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MATH PHRASES PRE-ALGEBRA THEN ALGEBRA 1 Study Guide for First Semester Geometry Mastery, 6-5-95 (old version, questions 1,2,3,4,5,6,7,9,10,11,13,25,28,31,33,34) Text: Geometry, Nichols et.al., Holt,, 1991. Chapters 1-7 & Pythagorean Theorem (Ch 9). midpoints (1.3) acute/obtuse/right/straight angles (1.4) adjacent angles and angle bisectors (1.5) supplements and complements of angles (1.6) vertical angles (2.8) parallel lines and transversals (3.2) alternate & Same Side Interior Angles (3.3) sum of angles in triangle (3.6) exterior and remote interior angles (3.7) congruence of triangles, SAS, SSS, ASA, AAS (4.2-4,6) isosceles, equilateral trianges (5.1) altitudes & medians of triangles (5.5) triangle angle/side inequalities (5.7-8) interior angles of polygons (6.2) parallelogram conditions (6.4-6.5) special quadrilateral conditions (7.2-3) the pythagorean theorem (9.2) Phrase Guide for Pre-Algebra, Nichols, et.al., Holt, 1992. Unit 1, Chapters 1 through 3: Introduction to Algebra Chapter 1, Lessons 1-1 through 1-9: Integers Lesson 1-1, pgs 2-6: The Integers the integers data bar graph zero positive negative above sea level below zero non-negative absolute value opposite of represents number line table calculator original integer one-millionth round number nearest million Pre-Algebra Lesson 1-2, pgs 7-10: Comparing and Ordering Integers number line ascending order descending order compare integers greater than less than inequality sign left of right of locate the numbers list the numbers chart mathematical sentence ordering integers Lesson 1-3, pgs 11-12: Problem Solving Exploration Using an Addition Model positive counter negative counter value of square opposite signs neutral pair add counters remove pairs same sign record the sum final value problem solving addition model Lesson 1-4, pgs 13-18: Adding Integers stock transactions add integers model this sum number line move right move left like signs absolute values neutral pair property of opposites set of integers find the profit greater value difference of addition sentence expression gained lost change in net change two at a time shortcut method find it mentally is always successive plays calculate final position total gained series of plays find the sum only if statement is false true statement Lesson 1-5, pgs 21-22: Problem Solving Exploration Using a Subtraction Model use counters model subtraction subtract from change the value greater than neutral counters negative number final value model shows absolute value subtraction model Lesson 1-6, pgs 23-25: Subtracting Integers subtraction addition are related subtracting integers is the same as adding the opposite rewrite problem subtraction rule expression same value difference is difference of calculator sequence change-of-sign inequality sign Lesson 1-7, pgs 26-27: Problem Solving Strategies Choosing a Method of Computation formulate a plan solve a problem more efficient use a calculator mental math use counters use a model paper & pencil use a computer exact answer estimate arrive at answer large numbers represent problem apply strategies divisible by sum is closer find the product cheaper way opposite direction accuracy method of computation Lesson 1-8, pgs 28-31: Multiplying Integers factors first factor second factor complete the pattern different signs same signs like signs unlike signs multiplying integers find the product correct statement times a loss numbered consecutively evenly spaced directly opposite Lesson 1-9, pgs 32-35: Dividing Integers yards per minute change in altitude amount of change algebra divisions fraction form inverse operations related rules dividing integers quotient divide by zero not defined like signs unlike signs zero by zero division statements total decrease evaluate inequality sign equal sign total decrease average drop Chapter 2, Lessons 2-1 through 2-8: Variables and Expressions Lesson 2-1, pgs 39-43: Evaluating Expressions algebraic expression represent the total symbol variable numerical expression the result is translate word expression added to sum of increased by more than subtracted from decreased by less than less times product of multiplied by divided by quotient of equivalent same number simplify expression simplified operations parentheses remove parentheses substitute for a given value word descriptions algebraic descriptions cost in cents for what value evaluate expression Lesson 2-2, pgs 44-45: Problem Solving Strategies Using a Step-by-Step Process understand plan look back apply better buy estimation approximate reasonable correct operations answer the question label a diagram evaluate expression how many different exactly the same distance around step-by-step process Lesson 2-3, pgs 46-50: Order of Operations compute the cost