Compare, contrast and order elements of the real number system into various subsystems and identify the characteristics of each subsystem. a. Natural numbers b. Whole numbers c. Integers d. Rational numbers e. Irrational numbers Clever Counting SE/TE: Investigation 1- Counting Possibilities, 5-14; Investigation 2- Opening Locks, 15-26; Investigation 3- Networks, 27-36; Investigation 4- Deciding Whether Order is Important, 37-46 Transparencies 85-98; Teaching the Investigation 14a-56b; Additional Practice 102-109 TECH: Calculators; Transparencies 1.1 to 5.1 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 TECH: Calculators; Transparencies 1.1 to 4.4C MO--P2.1 MA5 Students will demonstrate an ability to compare and contrast characteristics of real numbers for inclusion in various subsystems through the use of Venn Diagrams and other types of graphic organizers and offer them according to different requirements. Students will compare and contrast various sets of numbers and by using the individual characteristics of each number determine its inclusion and order in each subsystem. (CR) SE = Student Edition TE = Teacher Edition 1
(continued) Say It with Symbols SE/TE: Investigation 1- Order of Operations, 5-19; Investigation 2- Equivalent Expressions, 20-33; Investigation 3- Some Important Properties, 34-52; Investigation 4- Solving Equations, 53-64; Investigation 5- Writing Expressions for Surface Area 65-70 Transparencies 112-127; Teaching the Investigation 52a-70h, Labsheet 3.3; Additional Practice 134-144 TECH: Calculators; Transparencies 1.1 to 5.1 Looking for Pythagoras SE/TE: Investigation 2- Finding Areas and Lengths, 17-26; Investigation 5- Irrational Numbers, 53-63; Investigation 6- Rational and Irrational Slopes, 64-72 Transparencies 116-118, 127-132; Teaching the Investigation 26a-26l, 63a-63g, 72a-73; Lab sheet 2.1 to 2.ACE, 6.2, 6.ACE1, 6.ACE2; Additional Practice 138-139, 147-148 TECH: Calculators; Transparencies 2.1 to 2.3, 5.3, 6.1A to 6.2 SE = Student Edition TE = Teacher Edition 2
Illustrate and apply the properties of real numbers and the properties of equality. a. Associative property b. Commutative property c. Distributive property d. Identity property e. Inverse property f. Reflexive property (=) g. Symmetric property (=) h. Addition/Subtraction property (=) i. Multiplication/Division property (=) Clever Counting SE/TE: Investigation 1- Counting Possibilities, 5-14; Investigation 2- Opening Locks, 15-26; Investigation 3- Networks, 27-36; Investigation 4- Deciding Whether Order is Important, 37-46 Transparencies 85-98; Teaching the Investigation 14a-56b; Additional Practice 102-109 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Say It with Symbols SE/TE: Investigation 1- Order of Operations, 5-19; Investigation 2- Equivalent Expressions, 20-33; Investigation 3- Some Important Properties, 34-52; Investigation 4- Solving Equations, 53-64; Investigation 5- Writing Expressions for Surface Area 65-70 Transparencies 112-127; Teaching the Investigation 52a-70h, Labsheet 3.3; Additional Practice 134-144 MO--1.6, 3.2, 3.3 MA1, 5 Students will justify each step in the solution of an algebraic equation by identifying the application of each property of real numbers or equality being used. Students will demonstrate their understanding by writing examples of and solve problems through the application of the properties of real numbers and the properties of equality. SE = Student Edition TE = Teacher Edition 3
(continued) Looking for Pythagoras SE/TE: Investigation 2- Finding Areas and Lengths, 17-26; Investigation 5- Irrational Numbers, 53-63; Investigation 6- Rational and Irrational Slopes, 64-72 Transparencies 116-118, 127-132; Teaching the Investigation 26a-26l, 63a-63g, 72a-73; Lab sheet 2.1 to 2.ACE, 6.2, 6.ACE1, 6.ACE2; Additional Practice 138-139, 147-148 Evaluate algebraic expressions involving: a. Varying quantities as variables b. Absolute values c. Order of operations Clever Counting SE/TE: Investigation 1- Counting Possibilities, 5-14; Investigation 2- Opening Locks, 15-26; Investigation 3- Networks, 27-36; Investigation 4- Deciding Whether Order is Important, 37-46 Transparencies 85-98; Teaching the Investigation 14a-56b; Additional Practice 102-109 MO--P1.6, 1.8, 3.3 Students will demonstrate the ability to evaluate algebraic expressions using order of operations (parentheses, exponents, multiplication, division, addition, and subtraction) as well as evaluate expression involving absolute values. Students will evaluate algebraic expressions of one or more variables given the value of each variable involved. SE = Student Edition TE = Teacher Edition 4
