Equations of Linear. Functions


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1 SECTION Trusted Content Common Core State W ith American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. Common Core State Initiative What is the goal of the Common Core State? The mission of the Common Core State is to provide a consistent, clear understanding of what students are epected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that students need for success in college and careers. Who wrote the standards? The National Governors Association Center for Best Practices and the Council of Chief State School Officers worked with representatives from participating states, a wide range of educators, content eperts, researchers, national organizations, and community groups. uations of Linear ear ctions Functions What are the major points of the standards? The standards seek to develop both students mathematical understanding and their procedural skill. The for Mathematical Practice describe varieties of epertise that mathematics teachers at all levels should seek to develop in their students. The for Mathematical Content define what students should understand and be able to do at each level in their study of mathematics. How do I implement the standards? The Common Core State are shared goals and epectations for what knowledge and skills your students need to succeed. You as a teacher, in partnership with your colleagues, principals, superintendents, decide how the standards are to be met. Glencoe Algebra is designed to help you devise lesson plans and tailor instruction to the individual needs of the students in your classroom as you meet the Common Core State. At the high school level the Common Core State are organized by conceptual category. To ease implementation four model course pathways were created: traditional, integrated, accelerated traditional and accelerated integrated. Glencoe Algebra, Glencoe Geometry, and Glencoe Algebra 2 follow the traditional pathway. Mathematical Unit 2 Linear Relationships Content Lester Lefkowitz/Photographer s Choice/Getty Images Equations of Linear Functions Linear Functions Get Ready for Chapter Eplore: Graphing Technology Lab Investigating SlopeIntercept Form Graphing Equations in SlopeIntercept Form F.IF.7a, S.ID.7 Etend: Graphing Technology Lab The Family of Linear Graphs F.BF.3, S.ID Writing Equations in SlopeIntercept Form Writing Equations in PointSlope Form Parallel and Perpendicular Lines MidChapter Quiz Scatter Plots and Lines of Fit S.ID.6a, S.ID.6c Etend: Algebra Lab Correlation and Causation S.ID Regression and MedianFit Lines Inverse Linear Functions A.CED.2, F.BF.4a Etend: Algebra Lab Drawing Inverses F.BF.4a ASSESSMENT Study Guide and Review Practice Test Preparing for Standardized Tests Standardized Test Practice, Chapters F.BF., F.LE.2 F.IF.2, F.LE.2 F.LE.2, S.ID.7 S.ID.6, S.ID.8 Mathematical Content Virtual Manipulatives pp. 58, 248 Graphing Calculator pp. 69, 25 Foldables pp. 52, 24 SelfCheck Practice pp. 207, 23 v T0 _iv_alg_s_fm_toc_ indd iv_alg_t_fm_toc_ indd v v 5/7/2 9:45 AM :9
2 029_ALG_S_C05_EXP2_ indd 29 5/9/2 5:47 PM 0005_0009_ALG_S_C0_L_ indd 5 5/9/2 2:35 PM How do I decode the standards? This diagram provides clarity for decoding the standard identifiers. Conceptual Category A = Algebra N = Number and Quantity F = Functions S = Statistics and Probability A.REI.2 Domain Standard Domain Names The Real l Number b System RN Quantities Seeing Structure in Epressions Arithmetic with Polynomials and Rational Epressions Creating Equations Reasoning with Equations and Inequalities Interpreting Functions Building Functions Linear, Quadratic, and Eponential Models Interpreting Categorical and Quantitative Data Abbreviations Variables and Epressions Q SSE APR CED REI IF BF LE ID equalities There are numerous tools for implementing the Common Core State available throughout the program, including: at pointofuse in the Chapter Planner and in each lesson of the Teacher Edition, Complete standards coverage in Glencoe Algebra ensures that you have all the content you need to teach the standards, Common Core State Standar Content A.REI.3 Solve linear equations Algebra and Lab i including equations with coefficients You can use algebra tiles to solve inequalities. Atiit Activity Sl Solve Inequalities ies Solve Step Solving Inequalities Use a selfadhesive note to cover the equals sign on the equation mat. Then write a symbol on the note. Model the inequality Step 3 Add 4 negative tiles to each side to isolate the tiles. Remove the zero pairs.  