WRITING NUMBERS IN VARIOUS FORMS ...........................................................................4
SECTION 1.4: EXTENDING PLACE VALUE TO LARGER NUMBERS .........................................................6
SECTION 1.5: WRITING WORD NAMES FOR LARGE NUMBERS ...............................................................7
SECTION 1.6: ORDERING NUMBERS USING PLACE VALUE .....................................................................8
SECTION 1.7: ROUNDING NUMBERS USING PLACE VALUE .....................................................................9
SECTION 1.8: ADDING AND SUBTRACTING WHOLE NUMBERS ............................................................ 10
SECTION 1.9: MULTIPLYING WHOLE NUMBERS ..................................................................................... 12
SECTION 1.10: DIVIDING WHOLE NUMBERS ............................................................................................ 15
UNIT 1 – PRACTICE PROBLEMS ......................................................................................................... 19
UNIT 1 – END OF UNIT ASSESSMENT ................................................................................................ 39
UNIT 2 – INTEGERS............................................................................................................................... 41
UNIT 2 – MEDIA LESSON ..................................................................................................................... 42
SECTION 2.1: INTEGERS AND THEIR APPLICATIONS ............................................................................. 42
SECTION 2.2: PLOTTING INTEGERS ON A NUMBER LINE ...................................................................... 43
SECTION 2.3: ABSOLUTE VALUE AND NUMBER LINES ........................................................................... 44
SECTION 2.4: OPPOSITES AND NUMBER LINES ........................................................................................ 45
SECTION 2.5: ORDERING INTEGERS USING NUMBER LINES ................................................................. 46
SECTION 2.6: REPRESENTING INTEGERS USING THE CHIP MODEL .................................................... 47
SECTION 2.7: THE LANGUAGE AND NOTATION OF INTEGERS ............................................................. 48
SECTION 2.8: ADDING INTEGERS ................................................................................................................ 49
SECTION 2.9: SUBTRACING INTEGERS ...................................................................................................... 51
SECTION 2.10: CONNECTING ADDITION AND SUBTRACTION ............................................................... 54
SECTION 2.11: USING ALGORITHMS TO ADD AND SUBTRACT INTEGERS .......................................... 55
SECTION 2.12: MULTIPLYING INTEGERS .................................................................................................. 56
SECTION 2.13: DIVIDING INTEGERS ........................................................................................................... 58
SECTION 2.14: CONNECTING MULTIPLICATION AND DIVISION .......................................................... 59
SECTION 2.15: USING ALGORITHMS TO MULTIPLY AND DIVIDE INTEGERS ..................................... 60
UNIT 2 – PRACTICE PROBLEMS ......................................................................................................... 63
UNIT 2 – END OF UNIT ASSESSMENT ................................................................................................ 89
UNIT 3 – ORDER OF OPERATIONS AND PROPERTIES ................................................................... 91
UNIT 3 – MEDIA LESSON ..................................................................................................................... 92
SECTION 3.1: ADDITION, SUBTRACTION AND THE ORDER OF OPERATIONS .................................... 92
SECTION 3.2: MULTIPLICATION, DIVISION AND THE ORDER OF OPERATIONS ............................... 93
SECTION 3.3: THE ORDER OF OPERATIONS FOR +, −, ×, ÷ ................................................................. 94
SECTION 3.4: PARENTHESES AS A TOOL FOR CHANGING ORDER ....................................................... 95
SECTION 3.5: EXPONENTS ............................................................................................................................ 96
SECTION 3.6: PEMDAS AND THE ORDER OF OPERATIONS .................................................................... 98
SECTION 3.7: THE COMMUTATIVE PROPERTY ........................................................................................ 99
SECTION 3.8: THE ASSOCIATIVE PROPERTY ......................................................................................... 102
SECTION 3.9: THE DISTRIBUTIVE PROPERTY ........................................................................................ 103
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SECTION 3.10: INVERSES, IDENTITIES, ONES, AND ZEROS .................................................................. 105
UNIT 3 – PRACTICE PROBLEMS ........................................................................................................107
UNIT 3 – END OF UNIT ASSESSMENT ...............................................................................................131
UNIT 4 – DIVISIBILITY, FACTORS, AND MULTIPLES ....................................................................133
UNIT 4 – MEDIA LESSON ....................................................................................................................134
SECTION 4.1: FACTORS AND DIVISIBILITY ............................................................................................. 134
SECTION 4.2: GREATEST COMMON FACTOR AND LEAST COMMON MULTIPLE ............................ 137
SECTION 4.3: PRIME AND COMPOSITE NUMBERS ................................................................................. 140
SECTION 4.4: PRIME FACTORIZATION, GCF, AND LCM ....................................................................... 143
UNIT 4 – PRACTICE PROBLEMS ........................................................................................................147
UNIT 4 – END OF UNIT ASSESSMENT ...............................................................................................161
UNIT 5 – INTRODUCTION TO FRACTIONS ......................................................................................165