(continued) Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Say It with Symbols SE/TE: Investigation 1- Order of Operations, 5-19; Investigation 2- Equivalent Expressions, 20-33; Investigation 3- Some Important Properties, 34-52; Investigation 4- Solving Equations, 53-64; Investigation 5- Writing Expressions for Surface Area 65-70 Transparencies 112-127; Teaching the Investigation 52a-70h, Lab sheet 3.3; Additional Practice 134-144 Looking for Pythagoras SE/TE: Investigation 2- Finding Areas and Lengths, 17-26; Investigation 5- Irrational Numbers, 53-63; Investigation 6- Rational and Irrational Slopes, 64-72 Transparencies 116-118, 127-132; Teaching the Investigation 26a-26l, 63a-63g, 72a-73; Labsheet 2.1 to 2.ACE, 6.2; Additional Practice 138-139, 147-148 SE = Student Edition TE = Teacher Edition 5
1. Solve algebraic equations and inequalities involving: a. One variable b. Absolute value c. Formulas for area, perimeter, surface area, and volume of various two and three-dimensional geometric figures. Clever Counting SE/TE: Investigation 1- Counting Possibilities, 5-14; Investigation 2- Opening Locks, 15-26; Investigation 3- Networks, 27-36; Investigation 4- Deciding Whether Order is Important, 37-46 Transparencies 85-98; Teaching the Investigation 14a-56b; Additional Practice 102-109 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Lab sheet 1.2; Additional Practice 120-121, 126-127 Thinking With Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-59; Additional Practice 116-125; Lab sheet 1.2, Say It with Symbols SE/TE: Investigation 3- Some Important Properties, 34-52; Investigation 5- Writing Expressions for Surface Area 65-70 MO--P3.2, 3.3 Students will use inverse operations to isolate the variable and then label appropriately. Students will demonstrate an ability to solve equations and inequalities by showing each step involved in isolating the variable. SE = Student Edition TE = Teacher Edition 6
2. (continued) Say It with Symbols Transparencies 112-119, 127; Teaching the Investigation 52a-52q, 70a-70h; Additional Practice 143; Labsheet 3.3, 5.1 Represent solutions of one variable algebraic equations and inequalities on a number line. Analysis Can be developed using Investigations: Looking for Pythagoras SE/TE: Investigation 6- Rational and Irrational Slopes, 64-72 Transparencies 127-132; Teaching the Investigation 72a-73; Labsheets 6.2, 6.ACE1, 6.ACE2; Additional Practice 147-148 MO--P1.6, 1.8, 3.6 Students will illustrate the differences between "equal", greater than", "less than", "greater than or equal to", and "less than or equal to" and review how to solve for a specific variable. Students will solve an equation or inequality involving one variable and then visually represent the answer on an appropriate graph or number line. SE = Student Edition TE = Teacher Edition 7
Rewrite linear equations and inequalities in different forms involving slope, intercepts or points on the line. a. Solve problems involving linear equations and inequalities by graphing. b. Represent linear equations in standard form. c. Identify and represent graphically x- and y-intercepts. d. Represent linear equations in slope-intercept form. e. Identify and calculate the slope of a line. f. Calculate the slope of a line parallel and perpendicular to a given line. g. Identify and write the equation of a line given the slope and a point on the line. h. Translate and reflect linear equations graphically. Analysis Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 Say It with Symbols SE/TE: Investigation 4- Solving Equations, 53-64 Transparencies 120-126; Teaching the Investigation 64a-64t; Additional Practice, 141-142 MO--P1.4, 1.6, 1.8, 2.1, 2.7, 3.3 Students will use algebraic skills and point-slope form to write an equation of a line and then graph the solution on a coordinate plane. Students will graphically represent linear equations on a coordinate plane. Evaluate and simplify algebraic expression involving radicals and exponents. Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2 MO--P1.4, 1.6, 3.3 Students will use order of operations and rules for radicals to simplify expressions. Students will simplify mathematical expressions using the appropriate rule of radicals and order of operations. SE = Student Edition TE = Teacher Edition 8