Model and Analyze 4 2 Step 2 Since you do not want to solve for a negative tile, eliminate the negative tiles by adding 2 positive tiles to each side. Remove the zero pairs Step 4 Separate the tiles into 2 groups. 2 or 2 Use algebra tiles to solve each inequality.. 3 < 9 { > 3} > 4 { < } { 3} { 2} 5. In Eercises 4, is the coefficient of in each inequality positive or negative? negative 6. Compare the inequality symbols and locations of the variable in Eercises 4 with those in their solutions. What do you find? See Ch. 5 Answer Appendi. 7. Model the solution for 3 2. How is this different from solving 3 2? 8. Write a rule for solving inequalities involving multiplication and division. (Hint: Remember that dividing by a number is the same as multiplying by its reciprocal.) See Ch. 5 Answer Appendi. 3 Assess Formative Assessment Use Eercises 5 and 6 to assess whether students understand that when they multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign changes. Common Core State Content A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. See Ch. 5 Answer Appendi. 29 From Concrete to Abstract Eercise 8 asks students to generalize what happens to the inequality when multiplying or dividing by positive or negative numbers. Focus Eplore 52 Objective Use algebra tiles to model solving inequalities. Materials for Each Group algebra tiles and equation mats selfadhesive blank notes Easy to Make Manipulatives Teaching Algebra with Manipulatives Templates for: algebra tiles, pp. 0 equation mat, p. 6 Teaching Tip Have students use a selfadhesive note to cover the equals sign on the equation mat. Write a symbol on the note. This will allow students to model inequalities with the equation mat and algebra tiles. 2 Teach Working in Cooperative Groups Put students in groups of two or three and demonstrate the Activity. Have groups complete Eercises and 2. Make sure the inequality sign on the selfadhesive note is pointed in the correct direction to match the inequality. Once students have isolated the tiles, remind them to separate the tiles into equal groups to correspond to the number of tiles. If the tiles end up on the right side of the inequality, students may rotate the mat 80 degrees to read the inequality with the variable on the left side. Practice Have students complete Eercises 3 8. Correlations that show at a glance where each standard is addressed in Glencoe Algebra. You can also visit to learn more about the Common Core State. There you can choose from an etensive collection of resources to use when planning instruction. Common Core State Content A.SSE.a Interpret Variables parts of and Epressions an epression, such as terms, factors, Then and Now Why? You performed Write verbal Cassie and her friends are at a baseball coefficients. operations on epressions for game. The stadium is running a promotion integers. algebraic epressions. where hot dogs are $0.0 each. Suppose d represents the number of hot dogs Cassie Write algebraic and her friends eat. Then 0.0d represents 2 epressions for verbal Jupiterimages/Comstock Images/Getty Images New Vocabulary algebraic epression variable term factor product power eponent base Common Core State Content A.SSE.a Interpret parts of an epression, such as terms, factors, and coefficients. A.SSE.2 Use the structure of an epression to identify ways to rewrite it. Mathematical Practices 4 Model with mathematics. epressions. Write Verbal Epressions An algebraic epression consists of sums and/or products of numbers and variables. In the algebraic epression 0.0d, the letter d is called a variable. In algebra, variables are symbols used to represent unspecified numbers or values. Any letter may be used as a variable. 0.0d z_ p q 4cd 3mn 6 A term of an epression may be a number, a variable, or a product or quotient of numbers and variables. For eample, 0.0d, 2 and 4 are each terms. The term that contains or other letters is sometimes referred to as the variable term A term that does not have a variable is a constant term. In a multiplication epression, the quantities being multiplied are factors, and the result is the product. A raised dot or set of parentheses are often used to indicate a product. Here are several ways to represent the product of and y. y y (y) ()y ()(y) An epression like n is called a power. The word n power can also refer to the eponent. The eponent indicates the number of times the base is used as a base eponent factor. In an epression of the form n, the base is. The epression n is read to the nth power. When no eponent is shown, it is understood to be. For eample, a = a. Eample Write Verbal Epressions Write a verbal epression for each algebraic epression. a. 3 4 b. 5 z three times to the fourth power the cost of the hot dogs they eat. GuidedPractice A. 6 u times u to the B. _ 2 a + _ 6b second power minus times z to the second power plus siteen one half of a plus the quotient of 6 times b and 7 5 Focus Vertical Alignment Before Lesson Perform operations on integers. Lesson Lesson Write verbal epressions for algebraic epressions. Write algebraic epressions for verbal epressions. After Lesson Evaluate algebraic epressions. 