8th Grade Algebra. Thursday, May 08, 2003 Page 1 of 28

Instructional Unit Unit 01-Difference of Squares: Organizing Data Unit 1 provides opportunities The student will be -Analyze the structure of -written analysis of 2.4.8.F, for students to understand the able to interpret graphs. graphs 2.5.8.C, routines and structure of the graphs to solve -Make inferences and -construction of 2.5.8.D, CPM program more deeply. problems comparisons from graphs to graphs based upon 2.11.8.A The main themes of this unit solve problems. relationships focus upon developing -Design graphs. -written homework concepts and skills with integer -unit quizzes operations, using patterns to -unit tests make inferences, and introducing the concept of variable. A variety of manipulatives are used to assist students in their developing integer operations and combining like terms. Other topics that are touched upon include interpretation of graphs, development of guess and check tables, scientific notation, and the concept of average. The unit ends with a theme problem that requires the students to search for Thursday, May 08, 2003 Page 1 of 28

Instructional Unit Unit 01-Difference of Squares: Organizing Data Unit 1 provides opportunities The student will be -Develop rules. -written homework 2.4.8.A, for students to understand the able to use patterns -Predict terms. -group analysis of 2.4.8.B, routines and structure of the to make inferences. -Use guess and check as a guess and check 2.4.8.D, CPM program more deeply. strategy to solve problems problems 2.5.8.A, The main themes of this unit -group development 2.5.8.B, focus upon developing -Perform simplification of of number 2.5.8.C, concepts and skills with integer rules/patterns 2.5.8.D, operations, using patterns to -algebra tile lab to 2.8.8.B, make inferences, and develop 2.8.8.C, introducing the concept of understanding of 2.8.8.D, variable. A variety of 2.8.8.G, manipulatives are used to 2.11.8.C assist students in their developing integer operations and combining like terms. Other topics that are touched upon include interpretation of graphs, development of guess and check tables, scientific notation, and the concept of average. The unit ends with a theme problem that requires the students to search for Thursday, May 08, 2003 Page 2 of 28

Instructional Unit Unit 01-Difference of Squares: Organizing Data Unit 1 provides opportunities The student will be -Add with integers. -algebra tile labs to 2.1.8.B, for students to understand the able to demonstrate -Subtract with integers. develop integer 2.1.8.C, routines and structure of the an understanding of -Multiply with integers. operation rules 2.1.8.F, CPM program more deeply. integer relationships -Divide with integers. -number family 2.2.8.A, The main themes of this unit through operations. -Demonstrate understanding pattern development 2.2.8.B, focus upon developing of addition, subtraction and for division 2.4.8.B, concepts and skills with integer multiplication with algebra -classroom discussion 2.4.8.C, operations, using patterns to tiles. 2.4.8.D, make inferences, and -Develop rules for integer -unit quizzes 2.4.8.E introducing the concept of operations. -unit test variable. A variety of - -journal entries manipulatives are used to assist students in their developing integer operations and combining like terms. Other topics that are touched upon include interpretation of graphs, development of guess and check tables, scientific notation, and the concept of average. The unit ends with a theme problem that requires the students to search for Thursday, May 08, 2003 Page 3 of 28

Instructional Unit Unit 02-Tiling the Kitchen Floor: Area/Subproblems In this unit, the students will The students will be -Determine the area of -written development 2.1.8.B, apply the use of subproblems able to solve regions. of area formulas with 2.2.8.A, to assist in solving problems. problems by using -Solve real-world the aid of plane figure 2.3.8.A, This problem solving strategy subproblems. applications problems in cut-out 2.3.8.D, will be woven throughout the group and individual -written homework 2.5.8.B, unit as students develop area settings. -class discussions 2.8.8.C, formulas for plane figures and -Construct area formulas -unit quizzes 2.9.8.G solve real world problems for plane figures including -unit test involving area. Development parallelograms, triangles, -group posters for of perimeter and circumference trapezoids and circles. theme problem occurs by way of hands-on -Construct the formula for techniques as the students circumference. derive various formulas. -Compute numeric Continued work with patterns expressions using the order allows the students to develop of operations. understandings of the -Identify the size of Distributive Property, order of numbers using scientific operation, and writing numbers in scientific notation. Thursday, May 08, 2003 Page 7 of 28