(continued) Additional Practice 120-121, 126-127 Say It with Symbols SE/TE: Investigation 1- Order of Operations, 5-19 Transparencies 112-127; Teaching the Investigation 19a-19i;103-107; Additional Practice 134-135 Apply the Pythagorean Theorem to authentic problem solving situation. Looking for Pythagoras SE/TE: Investigation 3- The Pythagorean Theorem, 27-40; Investigation 4- Using the Pythagorean Theorem, 41-52 Transparencies 119-126; Teaching the Investigation 40a-40n, 52a-52i; Labsheets, 3.2A to 3.3, 4.2; 3.1 to 3.4B, 4.1 to 4.3; Additional Practice 142-146 MO--P3.1, 3.2, 3.3, 3.6 MA2 Students will use the Pythagorean Theorem to find a missing side of a triangle, define and apply parts of a right triangle to realistic situations to find the missing measurement. Solve problems using systems of linear equations and inequalities. a. Solve by graphing. b. Solve by substitution. c. Solve by elimination. Thinking With Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-59; Additional Practice 116-125; Lab sheet 1.2 MO--P1.6, 1.8, 3.3 Students will use their skills of graphing and solving algebraically to solve problems with two or more equations. Students will solve for each variable using their method of choice when given a problem with two or more equations. SE = Student Edition TE = Teacher Edition 9
Identify and solve problems involving quadratic equations. a. Solve graphically. b. Solve by factoring. c. Solve by quadratic formula. Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 MO--P1.6, 1.8, 3.3 Students will find solutions to quadratic equations by using x-y charts and graphing as well as factoring and the quadratic formula. Students will demonstrate their ability to find the solution of an equation by using all methods of factoring. Identify and simplify polynomials by adding, subtracting and multiplying monomial, binomial, and polynomial expressions. Analysis Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 MO--P1.6 SE = Student Edition TE = Teacher Edition 10
(continued) Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Samples and Population SE/TE: Investigation 1- Comparing Data Sets, 5-23; Investigation 2- Conducting Surveys, 24-36; Investigation 3- Random Samples, 37-48; Investigation 4- Solving Real World Problems, 49-62 Transparencies 103-122; Teaching the Investigation 23a-62k; Additional Practice 130-135; Lab sheets 1.1,;3.2A to 3.3 SE = Student Edition TE = Teacher Edition 11
Solve polynomial equations as relations or functions. Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 MO--P1.6, 1.8, 3.3 MA SE = Student Edition TE = Teacher Edition 12
(continued) Frogs, Fleas, and Painted Cubes Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Samples and Population SE/TE: Investigation 1- Comparing Data Sets, 5-23; nvestigation 2- Conducting Surveys, 24-36; Investigation 3- Random Samples, 37-48; Investigation 4- Solving Real World Problems, 49-62 Transparencies 103-122; Teaching the Investigation 23a-62k; Additional Practice 130-135; Lab sheets 1.1,;3.2A to 3.3 Identify algebraic equations as relations or functions. Analysis Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 MO--P1.6, 1.8, 3.3, 3.6 SE = Student Edition TE = Teacher Edition 13
(continued) Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Samples and Population SE/TE: Investigation 1- Comparing Data Sets, 5-23; nvestigation 2- Conducting Surveys, 24-36; Investigation 3- Random Samples, 37-48; Investigation 4- Solving Real World Problems, 49-62 SE = Student Edition TE = Teacher Edition 14