2 Teach Scaffolding Questions Have students read the Why? section of the lesson. Ask: How do you find the cost of the hot dogs that Cassie and her friends eat? Multiply the number of hot dogs by $0.0. What does the epression 0.0d stand for? 0.0 times d, the number of hot dogs What other variable could you use to represent the number of hot dogs? Sample answer: h Write Verbal Epressions Eample shows how to translate an algebraic epression into a verbal epression. Lesson Resources Resource Approaching Level AL On Level OL Beyond Level BL English Learners ELL Teacher Edition Differentiated Instruction, p. 6 Differentiated Instruction, pp. 6, 9 Differentiated Instruction, p. 9 Differentiated Instruction, p. 6 Study Guide and Intervention, pp. 5 6 Study Guide and Intervention, pp. 5 6 Practice, p. 8 Study Guide and Intervention, pp. 5 6 Chapter Skills Practice, p. 7 Skills Practice, p. 7 Word Problem Practice, p. 9 Skills Practice, p. 7 Resource Practice, p. 8 Practice, p. 8 Enrichment, p. 0 Practice, p. 8 Masters Word Problem Practice, p. 9 Word Problem Practice, p. 9 Word Problem Practice, p. 9 Enrichment, p. 0 5Minute Check 5Minute Check 5Minute Check 5Minute Check Other Study Notebook Study Notebook Study Notebook Study Notebook _ALG_T_C05_EXP2_ indd :5 0005_0009_ALG_T_C0_L_ indd _0009_ALG_S_C0_L_ indd :24 T
3 SECTION Trusted Content Common Core State Common Core State, Traditional Algebra I Pathway, Correlated to Glencoe Algebra, Common Core Edition Lessons in which the standard is the primary focus are indicated in bold. Number and Quantity The Real Number System NRN Etend the properties of eponents to rational eponents.. Eplain how the definition of the meaning of rational eponents follows from etending the properties of integer eponents to those values, allowing for a notation for radicals in terms of rational eponents. 2. Rewrite epressions involving radicals and rational eponents using the properties of eponents. Use properties of rational and irrational numbers. 3. Eplain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational , 03, Etend 03, , , , Etend Quantities NQ Reason quantitatively and use units to solve problems.. Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Throughout the tet; for eample, 26, 27, 28, 29, Etend 32, 45, 75 Throughout the tet; for eample, 7, 9 24, 26 3, 32 38, 69 70, , Define appropriate quantities for the purpose of descriptive modeling. 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Etend Etend Mathematical Modeling T2
4 Correlation Algebra Seeing Structure in Epressions ASSE Interpret the structure of epressions. Interpret epressions that represent a quantity in terms of its contet. a. Interpret parts of an epression, such as terms, factors, and coefficients. b. Interpret complicated epressions by viewing one or more of their parts as a single entity., 4, 8, 9 5 9, 25 3, , , 3, , 6 22, Use the structure of an epression to identify ways to rewrite it., 2, 3, 4, 7, 72, 73, 74, Eplore 85, 85, Eplore 86, 86, 87, 88, , 0 5, 6 22, 25 3, , , , , 493, , , , 50 55, 56 52, Write epressions in equivalent forms to solve problems. 3. Choose and produce an equivalent form of an epression to reveal and eplain properties of the quantity represented by the epression. a. Factor a quadratic epression to reveal the zeros of the function it defines. b. Complete the square in a quadratic epression to reveal the maimum or minimum value of the function it defines. c. Use the properties of eponents to transform epressions for eponential functions. 85, 86, 87, 88, , , 50 55, 56 52, , 94, Etend , , Etend Arithmetic with Polynomials and Rational Epressions AAPR Perform arithmetic operations on polynomials.. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Eplore 8, 8, 82, Eplore 83, 83, , , , , , Creating Equations ACED Create equations that describe numbers or relationships.. Create equations and inequalities in one variable and use them to solve problems. 5, 2, 22, 23, 24, 25, 29, 32, 5, 52, 53, 54, 55, 76, 85, 86, 87, 94, 95, 04, , 75 80, 83 89, 9 96, 97 02, 03 09, 32 38, 63 68, , , , 306 3, 32 36, , , , 50 55, , , , T3