one expression two values rules are needed simplify expression same result order of operations enclosed in parenthesis perform operation numerator denominator left-to-right algebraic expression variable evaluate equivalent indicates the product scientific calculator Lesson 2-4, pgs 51-52 Problem Solving Exploration Making Generalizations generalization specific instance pattern only one instance counterexample does not equal every instance pattern Lesson 2-5, pgs 54-58: Basic Properties and Mental Computations commutative property change the sum product associative property identity property of addition of multiplication simplify mentally addition of opposites numerical expression counterexample commutative operation share equally Lesson 2-6, pgs 59-63: Using the Distributive Property distributive property multiplication over addition addends numerical coefficient like terms add like terms recognize instances values equivalent expressions product symbol Lesson 2-7, pgs 64-68: Formulas: Perimeter, Area, Average rectangle perimeter distance around area square units formula square 2L+2W LW length times width meters square meters average substitute Lesson 2-8, pgs 69-74: Area Formulas: Parallelograms, Triangles, and Trapezoids geometric figure rectangle parallelogram opposite sides same length parallel graph paper base times height diagram triangle diagonal size and shape trapezoid figure ABCD double the height Chapter 3, Lessons 3-1 to 3-9: Equations and Problem Solving Lesson 3-1, pgs 80-84: Equations and Inequalities equation mathematical sentence number replacement solution equal sign expression variable set members elements solution set inequality each member of Lesson 3-2, pgs 85-88: Solving Equations write an equation represent what number guess-and-check solve an equation reasonable guess mental math added to times a number divided by equivalent expressions Lesson 3-3, pgs 89-90: Problem Solving Strategies Choosing Strategies total number of guess-and-check draw a diagram simpler problem look for pattern digits Lesson 3-4, pgs 91-94: Solving Addition and Subtraction Equations solve equations substitute values replacement set mental math guess-and-check general method addition property equality equivalent equations opposites identity should be added Lesson 3-5, pgs 95-99: Solving Multiplication and Division Equations what is the question choose a variable in words in algebra think solution check multiplication property of equality division property solve and check multiply each side original equation not true for zero multiply each side divide each side Lesson 3-6, pgs 101-104: Inverse Operations inverse operations undo each other both sides apply the inverse perform operations insert parentheses Lesson 3-7, pgs 105-109: Solving Multi-Step Equations distributive property remove parentheses original equation combine terms taking the opposite rewrite expression sequence term Lesson 3-8, pgs 110-113: Translating Word Expressions to Algebraic Expressions translate word expression algebraic expression essential skill same symbol more than one addition expression sum of add to more than increased by total of subtraction expression minus difference of subtract from decreased by less less than multiplication expression times product of multiplied by twice triple division expressions divided by quotient of times the quantity terms enclosed in parentheses represent algebraic symbols variable operation symbols distance traveled Lesson 3-9, pgs 114-118: Problem Solving Writing an Equation deposited some money what is question what is given consecutive numbers one more than represent unknowns number of total number write equations connect conditions check conditions Unit 2, Chapters 4-5: Rational Numbers Chapter 4, Lessons 4-1 through 4-8: Number Theory Lesson 4-1, pgs 126-130: Factors and Multiples form a product factor of multiple of divisible by natural number remainder mentally divide quotient multiples infinite set continue without end consecutive months divide evenly illustrate your answer Lesson 4-2, pgs 131-136: Tests for Divisibility whole-dollar divisibility determining add the digits is divisible by even numbers odd numbers number formed by members of set factors nonzero Lesson 4-3, pgs 137-138: Problem Solving Exploration Factors and Patterns unit square all possible ordered pair horizontal dimension vertical one-rectangle number prediction Lesson 4-4, pgs 139-141: Prime Numbers different factors prime number composite number natural number twin primes distinct parts reversal primes sieve Eratosthenes Lesson 4-5, pgs 143-146: Prime Factorization to factor express as a product natural number factor completely prime factorization factor tree divisibility test ascending order evaluate expression Lesson 4-6, pgs 148-149: Problem Solving