Instructional Unit Unit 02-Tiling the Kitchen Floor: Area/Subproblems In this unit, the students will The student will be -Formalize inductive -algebra tile lab to 2.4.8.A, apply the use of subproblems able to use the patterns into an algebraic develop the 2.5.8.B, to assist in solving problems. distributive property rule. distributive property 2.5.8.C, This problem solving strategy to manipulate -Use algebra tiles to design -written homework 2.8.8.A, will be woven throughout the algebraic situations reflecting the -unit quizzes 2.8.8.B, unit as students develop area distributive property. -unit test 2.8.8.D, formulas for plane figures and -Manipulate algebraic -class discussion solve real world problems expressions symbolically -journal entry involving area. Development -calculator activity to of perimeter and circumference develop the order of occurs by way of hands-on operations (optional) techniques as the students -demonstration of derive various formulas. both symbolic and Continued work with patterns manipulative allows the students to develop understandings of the understandings of the distributive property Distributive Property, order of operation, and writing numbers in scientific notation. Thursday, May 08, 2003 Page 8 of 28

Instructional Unit Unit 03-The Burning Candle: Patterns and Graphs The Burning Candle Unit The students will be -Determine the algebraic -silent board games 2.8.8.A, promotes the use of patterns able to interrelate rule based upon an x-y data -algebra walk 2.8.8.B, to investigate graphs on the symbolic and table. -written homework 2.8.8.C, coordinate plane and symbolic graphic -Determine the algebraic -unit quizzes 2.8.8.G, representations. By the end of representations of rule for a graph based upon -unit test 2.8.8.H the unit, students will have analysis of points. -class discussion graphed both linear and -Recognize the shape of a -individual student non-linear equations. Scaling graph based upon its design of silent board of axes, identification of games (optional) intercepts, and the use of -partner quiz (optional) graphs to make inferences are developed throughout the unit. -concept theme Students also use silent board posters (optional) games to synthesize number patterns into algebraic rules. This is extended to equation development from graphs of those equations. The theme problem asks the students to collect data from a video presentation. Analysis of this data follows so that one can make predictions based upon the graphed data. Thursday, May 08, 2003 Page 9 of 28

Instructional Unit Unit 03-The Burning Candle: Patterns and Graphs The Burning Candle Unit The students will be -Demonstrate the difference -written homework 2.6.8.C, promotes the use of patterns able to apply their between linear and -unit quizzes 2.7.8.B, to investigate graphs on the patterning skills to non-linear equations and -unit tests 2.7.8.C, coordinate plane and symbolic graphing equations. graphs. -class discussions 2.8.8.B, representations. By the end of -Recognize the relationship -group construction of 2.8.8.F, the unit, students will have between an algebraic graphs 2.8.8.G, graphed both linear and formula and its graph. -group analysis of 2.8.8.H non-linear equations. Scaling -Estimate x and y data collected (The of axes, identification of intercepts. Burning Candle Video) intercepts, and the use of graphs to make inferences are -partner quiz (optional) developed throughout the unit. Students also use silent board -concept theme games to synthesize number posters (optional) patterns into algebraic rules. -class-sized graph This is extended to equation construction (The development from graphs of those equations. The theme problem asks the students to collect data from a video presentation. Analysis of this data follows so that one can make predictions based upon the graphed data. Thursday, May 08, 2003 Page 10 of 28

Instructional Unit Unit 04-Choosing Phone Plan: Write/Solve Equations The main purpose of this unit is The students will be -Write algebraic expressions -written plan to solve 2.3.8.A, for students to be able to write able to formulate from guess and check the unit theme 2.3.3.B, equations for word problems equations from word tables. problem 2.5.8.A, and to solve equations. problem settings. -Model word problem -written homework 2.5.8.B, Students learn to write situations using symbolic -unit quizzes 2.5.8.D, equations through the use of -unit test 2.8.8.G guess and check tables. -large poster sheet Pattern recognition in the guess and check tables leads to student development of algebraic expressions and equations. Students also begin to solve equations in this unit. Equation solving begins with manipulatives from which symbolic manipulation eventually occurs. Equations involving decimals, fractions, and formulas are solved. The theme problem asks the students to use equations to determine an appropriate phone Thursday, May 08, 2003 Page 11 of 28