(continued) Samples and Population Transparencies 103-122; Teaching the Investigation 23a-62k; Additional Practice 130-135; Lab sheets 1.1,;3.2A to 3.3. Use properties of real numbers and equalities to solve ratio and proportion problems in authentic problem-solving situations Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 TECH: Calculators; Transparencies 1.1 to 4.4C MO--P1.6, 1.8, 3.3 Identify and justify appropriate units of measure in authentic problemsolving situations. a. Use unit analysis to solve problems involving rates. b. Analyze the effects of computation on precision. c. Determine appropriate units to be used when calculating area, perimeter, surface area, and volume of geometric figures. Evaluation Frogs, Fleas, and Painted Cubes SE/TE: Investigation 5- Painted Cubes, 71-84 Transparencies 138-140; Teaching the Investigation 58a-58n, 84a-84p; Additional Practice 154 Say It with Symbols SE/TE: Investigation 5- Writing Expressions for Surface Area, 65-70 Transparency 127; Teaching the 70a-70h; Additional Practice 143, 5.1 MO--P3.3, 4.1 MA1, 2 SE = Student Edition TE = Teacher Edition 15
Generalize patterns using explicitly and recursively defined functions. Analysis Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 MO--P1.6, 1.8, 3.3 SE = Student Edition TE = Teacher Edition 16
(continued) Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Draw and use the properties of graph theory to find optimal solutions. a. Identify nodes and edges. b. Identify traceable and nontraceable networks. Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2; Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40 MO--P1.6, 1.8, 3.2, 3.3, 3.6 MA6 SE = Student Edition TE = Teacher Edition 17
(continued) Frogs, Fleas, and Painted Cubes SE/TE: Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4- What is a Quadratic Function?, 52-70; Investigation 5-Painted Cubes, 71-84 Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Use basic statistical concepts to determine central tendencies, data range and display data in various graphical representations. a. Apply statistical concepts to solve problems b. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of best fit. c. Given a scatterplot, determine an equation for a line of best fit. d. Formulate questions, design studies and collect data about characteristics. e. Solve problems and distinguish between a statistic and parameter. Thinking with Mathematical Models SE/TE: Investigation 1- Linear Models, 5-25; Investigation 2- Nonlinear Models, 26-36; Investigation 3- More Nonlinear Models, 37-46; Investigation 4- A World of Patterns, 47-59 Transparencies 94-109; Teaching the Investigation 25a-25n, 36a-36i, 46a-46i, 59a-59f; Labsheets 1.2, 3.ACE; Additional Practice 116-125 Transparencies 97-113; Teaching the Investigation 16a-16i, 60a-60o; Labsheet 1.2 MO--P3.2, 3.3, 3.6 MA6 SE = Student Edition TE = Teacher Edition 18
(continued) Additional Practice 120-121, 126-127 Frogs, Fleas, and Painted Cubes SE/TE: Investigation 1- Introduction to Quadratic Relationships, 5-18; Investigation 2- Quadratic Expressions, 19-40; Investigation 3- Quadratic Patterns of Change, 41-51; Investigation 4-What is a Quadratic Function?, 52-70; Investigation 5- PaintedCubes, 71-84 Transparencies 115-140; Teaching the Investigation 18a-18q, 40a-40cc, 51a-51m, 70a-70q, 84a-84p; Labsheets 2.4, 4.3A to 4.3B; Additional Practice 145-154 Samples and Population SE/TE: Investigation 1- Comparing Data Sets, 5-23; Investigation 2- Conducting Surveys, 24-36; Investigation 3- Random Samples, 37-48; Investigation 4- Solving Real World Problems, 49-62 Transparencies 103-122; Teaching the Investigation 23a-62k; Additional Practice 130-135; Lab sheets 1.1,;3.2A to 3.3 SE = Student Edition TE = Teacher Edition 19
Use and describe the concepts of conditional probability and independent events. a. Describe the concepts of sample space and probability distribution. Evaluation Samples and Populations SE/TE: Investigation 3- Random Samples, 37-48; Investigation 4- Solving Real-World Problems, 49-62 Transparencies 116-122; Teaching the Investigation 36a-36e, 48a-48i, 62a-62k; Labsheets 3.2A to 3.3; Additional Practice 137-140 Clever Counting SE/TE: Investigation 1- Counting Possibilities, 5-14; Investigation 2- Opening Locks, 15-26 Transparencies 85-89; Teaching the Investigation 14a-14g, 26a-26h; Additional Practice 102-105 MO--P1.6, 1.8, 3.2, 3.3, 3.5, 3.6 MA6 SE = Student Edition TE = Teacher Edition 20