Strategies Solving a Simpler Problem divisible by related problem simpler problem Lesson 4-7, pgs 150-153: Exponents prime factorization base exponent power fourth power squared cubed simplify expression order of operation parentheses formula volume key sequence multiples algebraic expression Lesson 4-8, pgs 154-158: LCM and GCF multiples of common multiple least common multiple LCM natural number divisible by prime number prime factors base exponent factor common factor greatest common factor GCF factorization relatively prime pictograph evaluate Chapter 5, Lessons 5-1 through 5-10: Fractions Lesson 5-1, pgs 163-167: Equivalent Fractions one half three quarters fraction whole number natural number numerator denominator proper improper equivalent equivalent fraction lowest terms relatively prime common factor GCF even numbers approximate rectangular Lesson 5-2, pgs 169-170: Problem Solving Exploration Modeling Multiplication horizontal lines vertical lines mathematical symbols mathematically product represented by Lesson 5-3, pgs 171-174: Multiplying Fractions two-thirds one-fifth multiplication rule numerator denominator product fraction divide common factor lowest terms divided equally share what remains Lesson 5-4, pgs 175-179: Multiplying Mixed Numbers mixed number improper fraction represent whole number fraction distributive property renaming common factors reasonable estimate at this rate Lesson 5-5, pgs 180-181: Problem Solving Strategies Organizing Information organizing information logical reasoning possibility conclusion must be Lesson 5-6, pgs 183-188: Using Reciprocals to Solve Equations product is one reciprocals multiplicative inverse is its own equality complex fraction dividend divisor Lesson 5-7, pgs 189-193: Dividing Fractions and Mixed Numbers square section pattern mathematical model division rule reciprocal multiplicative inverse number line inverse operation division rule mixed number common factor improper fraction quotient multiplication expression counterexample Lesson 5-8, pgs 194-199: Fractions with Like Denominators organizing data make comparisons formulate questions draw conclusions make decisions apply the property commutative property associative property adding fractions like denominators express answer lowest terms fractional part denominators numerators Lesson 5-9, pgs 200-205: Adding and Subtracting Fractions: Unlike Denominators estimate to the nearest whole number sum difference is about equivalent fractions least common denominator LCD conjecture Lesson 5-10, pgs 206-209: Subtracting Mixed Numbers estimate rename LCM density property solution set replacement set Unit 3, Chapters 6-8: Using Ratios Chapter 6, Lessons 6-1 through 6-9: Probability Lesson 6-1, pgs 216-220: Ratio and Proportion ratio compare data 3 out of 5 3 to 5 lowest terms first term second term equivalent ratios proportion means extremes cross-products generalization Lesson 6-2, pgs 221-225: Problem Solving Using Proportions proportions equivalent ratios cross-product variables simplify quality control rate expected number cents per ounce unit rate Lesson 6-3, pgs 226-230: Ratio and Measurement basic unit capacity weight length fluid ounce cup pint quart gallon ounce pound ton inch foot yard mile ratio measurement relationship proportion actual distance map distance cross-multiply represents the scale scale drawing actual length compare ratios Lesson 6-4, pgs 231-232: Problem Solving Strategies Collecting Data prepare the report gather information analyze data Lesson 6-5, pgs 234-235: Problem Solving Exploration Recording Chances cube numbered sides ordered pair summary table tally mark chances of how many different are possible successful throw Lesson 6-6, pgs 236-240: Probability as likely to fair way outcomes equally likely event possible outcome sample space probability chance ratio successful outcome total number more likely certain to happen less likely cannot happen drawn at random odds in favor unsuccessful experiment Lesson 6-7, pgs 241-246: Independent and Dependent Events probability independent event sample space successful event chosen at random dependent event outcomes mutually exclusive Lesson 6-8, pgs 247-251: Making Choices different choices tree diagram model fundamental counting principle number of events sample space probability equally likely random survey Lesson 6-9, pgs 252-257: Permutations tree diagram possible outcome permutation ordered arrangement number of ways factorial notation fundamental counting principal evaluate Chapter 7, Lessons 7-1 through 7-10: Decimals Lesson 7-1, pgs 262-266: Rational Expressions algebra formula expression ratio of algebraic expression rational rational expression evaluate substitute values for variables rational number integers denominator not equal zero irrational pi square