Instructional Unit Unit 05-Estimating Fish Pop: Geo/Alg Ratios A conceptual understanding of The students will be -Solve equations through -written homework ratios is critical to any able to solve the use of manipulatives. -unit quizzes complete understanding of equations in a -Solve equations -unit tests mathematics. In this unit, variety of ways. symbolically. -unit theme problem algebraic and geometric ratios -Solve literal equations for -algebra tile labs are integrated to give students -class discussion a more thorough experience -group problem with the concept. Students focus upon the notions of similarity, particularly with triangles. This is building toward a later development of slope. Area and perimeter ratios as they relate to similar figures are discussed. Problems involving percentage ratios and proportions are also Thursday, May 08, 2003 Page 12 of 28

Instructional Unit Unit 05-Estimating Fish Pop: Geo/Alg Ratios A conceptual understanding of The students will be -Solve proportions -written homework 2.1.8.D, ratios is critical to any able to apply symbolically. -unit quizzes 2.8.8.C, complete understanding of proportional -Determine the similar figure -unit test 2.8.8.E, mathematics. In this unit, relationships to a relationships dealing with -unit theme problem 2.3.8.D, algebraic and geometric ratios variety of scale factors, areas, and (estimating fish 2.3.8.E, are integrated to give students perimeters. populations) 2.3.8.F, a more thorough experience -Solve word problems -class discussions 2.5.8.A, with the concept. Students involving proportional -similar-figure 2.5.8.B, focus upon the notions of relationships. constructions 2.9.8.J, similarity, particularly with -Construct similar figures -large grid paper 2.10.8.A, triangles. This is building based upon a given scale 2.10.8.B toward a later development of factor. slope. Area and perimeter -Solve proportion problems ratios as they relate to similar involving percents. figures are discussed. -Graph relationships Problems involving percentage involving proportional ratios and proportions are also relationships. Thursday, May 08, 2003 Page 13 of 28

Instructional Unit Unit 06-World Records: Graphing/Systems Throughout this unit, students The students will be -Solve systems of -daily homework 2.5.8.B, will advance their study of able to design equations using graphs. -unit quizzes 2.5.8.C, systems of equations. The analyses of -Solve systems of -unit test 2.6.8.C, study of these systems will competing situations equations using substitution. -class discussions 2.6.8.F, focus upon algebraic, numeric, by using a variety -unit theme problem 2.7.8.B, and graphed solutions. of mathematical -Use a system of equations (comparing Olympic 2.8.8.F, Students will also focus upon techniques. to model a word problem swimmers) real world settings that could be setting. -TI73 graph solved using a system of -Analyze the graphs of representations equations. It is hoped that competing situations. -large graph paper students will recognize the -Compare the solutions class presentations power of the algebraic technique, with substitution being the main method chosen. Elimination is covered at a later time in the course. A second major topic in this unit is the multiplication of binomials. A connection is made to the Distributive Property, as students build their understanding of multiplication through the use Thursday, May 08, 2003 Page 14 of 28

Instructional Unit Unit 06-World Records: Graphing/Systems Throughout this unit, students The students will be -Multiply binomials using -daily homework 2.1.8.E, will advance their study of able to multiply manipulatives. -unit quizzes 2.8.8.B, systems of equations. The binomials in multiple -Multiply binomials -unit test 2.8.8.D study of these systems will representations algebraically. -algebra tile labs focus upon algebraic, numeric, -Diagram binomial -class discussion and graphed solutions. multiplication using a Students will also focus upon generic rectangle. real world settings that could be -Plan a technique to multiply solved using a system of any set of polynomials equations. It is hoped that without the use of students will recognize the power of the algebraic technique, with substitution being the main method chosen. Elimination is covered at a later time in the course. A second major topic in this unit is the multiplication of binomials. A connection is made to the Distributive Property, as students build their understanding of multiplication through the use Thursday, May 08, 2003 Page 15 of 28

