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Algebra 1 Daily Learning Guide Core Content: Reasoning, Problem Solving and Communication (Chapter 1 Problem Solving) STANDARD ELD Standard Performance Lessons and Objectives Vocabulary A.1.8.E Read and interpret diagrams, graphs and text containing the symbols, language and conventions of mathematics. A.1.8.E Read and interpret diagrams, graphs and text containing the symbols, language and conventions of mathematics. I can read and interpret points on a coordinate graph. A.1.8.E Read and interpret diagrams, graphs and text containing the symbols, language and conventions of mathematics. A.1.8.C Evaluate a solution for reasonableness, verify its accuracy and interpret the solution in the context of the original problem. A.1.8.G Synthesize information to draw conclusions and evaluate the arguments and conclusions of others. I can plot a point using its (x,y) coordinates. Justify Area Perimeter Timeline: 8 Days, 9/7-9/16 Formative Assessment Resources and Pacing 1.1.1 Interpreting Graphs Notes and Self Reflection Page 5 Math Notes: Perimeter and Area of a Figure (1 day) I can plot a point using its (x,y) coordinates. I can read and interpret points on a coordinate graph. I can read and interpret points on a coordinate graph. coordinate system x-axis y-axis quadrant origin ordered pair coordinates 1.1.2 Using the (x,y) plane Page 10 Math Notes: Axes, Quadrants, and Coordinates dependent variable independent variable generalize integer 1.1.3 Collecting, Organizing, and Analyzing Data Page 15 Math Notes: Adding and Subtracting Integers (2 days) 1-15 & 16 Newton’s Revenge: Keep student work for use in 7.2.1 (1 day) 1 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.8.E Read and interpret diagrams, graphs and text containing the symbols, language and conventions of mathematics. I can recognize patterns and use the patterns to make predictions. 1.1.4 Finding and Generalizing Patterns Page 19 Math Notes: Fractions, Decimals and Percents (1-2 Days) I can collect and analyze data with tables & graphs. A.1.8.B Select and apply strategies to solve problems. I can solve problems with guess and check method. A.1.8.B Select and apply strategies to solve problems. I can solve problems with guess and check method. A.1.8.B Select and apply strategies to solve problems. patterns Direct variation Direct proportion Inverse variation Inverse proportion 1.2.1 Solving Problems with Guess and Check Twice Sum Product More than Less than Times more than I can solve problems with guess and check method. A.1.2.A Know the I can compare and order real relationship between numbers. real numbers and the number line, and I can write real numbers in compare and order equivalent forms as percents, real numbers with and decimals, fractions and using without the number scientific notation. line. Assessment: Chapter 1 Closure (page 33-36) (1 day) + Test (1 day) Additional Topic 1.1 Investigating the Growth of Patterns (1 Day) 1.2.2 More Guess and Check Optional; Lab style activity, gives early introduction to linear and non-linear patterns Math Note: Direct and Inverse Variation Page 24 Math Notes: Multiplication and Division of Integers Page 28 Math Notes: Word Problem Vocabulary (1 day) 1.2.3 More Guess and Check real numbers number line scientific notation (1day) Online supplement M&M Page 19 (1 Day) 2 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Variables and Expressions (Chapter 2 Variables and Proportions) STANDARD A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. ELD Standard Performance Lessons and Objectives Vocabulary I can simplify an expression by combining like terms. Variables Non-commensurate evaluate I can evaluate an expression given values for unknown variables. I can simplify an expression by combining like terms. I can use an expression mat to represent an algebraic expression. Formative Assessment Resources and Pacing 2.1.1 Exploring Variables and Combining Like Terms Notes and Self Reflection Page 42 Math Notes: Non-Commensurate (1 day) Commutative Property of Addition Commutative Property of Multiplication I can write algebraic expressions in equivalent forms. Timeline: 12 Days, 9/19-10/4 Expression mat Reverse Order of operations Evaluate Parentheses Exponents Multiplication Division Addition 2.1.2 Simplifying Expressions by Combining like Terms Page 45 Math Notes: Commutative Properties (1 day) 2.1.3 Writing Algebraic Expressions (1 day) Page 49 Math Notes: Evaluating Expressions and the Order of Operations 3 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A.1.2.F Add, subtract, multiply, and divide polynomials. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor subtraction I can simplify an expression by combining like terms. I can use an expression mat to represent an algebraic expression. I can simplify and compare expressions Associative property of Addition Associative property of Multiplication Identity property of Addition Identity property of Multiplication 2.1.4 Using Zero to Simplify Algebraic Expressions Expression Comparison Mat Combining Like Terms term 2.1.5 Using Algebra Tiles to Simplify Algebraic Expressions Page 53 Math Notes: Associative and Identity Properties (1 day) Page 57 Math Notes: Combining Like Terms (1 day) I can simplify and compare expressions 2.1.6 Using Algebra Tiles to Compare Expressions Page 60 Math Notes: Simplifying an Expression (1 day) 4 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide and combine like terms in polynomials. A.1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A.1.4.A Write and solve linear equations and inequalities in one variable A.1.4.A Write and solve linear equations and inequalities in one variable Grade 7 PE Grade 7 PE I can simplify an expression by combining like terms. 2.1.7 Simplifying and Recording Work I can simplify and compare expressions (1 day) I can solve a one-variable equation. Apply Equation mat solve I can solve a one-variable equation. solution Additive Inverse Prop. Multiplicative Inverse Property reciprocal I can identify and use algebraic properties to decide if statements are true. I can solve a problem using proportional reasoning. Grade 7 PE I can solve a problem using proportional reasoning. Grade 7 PE I can solve a problem using proportional reasoning. Page 65 Math Notes: Solving Problems with Guess and Check 2.1.8 Using Algebra Tiles to Solve for x Page 69 Math Notes: Using an Equation Mat (1 day) 2.1.9 More Solving Equations Page 72 Math Notes: Inverse Properties (1 day) Additional Topic 1.2 Algebra Properties Proportional relationships Fractals Sierpinski Triangle 2.2.1 Solving problems with proportional intuition (1 Day) 2.2.2 Sharing Proportion-Organizing Strategies (1 day) 2.2.3 Using Proportional Relationships (1 day) Optional: not HS PEs Optional: not HS PEs Page 78 Math Notes: Similar Optional: not HS PEs M&M Lab 2-108 Page 82 Math Notes: Fractals Assessment: Chapter Closure p. 84-90 (1 day) + Test (1 day) 5 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Graphs and Equations (Chapter 3 Graphs & Equations) STANDARD A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.1.A Select and justify functions and equations to model and solve problems. A.1.8.A Analyze a problem situation and represent it mathematically. A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.1.A Select and justify functions and equations to model and solve problems. A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.8.A Analyze a ELD Standard Performance Lessons and Objectives Vocabulary I can find and extend a pattern in a table. Extend Connections Generalize Fibonacci sequence Timeline: 13 days, 10/5-10/21 Formative Assessment Resources and Pacing 3.1.1 Extending Patterns and Finding Rules Notes and Self Reflection Page 95 Math Notes: Patterns in Nature (1 Day) I can write an algebraic rule to match a pattern in a table. 3.1.2 Using Tables, Graphs, and Rules to Make Predictions I can use tables, graphs and rules to make predictions. (1 day) I can represent a data pattern with a table, graph and rule. I can write an algebraic rule to match a pattern in a table. I can use tables, graphs and rules to make predictions. discrete continuous 3.1.3 Using the graphing calculator and identifying solutions (1 day) I can represent a data pattern with a table, graph and rule. 3-19 First introduction to graphing calculator Page 102 Math Notes: Discrete and Continuous Relationships 6 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide problem situation and represent it mathematically. A.1.1.A Select and justify functions and equations to model and solve problems. A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.8.A Analyze a problem situation and represent it mathematically. A.1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A1.3.B Represent a I can write an algebraic rule to match a pattern in a table. Parabola vertex I can use tables, graphs and rules to make predictions. 3.1.4 Completing Tables and Drawing Graphs (1 day) I can represent a data pattern with a table, graph and rule. I can make a table and graph for a given rule. Dependent variable Independent variable I understand the important characteristics of a coordinate graph. I can make a table and graph for a given rule. I understand the important characteristics of a coordinate graph. 3.1.5 Graphs, Tables, and Rules Page 110 Math Notes: Independent and Dependent Variables (1 day) y- intercepts x-intercepts 3.1.6 Complete Graphs (1 day) 7 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A1.3.B Represent a function with a symbolic expression as a graph, in a table, and using words, and make connections among these representations. A.1.8.G Synthesize information to draw conclusion, and evaluate the arguments and conclusions of others. A.1.4.A Write and solve linear equations and inequalities in one variable A.1.8.C Evaluate a solution for reasonableness, verify its accuracy A.1.4.A Write and solve linear equations and inequalities in one variable A.1.1.A Select and justify functions and equations to model and solve problems. A.1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. I can make a table and graph for a given rule. 3.1.7 Identifying Common Graph Errors I understand the important characteristics of a coordinate graph. (1 day) I can solve a linear equation algebraically and check to see if the solution is correct. solution 3.2.1 Solving Equations and Testing the Solution Page 119 Math Notes: Complete Graph (1 day) I can determine the number of solutions for a linear equation. 