root expressed as fractional part lowest terms inverse identity property Lesson 7-2, pgs 267-270: Rational Numbers number line denominator opposite sum is zero rational numbers equivalent fractions Lesson 7-3, pgs 271-274: Decimals and Fractions mileage indicator odometer extreme right tenths of a mile decimal basic symbols decimal system digit separately in combination with place value tens ones tenths hundredths thousandths expanded form negative decimal equivalent fraction mixed number lowest terms decimeter decigram deciliter exponents base ten quotient Lesson 7-4, pgs 275-276: Problem Solving Strategies Drawing a Diagram connecting lines completely rhymed draw diagram lady murasaki incompletely rhymed segment opposite corners right angle 90 degrees Lesson 7-5, pgs 277-280: Repeating Decimals rational number terminating repeating decimal repeats without end use a bar digits that repeat unending exact value round the decimal irrational irrational number pi nearest hundredth statement reason Lesson 7-6, pgs 282-286: Estimating Sums and Differences bar graph compare data estimate sum difference round to tenths break the record front digits exact answer Lesson 7-7, pgs 287-288: Problem Solving Exploration Powers of Ten relationship exponent number of zeros product factors powers of ten generalization integers whole numbers Lesson 7-8, pgs 289-294: Scientific Notation approximate age billion years scientific notation product two factors greater than or equal power of ten standard notation decimal point positive exponent zero exponent negative exponent scientific calculator multiplying powers regroup represented by calculator display degrees Celsius helium atom centimeters kilometers decimal system Lesson 7-9, pgs 295-296: Problem Solving Exploration The Metric System decimal point write a rule test a rule metric system length meter mass gram capacity liter prefix kilo- hecto- deka- basic unit deci- centi- milli- dekagram decigram kiloliter milliliter kilometer millimeter centigram converting units metric units Lesson 7-10, pgs 297-300: Estimating Products and Quotients of Decimals estimate rounding nearest whole number difference estimated answer calculated answer a little less than a little more than fuel economy miles per gallon quotient best describes underestimate overestimate Chapter 8, Lessons 8-1 through 8-9: Percent Lesson 8-1, pgs 305-308: The Meaning of Percent write a ratio to compare denominator is 100 percent proportion division property equality numerator denominator variable Lesson 8-2, pgs 309-312: Decimals and Percents prediction percent chance specific designed area chances are that percent per hundred hundredths decimal percent symbol equivalent to Lesson 8-3, pgs 313-316: Estimating the Percent of a Number yearly budget million multiple of use fractions estimate fractional equivalents is between closer estimate difference between memorize table best estimate about how many solve by estimation Lesson 8-4, pgs 317-318: Problem Solving Strategies Deciding on Estimates table figures average estimate bar graph relative sizes compare amounts total daily usage approximate exact area of square miles how accurate Lesson 8-5, pgs 319-322: Finding the Percent of a Number estimate practical use expected to use exact answer nearest tenth approximation percent decimal actual percent commission on sales cannot be used generalization Lesson 8-6, pgs 324-328: Interest interest money paid for the use of money borrow money principal rate of interest percent of principal yearly percent computing simple interest rate-per-year time-in-years amount paid back compound interest money accumulated compounded yearly Lesson 8-7, pgs 330-333: Discount discount amount subtracted regular price list price rate of discount sale price amount of discount net price marked down counterexample Lesson 8-8, pgs 334-337: Solving Percent Equations and Proportions percent discount original number write an equation write a proportion let n equal what percent of what is 8% of Lesson 8-9, pgs 338-341: Percent Increase and Decrease approximate percent increase ratio amount of increase original amount percent decrease whole percent Unit 4, Chapters 9-11: Using Graphs Chapter 9, lesson 9-1 through 9-7: Analyzing Data Lesson 9-1, pgs 348-350: Misleading Graphs information graphs misinterpreted horizontal scale vertical scale approximate mileage Dallas Beaumont Corpus Christi missing information four-month period bar graph line graph Lesson 9-2, pgs 351-354: Using Data from Graphs and Tables organized in tables inflation rate estimate the cost rate of increase monthly payments indicated rates braking distance presenting data Lesson 9-3, pgs 355-357: Organizing and Presenting Data estimate average time frequency table histogram interval tally frequency what percent