UNIT 5 – MEDIA LESSON ....................................................................................................................166
SECTION 5.1: WHAT IS A FRACTION? ....................................................................................................... 166
SECTION 5.2: REPRESENTING UNIT FRACTIONS ................................................................................... 169
SECTION 5.3: COMPOSITE FRACTIONS.................................................................................................... 171
SECTION 5.4: IMPROPER FRACTIONS AND MIXED NUMBERS ............................................................ 174
SECTION 5.5: EQUIVALENT FRACTIONS ................................................................................................. 175
SECTION 5.6: WRITING FRACTIONS IN SIMPLEST FORM .................................................................... 176
SECTION 5.7: COMPARING FRACTIONS................................................................................................... 178
UNIT 5 – PRACTICE PROBLEMS ........................................................................................................183
UNIT 5 – END OF UNIT ASSESSMENT ...............................................................................................199
UNIT 6 – OPERATIONS WITH FRACTIONS ......................................................................................203
UNIT 6 – MEDIA LESSON ....................................................................................................................204
SECTION 6.1: ADDING FRACTIONS ........................................................................................................... 204
SECTION 6.2: SUBTRACTING FRACTIONS ............................................................................................... 209
SECTION 6.3: MULTIPLYING FRACTIONS ............................................................................................... 213
SECTION 6.4: DIVIDING FRACTIONS ........................................................................................................ 220
SECTION 6.5: SIGNED FRACTIONS AND THE ORDER OF OPERATIONS ............................................. 225
UNIT 6 – PRACTICE PROBLEMS ........................................................................................................227
UNIT 6 – END OF UNIT ASSESSMENT ...............................................................................................245
UNIT 7 – INTRODUCTION TO DECIMALS ........................................................................................249
UNIT 7 – MEDIA LESSON ....................................................................................................................250
SECTION 7.1: WHAT IS A DECIMAL? ........................................................................................................ 250
SECTION 7.2: PLACE VALUE AND DECIMALS ......................................................................................... 253
SECTION 7.3: PLOTTING DECIMALS ON THE NUMBER LINE .............................................................. 259
SECTION 7.4: ORDERING DECIMALS ........................................................................................................ 261
SECTION 7.5: ROUNDING DECIMALS ....................................................................................................... 263
SECTION 7.6: WRITING AND ROUNDING DECIMALS IN APPLICATIONS ........................................... 265
UNIT 7 – PRACTICE PROBLEMS ........................................................................................................267
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UNIT 7 – END OF UNIT ASSESSMENT ...............................................................................................281
UNIT 8 – CONNECTING FRACTIONS AND DECIMALS ...................................................................285
UNIT 8 – MEDIA LESSON ....................................................................................................................286
SECTION 8.1: VISUALIZING CONVERTING FRACTIONS TO DECIMALS ............................................ 286
SECTION 8.2: USING PLACE VALUE TO CONVERT FRACTIONS TO DECIMALS ............................... 288
SECTION 8.3: USING FACTORING TO CONVERT FRACTIONS TO DECIMALS ................................... 289
SECTION 8.4: CONVERTING DECIMALS TO FRACTIONS ...................................................................... 292
SECTION 8.5: COMPARING DECIMALS AND FRACTIONS ..................................................................... 294
UNIT 8 – PRACTICE PROBLEMS ........................................................................................................295
UNIT 8 – END OF UNIT ASSESSMENT ...............................................................................................301
UNIT 9 – OPERATIONS WITH DECIMALS ........................................................................................305
UNIT 9 – MEDIA LESSON ....................................................................................................................306
SECTION 9.1: ADDING DECIMALS USING THE AREA MODEL .............................................................. 306
SECTION 9.2: ADDING DECIMALS USING PLACE VALUE ..................................................................... 307
SECTION 9.3: SUBTRACTING DECIMALS USING THE AREA MODEL .................................................. 308
SECTION 9.4: SUBTRACTING DECIMALS USING PLACE VALUE ......................................................... 310
SECTION 9.5: ADDING AND SUBTRACTING SIGNED DECIMALS ......................................................... 311
SECTION 9.6: MULTIPLYING DECIMALS USING THE AREA MODEL .................................................. 312
SECTION 9.7: MULTIPLYING DECIMALS USING PLACE VALUE ......................................................... 314
SECTION 9.8: DIVIDING DECIMALS USING THE AREA MODEL ........................................................... 315
SECTION 9.9: DIVIDING DECIMALS USING PLACE VALUE .................................................................. 316
SECTION 9.10: MULTIPLYING AND DIVIDING DECIMALS BY POWERS OF 10 .................................. 317
SECTION 9.11: DECIMAL OPERATIONS ON THE CALCULATOR .......................................................... 318
SECTION 9.12: APPLICATIONS WITH DECIMALS ................................................................................... 319