5 SECTION Trusted Content Common Core State Continued 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate aes with labels and scales. Etend 7, 3, 34, 35, 36, 4, 42, 43, 44, 45, 46, 47, 6, Etend 6, 62, 63, 64, 65, 75, 76, 86, 87, 88, 9, 92, 94, 95, 0, Etend 0, 04, 2, 8 55, 55 62, 82 88, 89 95, , , , , , , , , , , , , , , , , , 50 55, 56 52, , , , , , 627, , , Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling contet. 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 42, 56, 6, , , , , 29, , 32 38, Reasoning with Equations and Inequalities AREI Understand solving equations as a process of reasoning and eplain the reasoning.. Eplain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve equations and inequalities in one variable. 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 5, 22, 23, 24, 25, 26, 29, 86, 87, , Eplore 22, 22, Eplore 23, 23, 24, 25, 26, 27, 28, 29, 5, Eplore 52, 52, 53, 54, 55, , 83 89, 9 96, 97 02, 02 09, 7, 32 38, , 50 55, , 8 82, 83 89, 90, 9 96, 97 02, 03 09, 7, 9 24, 26 3, 32 38, , 29, , , 306 3, 32 36, Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in into an equation of the form ( p) 2 = q that has the same solutions. Derive the quadratic formula from this form. 94, 95, , , b. Solve quadratic equations by inspection (e.g., for 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives comple solutions and write them as a ± bi for real numbers a and b. Mathematical Modeling 86, 87, 88, 92, 94, Etend 94, , 50 55, 56 52, , , , T4
6 Correlation Solve systems of equations. 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions Solve systems of linear equations eactly and approimately (e.g., with graphs), focusing on pairs of linear equations in two variables. 6, Etend 6, 62, 63, 64, 65, Etend , , , , , , Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Etend Represent and solve equations and inequalities graphically. 0. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).. Eplain why the coordinates of the points where the graphs of the equations y = f ( ) and y = g ( ) intersect are the solutions of the equation f ( ) = g ( ); find the solutions approimately, e.g., using technology to graph the functions, make tables of values, or find successive approimations. Include cases where f ( ) and/or g ( ) are linear, polynomial, rational, absolute value, eponential, and logarithmic functions. 2. Graph the solutions to a linear inequality in two variables as a halfplane (ecluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. 6, 7, 3, 32, 34, 75, 9, 0 Etend 6, Etend 75, Etend 93, 97, Etend , Etend 56, 66, Etend , 47 54, 55 62, 63 68, 82 88, , , , , , , , 323, , 377 Functions Interpreting Functions FIF Understand the concept of a function and use function notation.. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain eactly one element of the range. If f is a function and is an element of its domain, then f ( ) denotes the output of f corresponding to the input. The graph of f is the graph of the equation y = f ( ). 6, , Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a contet. 7, 36, 43, 75, 76, 9, , , , , , , Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. 35, 77, , , T5
7 SECTION Trusted Content Common Core State Continued Interpret functions that arise in applications in terms of the contet. 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. 8, Eplore 3, 3, Etend 4, 75, 9, 97, , 53 54, 55 62, , , , , Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 7, 75, 76, 9, , , , , Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Analyze functions using different representations. 7. Graph functions epressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maima, and minima. b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. Eplore 33, 33, Etend 77, Etend 9, 96 3, 32, Etend 32, 34, 4, Etend 4, 9, 92, Eplore 93, 93, Etend , Etend 97, 0, Etend 0 7, 72 80, 444, 554, , 63 68, 69 70, 82 88, , , , , , , , 606, , 627 e. Graph eponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 8. Write a function defined by an epression in different but equivalent forms to reveal and eplain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, etreme values, and symmetry of the graph, and interpret these in terms of a contet. Eplore 75, , , 93, 94, Etend , , , b. Use the properties of eponents to interpret epressions for eponential functions. 7, 72, 75, 76, Etend , , , , Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 7, 36, 43, 78, 9, , , , , , Building Functions FBF Build a function that models a relationship between two quantities.. Write a function that describes a relationship between two quantities. a. Determine an eplicit epression, a recursive process, or steps for calculation from a contet. 7, 3, 34, 36, 4, 42, 43, 44, 45, 46, 47, 76, , 55 62, 82 88, , , , , , , , , , T6 b. Combine standard function types using arithmetic operations. 42, 76, , , Mathematical Modeling