reasonable time Lesson 9-4, pgs 359-362: Measures of Central Tendency most common mode average mean in the middle median measures of central tendency set of data statistic representative typical number assumed mean Lesson 9-5, pgs 364-365: Problem Solving Strategies Analyzing Sample Data salmon freshwater stream spawn tagging sample total population sample data estimate size make predictions proportion formula substitute known values cross-multiply simplify good estimate reliable sample Lesson 9-6, pgs 366-369: Stem and Leaf Plots stem-leaf plot highest score lowest score tens digit stems vertical line units digit leaf plot range interval range difference inauguration histogram Lesson 9-7, pgs 370-372: Box and Whisker Plots data collected organized analyzed box and whisker plot central tendency extremes greatest value least value median above upper quartile lower quartile extreme points appropriate scale what percent Chapter 10, Lessons 10-1 through 10-7: The Number Line Lesson 10-1, pgs 377-381: The Set of Real Numbers decimal digit terminate repeat a pattern fraction nonrepeating infinite decimal randomly irrational number the set of all real numbers corresponds point number line one-to-one correspondence the graph of open ray not included solution set open circle endpoint closed circle closed ray all real numbers inequality replacement set finite comparison statements decreased by one Lesson 10-2, pgs 382-385: The Addition Property of Inequality strategy inequality logical reasoning represent the unknown let x represent original amount addition property of inequality if-then solve and graph Lesson 10-3, pgs 386-389: The Multiplication Property of Inequality multiplication property inequality area rectangle square centimeters Lesson 10-4, pgs 390-391: Problem Solving Strategies Using Generalizations magic numbers any integer formed generalization special numbers triangle square pentagon entries in pattern investigating Lesson 10-5, pgs 393-397: Solving Inequalities understand problem what question what given develop plan strategy carry out plan represent unknown think write inequality solve inequality look back check reverse the symbol consecutive numbers whole numbers multi-step process Lesson 10-6, pgs 399-402: Conjunctions mathematics the word "and" join sentences conjunctions only if both are true graph the solution set of common to both closed interval intersection open interval empty set Lesson 10-7, pgs 403-405: Disjunctions special meaning in mathematics the word "or" disjunction if either is true either or both union chosen at random Chapter 11, Lessons 11-1 through 11-8: The Coordinate Plane Lesson 11-1, pgs 410-413: Coordinate Graphs latitude longitude ordered pair coordinate graph rectangular coordinate system perpendicular lines axes origin horizontal axis x-axis x-coordinate vertical axis y-axis y-coordinate right is positive left is negative up is positive down is negative quadrants vertex vertices Lesson 11-2, pgs 414-417: Graphing Linear Equations function let x represent equation ordered pair solution replacement set set of real numbers infinite number pass through graph the solution straight line linear function Lesson 11-3, pgs 418-421: The Standard Form of a Linear Equation linear equation graph is straight line standard form represent integers intercepts x-intercept y-intercept crosses the axis parallel to Lesson 11-4, pgs 422-426: The Slope of a Line average steepness rate of change nearly flat slope slope of a line ratio change vertical units horizontal units as x increases by change in corresponding undefined slope linear equation two given points perpendicular Lesson 11-5, pgs 428-429: Problem Solving Strategies Revising the Solution revise the solution easier method efficient method Lesson 11-6, pgs 430-434: Graphing Equations and Inequalities coordinate plane equation slope y-intercept slope-intercept form slope m y-intercept b rewrite the equation draw the graph graph of inequality dashed line half-plane open half-plane solid-line shade the half-plane closed half-plane Lesson 11-7, pgs 435-439: Problem Solving Using Two Variables solve equations two variables let x represent let y represent graph equations same coordinate plane intersect solution to both system of equations solution of the system solve by graphing Lesson 11-8, pgs 440-443: Translations basic pattern overall design sliding translating units to the right image point translation right is positive upward is positive translate left is negative downward is negative geometric figure original point congruent figures same size same shape Unit 5, Chapters 12-13: Using Real Numbers Chapter 12, Lessons 12-1 through 12-6: Square Roots and Right Triangles Lesson 12-1, pgs 450-451: Problem Solving Exploration Square Roots area square square meters s squared