Instructional Unit Unit 07-The Big Race: Slopes/Rates of Change The major components of a The students will be -Determine slopes and -daily homework 2.3.8.A, linear graph will be focused able to distinguish intercepts visually. -unit quizzes 2.3.8.D, upon in this unit. Slope and various linear graphs -Calculate slopes given two -unit test 2.8.8.G, intercepts will be connected to based upon the points. -class discussion linear situations in algebraic relationships of -Calculate intercepts given -slope lab using the and graphical situations. The slopes and a formula. TI73 calculators idea that slope is a rate of -Recognize the relationship (optional) change will be represented in a between a linear equation, -unit theme problem variety of ways. Intercepts its slope and y-intercept. (The Big Race) and, in particular, the -Graph linear relationships -string problems to y-intercept will be explained in using a slope and have students a variety of contexts as well. y-intercept. determine slope Linear graphs will be made -Solve systems of without a grid using slope and intercept, and equations, using ideas of (optional) the connection to the "y=mx+b" slope and y-intercepts to form will be discovered in this facilitate graphing. unit. The Big Race theme -Determine the relationship problem will tie together the between a type of slope and students' understanding of its effect on a graph. slope, intercepts, and systems of equations. Thursday, May 08, 2003 Page 16 of 28

Instructional Unit Unit 08-The Amusement Park: Factoring Quadratics Students will revisit the use of The students will be -Build factored -daily homework 2.1.8.E, algebra tiles in the construction able to factor representations of -unit quizzes 2.4.8.A, of polynomials. Students will polynomials, using polynomials. -unit test 2.5.8.A, look at the inverse of multiple -Factor polynomials -algebra tile labs 2.5.8.C, multiplyingor, in this case, representations. symbolically. -class discussion 2.8.8.D, factoring. Relationships -Determine patterns -unit theme problem 2.8.8.G, between the polynomial and its between concrete (construction of an 2.8.8.B factor parts will be sought. The representations and amusement park) unit also has students begin to symbolic representations of -written analyses of solve a new type of equation: factored polynomials. patterns found with the quadratic equation. To -Determine factoring factoring special foster this, the Zero Product patterns for special Property is developed. The polynomials such as perfect unit closes with a theme square trinomials and problem that requires factoring to solve it. differences of squares. -Identify the greatest common factor within a polynomial. Thursday, May 08, 2003 Page 17 of 28

Instructional Unit Unit 08-The Amusement Park: Factoring Quadratics Students will revisit the use of The students will be -Solve equations using the -daily homework 2.8.8.E, algebra tiles in the construction able to solve Zero Product Property. -unit quizzes 2.8.8.B, of polynomials. Students will problems that are -Communicate a conceptual -unit test 2.5.8.A, look at the inverse of based upon understanding of the Zero -class discussion 2.5.8.B, multiplyingor, in this case, quadratic Product Property. -unit theme problem 2.5.8.C factoring. Relationships -Recognize the type of (construction of an between the polynomial and its equation requiring the use of amusement park) factor parts will be sought. The the Zero Product Property. -written analyses of unit also has students begin to patterns found with solve a new type of equation: factoring special the quadratic equation. To foster this, the Zero Product Property is developed. The unit closes with a theme problem that requires factoring to solve it. Thursday, May 08, 2003 Page 18 of 28

Instructional Unit Unit 09-Birthday Party Pinata: Dia/Write Equations Three major objectives are met The students will be -Determine the Pythagorean -daily homework 2.1.8.A, in Unit 9. First, students work able to apply the relationship based upon -unit quizzes 2.1.8.B, with the Pythagorean Pythagorean data analysis. -unit test 2.1.8.C, Theorem. Students will solve a Theorem, when -Solve for missing lengths -right triangle lab to 2.1.8.G, variety of word problems appropriate, to in right triangles, using the develop the 2.2.8.D, using the theorem. Out of this, solve real world Pythagorean Theorem. Pythagorean Theorem 2.4.8.A, solutions to quadratic -Solve equations involving 2.4.8.E, equations involving radical square roots. -class discussion 2.5.8.A, answers are developed. -Simplify square roots. -unit theme problem 2.8.8.E, Simplification of square roots -Estimate the meaning of a (The Birthday Party 2.10.8.A is also touched upon. A square root as a number. Piñata) second objective focuses upon -Graph equations involving -cooperative learning students solving equations square roots. to solve word involving fractions. Referred -Determine the distance to as fraction busters, students between two points, using will learn to 'clear out' the Pythagorean Theorem. denominators by multiplying with the least common multiple. The third objective is for the students to learn how to determine the equation of a line without using a graph. The theme problem of this unit involves the construction of a diagram to determine the amount of rope needed to hang a pinata. The Pythagorean Theorem is used to lead the Thursday, May 08, 2003 Page 19 of 28