UNIT 9 – PRACTICE PROBLEMS ........................................................................................................321
UNIT 9 – END OF UNIT ASSESSMENT ...............................................................................................333
UNIT 10 – MULTIPLICATIVE AND PROPORTIONAL REASONING ..............................................337
UNIT 10 – MEDIA LESSON...................................................................................................................338
SECTION 10.1: ADDITIVE VERSUS MULTIPLICATIVE COMPARISONS ............................................... 338
SECTION 10.2: RATIOS AND THEIR APPLICATIONS .............................................................................. 342
SECTION 10.3: RATIOS AND PROPORTIONAL REASONING .................................................................. 344
SECTION 10.4: RATES, UNIT RATES, AND THEIR APPLICATIONS ....................................................... 349
SECTION 10.5: RATES AND PROPORTIONAL REASONING .................................................................... 352
SECTION 10.6: SIMILARITY AND SCALE FACTORS................................................................................ 355
UNIT 10 – PRACTICE PROBLEMS ......................................................................................................361
UNIT 10 – END OF UNIT ASSESSMENT .............................................................................................375
UNIT 11 – PERCENTS ...........................................................................................................................379
UNIT 11 – MEDIA LESSON...................................................................................................................380
SECTION 11.1: INTRODUCTION TO PERCENTS ....................................................................................... 380
SECTION 11.2: FINDING PERCENTS GIVEN AN AMOUNT AND A WHOLE .......................................... 386
SECTION 11.3: FINDING AN AMOUNT GIVEN A PERCENT AND A WHOLE ........................................ 389
SECTION 11.4: FINDING THE WHOLE GIVEN A PERCENT AND AN AMOUNT ................................... 395
SECTION 11.5: PERCENT INCREASE AND DECREASE ........................................................................... 398
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UNIT 11 – PRACTICE PROBLEMS ......................................................................................................403
UNIT 11 – END OF UNIT ASSESSMENT .............................................................................................419
UNIT 12 – SYSTEMS OF MEASURE AND UNIT CONVERSIONS .....................................................421
UNIT 12 – MEDIA LESSON...................................................................................................................422
SECTION 12.1: UNDERSTANDING DIMENSION ........................................................................................ 422
SECTION 12.2: MEASURING LENGTH ....................................................................................................... 423
SECTION 12.3: MEASURING AREA............................................................................................................. 427
SECTION 12.4: MEASURING VOLUME ...................................................................................................... 429
SECTION 12.5: INTRODUCTION TO CONVERTING MEASURES ............................................................ 431
SECTION 12.6: DIMENSIONAL ANALYSIS AND U.S. CONVERSIONS .................................................... 434
SECTION 12.8: CONVERSIONS BETWEEN U.S. AND METRIC MEASURES ........................................... 442
UNIT 12 – PRACTICE PROBLEMS ......................................................................................................445
UNIT 12 – END OF UNIT ASSESSMENT .............................................................................................455
UNIT 13 – PERIMETER AND AREA ....................................................................................................459
UNIT 13 – MEDIA LESSON...................................................................................................................460
SECTION 13.1: PERIMETER ........................................................................................................................ 460
SECTION 13.2: CIRCUMFERENCE .............................................................................................................. 464
SECTION 13.3: STRATEGIES FOR FINDING AREA .................................................................................. 467
SECTION 13.4: FORMULAS FOR FINDING AREA ..................................................................................... 471
UNIT 13 – PRACTICE PROBLEMS ......................................................................................................481
UNIT 13 – END OF UNIT ASSESSMENT .............................................................................................489
UNIT 14 – VOLUME AND THE PYTHAGOREAN THEOREM ..........................................................491
UNIT 14 –MEDIA LESSON ...................................................................................................................492
SECTION 14.1: VOLUME OF PRISMS ......................................................................................................... 492
SECTION 14.2: VOLUME OF A CYLINDER ................................................................................................ 495
SECTION 14.3: VOLUMES OF OTHER SHAPES ......................................................................................... 499
SECTION 14.4: INTRODUCTION TO THE PYTHAGOREAN THEOREM ................................................ 501
SECTION 14.5: SQUARE ROOTS .................................................................................................................. 503
SECTION 14.6: APPLYING THE PYTHAGOREAN THEOREM ................................................................. 505
UNIT 14 –PRACTICE PROBLEMS .......................................................................................................509
UNIT 14 –END OF UNIT ASSESSMENT ..............................................................................................515

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