good estimate nearest thousandth approximate decimal places square root irrational number Lesson 12-2, pgs 452-456: Using Square Roots square root radical symbol perfect square positive root whole number simplify expression multiply radicals product denominator rational expression rationalize Lesson 12-3, pgs 457-462: The Pythagorean Theorem Nile River Egyptians right triangle square corner ancient Greeks Pythagoreans Pythagorean Theorem hypotenuse legs simplify radicals Pythagorean Triples segment endpoints translation triangle vertices Lesson 12-4, pgs 463-464: Problem Solving Strategies Formulating Questions how long is how wide is diagonal Lesson 12-5, pgs 466-472: Similar Triangles similar triangles indirectly same shape corresponding angles equal measure corresponding sides same ratio angle-angle-angle AAA proportion cross-products image-triangle Lesson 12-6, pgs 474-480: The Tangent Ratio right triangle acute angle measure of ninety degrees similar triangles proportions decimal represents ratio right angle opposite side hypotenuse legs adjacent side tangent ratio tan A tangent of angle round nonterminating four decimal places Chapter 13, Lessons 13-1 through 13-9: Polynomials Lesson 13-1, pgs 485-490: Adding Polynomials rectangular dimensions perimeter equation combine like terms monomial binomial polynomial computation tiles to model x-tile x-squared tile positive tile corresponding negative tile neutral pair coefficients constant terms counterexample equivalent expression expanded simplify Lesson 13-2, pgs 491-493: Subtracting Polynomials model subtraction of polynomials use tiles remove tiles x-squared tiles the opposite of each term of like terms missing variables coefficient of zero Lesson 13-3, pgs 494-495: Problem Solving Exploration Using a Multiplication Model grid rectangle product polynomial Lesson 13-4, pgs 496-500: Multiplying Binomials product monomial binomial rectangle dimensions diagram Lesson 13-5, pgs 501-502: Problem Solving Strategies Too Much/Too Little Data information clue not enough can't tell divide evenly ratio of square of average speed value of integers Lesson 13-6, pgs 504-507: Using the Distributive Property distributive property find the product generalization two binomials vertical arrangement FOIL method first terms outside terms inside terms last terms shaded region Lesson 13-7, pgs 508-511: Special Products use a model distributive property FOIL method trinomial perfect square pattern binomials sum and difference same two terms Lesson 13-8, pgs 512-515: Common Factors to factor an expression as a product polynomial common factor factor out greatest common factor distributive terms original binomial common binomial factor GCF monomial factor rational expression lowest terms Lesson 13-9, pgs 516-519: Factoring a Trinomial product of two binomials factor trinomial last term middle term numerical coefficient complete the pattern pair of integers quadratic quadratic trinomial coordinate plane linear graph solution set Unit 6, Chapters 14-15: Using Equations Chapter 14, Lessons 14-1 through 14-7: Equations in Geometry Lesson 14-1, pgs 526-531: Angles and Angle Measures plane flat surface set of points angle plane figure rays endpoint common endpoint vertex angle ABC measured in degrees protractor classify right angle acute angle obtuse angle pair of angles complementary supplementary ninety degrees one hundred eighty point of intersection Lesson 14-2, pgs 532-536: Parallel and Perpendicular Lines intersect single point be parallel right angles perpendicular opposite angles vertical angles supplementary complementary transversal exterior angles interior angles corresponding angles are equal congruent alternate interior alternate exterior logical argument segment conjecture Lesson 14-3, pgs 437-438: Problem Solving Strategies Extending Patterns design turned ninety degrees identify pattern sequence of geometric figures extend the sequence visualize next figure Lesson 14-4, pgs 539-544: Triangles endpoints triangle rigid figure sides segment measure of classified equiangular right acute obtuse scalene isosceles equilateral triangle sum one hundred eighty degrees protractor generalization opposite sides equal measures exterior angle remote interior parallel lines intersected by transversal corresponding angles alternate interior equal measure Lesson 14-5, pgs 546-550: Polygons simple closed curve crossing itself line segments polygon triangle quadrilateral pentagon hexagon octagon parallelogram rectangle square rhombus trapezoid vertices diagonal vertex degrees regular polygon same length same measure Lesson 14-6, pgs 551-556: Circumference and Area shape of a circle set of points in a plane same distance center segment radius chord diameter distance around circumference ratio pi 3.14 22/7 approximation