Instructional Unit Unit 09-Birthday Party Pinata: Dia/Write Equations Three major objectives are met The student will be -Calculate the slope of a -daily homework 2.8.8.B, in Unit 9. First, students work able to express an line using two points. -unit quizzes 2.8.8.F, with the Pythagorean equation for a line -Determine the y-intercept -unit test 2.8.8.G, Theorem. Students will solve a without using a of a linear equation using -class discussion 2.8.8.H, variety of word problems the formula y=mx+b. -cooperative learning 2.8.8.A using the theorem. Out of this, -Write the linear equation in groups solutions to quadratic the form y=mx+b when equations involving radical knowing the slope and answers are developed. y-intercept. Simplification of square roots is also touched upon. A second objective focuses upon students solving equations involving fractions. Referred to as fraction busters, students will learn to 'clear out' denominators by multiplying with the least common multiple. The third objective is for the students to learn how to determine the equation of a line without using a graph. The theme problem of this unit involves the construction of a diagram to determine the amount of rope needed to hang a pinata. The Pythagorean Theorem is used to lead the Thursday, May 08, 2003 Page 20 of 28

Instructional Unit Unit 09-Birthday Party Pinata: Dia/Write Equations Three major objectives are met The students will be -Determine the least -daily homework 2.8.8.E in Unit 9. First, students work able to solve common multiple of -unit quizzes with the Pythagorean fractional equations. denominators in fractional -unit test Theorem. Students will solve a equations. -class discussion variety of word problems -Solve fractional equations using the theorem. Out of this, by first 'clearing out' the solutions to quadratic equations involving radical answers are developed. Simplification of square roots is also touched upon. A second objective focuses upon students solving equations involving fractions. Referred to as fraction busters, students will learn to 'clear out' denominators by multiplying with the least common multiple. The third objective is for the students to learn how to determine the equation of a line without using a graph. The theme problem of this unit involves the construction of a diagram to determine the amount of rope needed to hang a pinata. The Pythagorean Theorem is used to lead the Thursday, May 08, 2003 Page 21 of 28

Instructional Unit Unit 10-Yearbook Sales: Exponents/Quadratics Unit 10 focuses upon the The student will be -Determine the values of a, -daily homework 2.1.8.C, development of exponent able to apply the b, and c in a quadratic -unit quizzes 2.2.8.C, rules. Students abilities to quadratic formula to equation. -unit test 2.8.8.E factor trinomials are enriched; solve quadratic -Evaluate answers for 'x' -class discussion and, an extension into equations. using values of a, b, and c -cooperative learning simplifying rational expressions in the quadratic formula. groups is explored. The unit ends with -Determine if a quadratic -unit theme problem an introduction to the quadratic equation is factorable using -graphing scenarios formula that is developed the discriminant. more formally in a later course. -Use the answers found with The theme problem of the unit the quadratic formula to forces the student to use the quadratic formula to solve an optimization problem relating price and sales of yearbooks. Unit 10 focuses upon the The student will be -Use FOIL to arrange -daily homework 2.4.8.A, development of exponent able to factor components of binomials in -unit quizzes 2.5.8.A, rules. Students abilities to trinomials where the their appropriate locations. -unit test 2.5.8.B, factor trinomials are enriched; coefficient of -Solve equations using -class discussion 2.8.8.A, and, an extension into x-squared is not 1. trinomials where the -cooperative learning simplifying rational expressions coefficient of x-squared is groups is explored. The unit ends with not 1. an introduction to the quadratic formula that is developed more formally in a later course. The theme problem of the unit forces the student to use the quadratic formula to solve an optimization problem relating price and sales of yearbooks. Thursday, May 08, 2003 Page 22 of 28

Instructional Unit Unit 10-Yearbook Sales: Exponents/Quadratics Unit 10 focuses upon the The student will be -Determine the rule for -daily homework 2.1.8.E, development of exponent able to develop power of a power. -unit quizzes rules. Students abilities to exponent rules of -Determine the rule for -unit test factor trinomials are enriched; mathematics monomial powers. -class discussion and, an extension into through inductive lab -Determine the rule for -cooperative learning simplifying rational expressions dividing powers. groups is explored. The unit ends with -Manipulate negative -lab settings an introduction to the quadratic exponent expressions into formula that is developed positive exponent more formally in a later course. expressions. The theme problem of the unit -Determine the value of any forces the student to use the base to the power of zero. quadratic formula to solve an -Simplify algebraic optimization problem relating price and sales of yearbooks. expressions symbolically using exponent rules. - Thursday, May 08, 2003 Page 23 of 28