8 Correlation 2. Write arithmetic and geometric sequences both recursively and with an eplicit formula, use them to model situations, and translate between the two forms. 35, 77, , , Build new functions from eisting functions. 3. Identify the effect on the graph of replacing f ( ) by f ( ) + k, kf ( ), f (k ), and f ( + k ) for specific values of k (both positive and negative); find the value of k given the graphs. Eperiment with cases and illustrate an eplanation of the effects on the graph using technology. Etend 4, Eplore 75, Etend 76, Eplore 93, 93, 0, Etend , , 437, , , , Find inverse functions. a. Solve an equation of the form f ( ) = c for a simple function f that has an inverse and write an epression for the inverse. 47, Etend 47, Eplore , 27, Linear, Quadratic, and Eponential Models FLE Construct and compare linear, quadratic, and eponential models and solve problems.. Distinguish between situations that can be modeled with linear functions and with eponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that eponential functions grow by equal factors over equal intervals. Eplore 33, 33, 35, 77, 96 7, 72 80, 89 95, , b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 35, 36, 76, 77, , , , , , 77, , , Construct linear and eponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 35, 36, 42, 43, 44, 45, 46, 75, 76, 77, 96, Etend , , , , , , , , , , , Observe using graphs and tables that a quantity increasing eponentially eventually eceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 96, Etend , Interpret epressions for functions in terms of the situation they model. 5. Interpret the parameters in a linear or eponential function in terms of a contet. 34, Eplore 4, 4, Etend 4, 45, 75, 76, 77, , 25, , , , , , , T7
9 SECTION Trusted Content Common Core State Continued Statistics and Probability Interpreting Categorical and Quantitative Data SID Summarize, represent, and interpret data on a single count or measurement variable.. Represent data with plots on the real number line (dot plots, histograms, and bo plots). 03, 23, 24 P40 P46, , Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 22, 23, 24, Etend , , , Interpret differences in shape, center, and spread in the contet of the data sets, accounting for possible effects of etreme data points (outliers). Summarize, represent, and interpret data on two categorical and quantitative variables. 5. Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the contet of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the contet of the data. Use given functions or choose a function suggested by the contet. Emphasize linear, quadratic, and eponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. Interpret linear models. 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the contet of the data. 8. Compute (using technology) and interpret the correlation coefficient of a linear fit. 23, , Etend , 46, Etend , , , , , Etend 4, 44, , , , Distinguish between correlation and causation. Etend Mathematical Modeling T8
10 Correlation Common Core State for Mathematical Practice, Correlated to Glencoe Algebra, Common Core Edition. Make sense of problems and persevere in solving them. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons 0, 8, 24, 34, 45, 54, 64, 75, 88, 93, 05,, and Reason abstractly and quantitatively. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons 3, 2, 33, 4, 5, 65, 72, 85, 9, 03, 8, and Construct viable arguments and critique the reasoning of others. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons 3, 25, Etend 35, 42, 55, 6, 74, 8, 92, 04, 2, and Etend Model with mathematics. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons, 29, 32, 45, 5, 65, 76, 87, 97, 04, 7, and Use appropriate tools strategically. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Etend 7, 24, Etend 32, 44, Etend 56, Etend 6, Etend 75, 82, Etend 96, 06, Etend 8, and Attend to precision. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Etend 3, 28, 34, 42, 52, 66, 74, 89, 95, 0, 6, and Look for and make use of structure. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons 2, 25, 36, Etend 4, 55, 63, 77, 86, 96, 02, 2 and Look for and epress regularity in repeated reasoning. Glencoe Algebra ehibits these practices throughout the entire program. Some specific lessons for review are: Lessons 4, 27, 3, 4, 54, 6, 7, 84, 93, 02, 5 and 26. T9
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