irrational number pi d 2 pi r area of circle pi r squared units square units square centimeters Lesson 14-7, pgs 558-561: Circle Graphs percent of each kind survey circle graph non-overlapping sections whole circle three hundred sixty degrees one hundred percent compass protractor center of circle vertex of angle labelled graph pie-shaped region amount budgeted tally sheet Chapter 15, Lessons 15-1 through 15-15-8: Volume and Surface Area Lesson 15-1, pgs 566-567: Problem Solving Exploration Surface Area and Volume rectangles centimeter graph paper surface area x units long y units wide Lesson 15-2, pgs 568-571: Volume of a Rectangular Prism prism base polygon lateral face triangular rectangular pentagonal hexagonal octagonal rectangular prism volume space occupied determined by cubic units multiply by number of layers dimensions cubic feet area of base volume is length times width times height cubic meters cube s cubed cubic yards Lesson 15-3, pgs 572-575: Surface Area of a Rectangular Prism rectangular prism face base surface area cube cubical box six s squared minimum amount Lesson 15-4, pgs 576-580: Volume of a Cylinder cylinder right cylinder circles bases radius height perpendicular distance form is rigid circumference parallelogram approximate prism pie-shaped wedges area of base pi r h squared Lesson 15-5, pgs 582-585: Volume of a Pyramid Egyptian pyramids 2600 B.C. pyramid vertex lateral face vertex faces intersect triangles polygon TransAmerica Building perform experiment compare volume congruent base one-third B h Lesson 15-6, pgs 586-589: Volume of a Cone cone properties base vertex height line segment perpendicular to volume one-third pi r squared h 3.14 Lesson 15-7, pgs 590-591: Problem Solving Strategies Making a Model patterns models three-dimensional figures cube triangular pyramid square pyramid straight line perpendicular line radius circumference pi semicircle cone Lesson 15-8, pgs 592-595: Volume and Area of a Sphere sphere least surface area given volume spherical object mathematician Archimedes volume of sphere four-thirds pi r cubed surface area four pi r squared radius hemisphere Mercury inequality Phrase Guide for Algebra 1, Nichols, et. al., Holt, 1986. Ernie's computer, file=c: \wp51\docs\algebra1.gui. 6-9-95, dml. Chapter 1, Sections 1.1 - 1.8: Operations, Variables, Formulas Section 1.1, pgs 1-3: Rules for Order of Operations objective simplify numerical expressions rules order of operations grouping symbols multiplication times sign raised dot parentheses brackets numerator denominator Section 1.2, pgs 4-6: Expressions with Variables evaluate algebraic expressions variables terms numerical coefficients represent the number replaced by numbers substitute Section 1.3, pgs 7-9: The Commutative and Associative Properties recognize commutative associative properties product operations computations rewrite regrouped illustrated prove justify Section 1.4, pgs 10-12: The Distributive Property distributive multiplier terms Section 1.5, pgs 13-15: Combining Like Terms simplify algebraic expressions combining like terms evaluate variables multiplicative identity coefficients numerical distributive understood to be complex expression rearrange terms grouped together Section 1.6, pgs 16-17: Factors and Exponents exponents product factor base whole number power of natural number raise to a power Section 1.7, pgs 18-19: Formulas in Geometry formula perimeter area geometric figure rectangle distance around square triangle area unit squares square centimeters trapezoid Section 1.8, pgs 21-22: Recognizing Solutions of Open Sentences solution open sentence true sentence false indicated value algebraic sentence variable Chapter 2, Sections 2.1 - 2.13: Real Numbers Section 2.1, pgs 28-31: Integers and the Number Line coordinates points graphed number line compare integers absolute value origin zero positive right negative left sets of numbers represented listing members three dots go on forever natural numbers counting numbers whole numbers integers shaded arrows order inequality less than greater than compute evaluate Section 2.2, pgs 32-33: Real Numbers identify numbers rational irrational division by zero undefined integers not zero terminating decimal repeating decimal nonzero digit block of digits nonterminating nonrepeating real numbers Section 2.3, pgs 34-36: Adding Real Numbers positive direction negative direction absolute value same sign different signs even integers odd integers closed under closure property of addition Section 2.4, pgs 37-39: Properties for the Addition of Real Numbers additive inverse opposite commutative associative additive identity property of addition associative Section 2.5, pgs 40-43: Multiplying Real Numbers to subtract add the opposite definition Section 2.6, pgs 41-43: Multiplying Real Numbers