Instructional Unit Unit 11-Cola Machine: Functions/Equality In the last unit of the Algebra I The student will be -Factor expressions -daily homework 2.1.8.E, course, students will explore able to simplify completely. -unit quizzes 2.4.8.D, the nature of relations and expressions -Cross-cancel like factors. -unit test 2.8.8.A functions in the context of involving -Determine if an expression -class discussion 'function machines.' Students multiplication and is completely simplified. -cooperative learning extend their work with solving groups systems by including the elimination method. They will also extend their understanding of rational expressions to include multiplying and dividing expressions. New to this unit will be work with absolute value graphs and equations, as well as solving equations involving square roots. Students will also formalize the properties of equality for real numbers. Thursday, May 08, 2003 Page 24 of 28

Instructional Unit Unit 11-Cola Machine: Functions/Equality In the last unit of the Algebra I The student will be -Determine least common -daily homework 2.8.8.E course, students will explore able to solve multiples of coefficients. -unit quizzes the nature of relations and systems of -Add/subtract equations to -unit test functions in the context of equations using eliminate variables. -class discussion 'function machines.' Students -Determine the correctness -cooperative learning extend their work with solving of solutions by evaluating groups systems by including the 'x' and 'y' values in the elimination method. They will also extend their understanding of rational expressions to include multiplying and dividing expressions. New to this unit will be work with absolute value graphs and equations, as well as solving equations involving square roots. Students will also formalize the properties of equality for real numbers. Thursday, May 08, 2003 Page 25 of 28

Instructional Unit Unit 11-Cola Machine: Functions/Equality In the last unit of the Algebra I The student will be -Determine if a relation is a -daily homework 2.5.8.B course, students will explore able to determine if function. -unit quizzes the nature of relations and an equation is a -Evaluate relations using -unit test functions in the context of relation through the function notation. -class discussion 'function machines.' Students use of numerical -Determine independent and -cooperative learning extend their work with solving and graphical dependent variables in a groups systems by including the relation. -unit theme problem elimination method. They will -Determine if a formula is a -graphing scenarios also extend their understanding relation via the vertical line of rational expressions to test. include multiplying and dividing -Determine the rule of a expressions. New to this unit relation give a set of (input, will be work with absolute value output) pairs. graphs and equations, as well as solving equations involving square roots. Students will also formalize the properties of equality for real numbers. Thursday, May 08, 2003 Page 26 of 28

Instructional Unit Unit 11-Cola Machine: Functions/Equality In the last unit of the Algebra I The student will be -Identify algebraic -daily homework 2.4.8.A, course, students will explore able to design properties of equality. -unit quizzes 2.4.8.B, the nature of relations and mathematical -Design examples of the -unit test 2.5.8.B, functions in the context of equations using algebraic properties of -class discussion 'function machines.' Students properties of equality. -cooperative learning extend their work with solving groups systems by including the elimination method. They will also extend their understanding of rational expressions to include multiplying and dividing expressions. New to this unit will be work with absolute value graphs and equations, as well as solving equations involving square roots. Students will also formalize the properties of equality for real numbers. Thursday, May 08, 2003 Page 27 of 28

Instructional Unit Unit 11-Cola Machine: Functions/Equality In the last unit of the Algebra I The student will be -Graph absolute value -daily homework 2.1.8.F, course, students will explore able to solve relations. -unit quizzes 2.8.8.E, the nature of relations and equations using -Graph absolute value in the -unit test 2.8.8.G functions in the context of absolute value and context of a distance from -class discussion 'function machines.' Students square roots. zero. -cooperative learning extend their work with solving -Solve absolute value groups systems by including the equations. elimination method. They will -Solve equations involving also extend their understanding square roots. of rational expressions to include multiplying and dividing expressions. New to this unit will be work with absolute value graphs and equations, as well as solving equations involving square roots. Students will also formalize the properties of equality for real numbers. Thursday, May 08, 2003 Page 28 of 28