product of two positives is a positive property of zero commutative associative positive and negative is a negative two negatives is positive closure property unique real number like signs positive product different signs negative product Section 2.7, pgs 44-46: Dividing Real Numbers multiplication division inverse operations quotient of like signs is positive different signs is negative division by zero undefined reciprocal multiplicative inverse nonzero unique real number division rule multiplication by the reciprocal quotient expressed as a product Section 2.8, pgs 47-48: Shortcuts in Adding and Subtracting Real Numbers enclosing the addends in parentheses associative commutative group numbers like signs interpreted innermost parentheses volume rectangular solids pyramids Section 2.9, pgs 49-50: Evaluating Algebraic Expressions simplify evaluate algebraic expressions negative value two variables distributive Section 2.10, pgs 51-52: Like Terms with Real Number Coefficients combining like terms real number coefficients distributive property unlike terms evaluate Section 2.11, pgs 53-54: Multiplication Properties of 1 and -1 product of positive one any number multiplicative identity prove negative one opposite of the Section 2.12, pgs 55-57: Simplifying Expressions Containing Parentheses simplify evaluate algebraic expressions containing parentheses distributive property Section 2.13, pgs 58-59: Subtracting Algebraic Expressions subtract algebraic expressions multiplication property of negative one distribute subtract from from something subtract subtract the opposite Chapter 3, Sections 3.1 - 3.7: Equations: An Introduction Section 3.1, pgs 64-66: Solving Equations: x+ b=c equation mathematical sentence equal numerical algebraic expression solve equation true statement add same each side equivalent equations addition property for equations undo the operation add the opposite subtraction property form x+ b=c Section 3.2, pgs 67-68: Solving Equations: ax=c; x/a=c division property multiplication property undo this operation multiply each side divide each side nonzero Section 3.3, pgs 69-71: Solving Equations: ax+b=c; x/a+b=c equivalent equations x alone two undoings combine like terms variable term first step to each side solve and check Section 3.4, pgs 72-73: Conditionals in Logic conditional logic hypothesis conclusion if-then form implication implies true false truth table Section 3.5, pgs 74-75: The Language of Algebra translate English phrases mathematical form mathematical symbols indicate various operations word problems key phrases decreased by made smaller by subtraction increased by made greater by addition let a variable represent the number less than more than twice a number times a number divided by Section 3.6, pgs 76-79: Steps for Solving Word Problems four basic steps solve word problems read identity given what to be found plan analyze information represent data write equation solve equation interpret check solution decide reasonable arranged compactly Section 3.7, pgs 80-81: Proving Statements properties real numbers assumed true operation commutative associative identity negative one inverse distributive equality reflexive symmetric transitive substitution replaced by definitions prove truth theorem statement reason validity Chapter 4, Sections 4.1 - 4.7: Equations and Word Problems Section 4.1, pgs 86-88: Equations with Variables on Each Side solve equations variable term on each side add the opposite combine like terms Section 4.2, pgs 89-91: Equations Containing Parentheses solve equations containing parentheses remove parentheses distributive property combine like terms sum is the same as circumference circle radius diameter pi Section 4.3, pgs 92-95: Number Problems word problem sentence express relationship variable represents in terms of let x equal read plan solve interpret their sum is separate into two parts representation basis of comparison the smaller of Section 4.4, pgs 96-99: Equations with Fractions with fractions transform without fractions multiply by the reciprocal product is one most efficient only one term least number divisible by denominators least common multiple LCM Section 4.5, pgs 100-102: Equations with Decimals equations that contain decimals multiply by 10 equivalent to move decimal point respectively decimals as fractions LCM convenient technique digits to the right Section 4.6, pgs 103-105: Using Algebra in Percent Problems percent per hundred to a decimal percent of is is what percent of decimal equation selling price profit cost inflation Section 4.7, pgs 106-108: Perimeter Formulas draw a picture perimeter distance around formula 2L+2W rectangle represent the length width representation triangle isosceles congruent sides legs

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