3.2.2 Determining the Number of Solutions I can solve a problem that can be represented by a linear function. (1 day) 3.2.3 Solving Equations to Solve Problems (1 day) 8 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.1.A Select and I can solve a problem that can be justify functions and represented by a linear function. equations to model and solve problems. A.1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A.1.1.A Select and I can collect inversely proportional justify functions and data and present that data with a equations to model graph and a rule. and solve problems. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Assessment: Chapter Closure p. 129-134 (1 day) + Test (1 day) Solution No solution All numbers 3.2.4 More Solving Equations to Solve Problems (1 day) Vary inversely Inversely proportional Direct variation Y varies directly with x Directly proportional Additional Topic 1.3 Modeling Data Math Notes: More on Direct and Inverse Variation (1 day) 9 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Linear Functions (Chapter 4 Multiple Representations) STANDARD A.1.1.A Select and justify functions and equations to model and solve problems. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.1.A Select and justify functions and equations to model and solve problems. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. ELD Standard Performance Lessons and Objectives Vocabulary I can describe the connections between the table, graph and rule for a linear function. Extend Generalize connections Timeline: 10 days, 10/24-11/4 END OF 1st QUARTER Formative Assessment Resources and Pacing Notes and Self Reflection 4.1.1 Finding Connections between Representations Figure 0 is vocabulary used for starting point of pattern (2 days) I can describe the connections between the table, graph and rule for a linear function. 4.1.2 Seeing Growth in Different Representations I can write an equation in slopeintercept form from the table or graph. (1 day) 4-12 creates a web to related different representations of linear patterns 10 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A.1.1.A Select and justify functions and equations to model and solve problems. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. I can describe the connections between the table, graph and rule for a linear function. 4.1.3 Connecting Linear Rules and Graphs I can write an equation in slopeintercept form from the table or graph. (1 day) I can interpret the slope and yintercept of a linear function. 11 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A.1.1.A Select and justify functions and equations to model and solve problems. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A.1.3.B Represent a function with a I can make connections between figure 0 and b and growth factor as m in y=mx+b. constants 4.1.4 y=mx+b (1 day) I can write an equation in slopeintercept form from the table or graph. I can describe the connections between the table, graph and rule for a linear function. I can write an equation in slopeintercept form from the table or 4.1.5 Checking the connections 12 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide symbolic expression, as a graph, in a table, and using words, and make connections among these representations. graph. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two I can describe the connections between the table, graph and rule for a linear function. (2 days) I can identify the slope and yintercept of a linear function given the equation, tables or graph. Reverse Y-intercept 4.1.6 Graphing a line without x y table (1 day) I can identify the slope and yintercept of a linear function given the equation, tables or graph. 4-53 (page 157) Learning Log has students write a stepby-step process for graphing directly from a rule I can graph a linear relationship without creating a table. I can describe the connections between the table, graph and rule for a linear function. Tile Pattern X y table Graph rule 4.1.7 Completing the Web Page 161 Math Notes: Multiple Representations (1 day) I can identify the slope and yintercept of a linear function given the equation, tables or graph. I can graph a linear relationship without creating a table. 13 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide points on the line, and translate between forms of linear equations. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities I can interpret the meaning of the solution to a system of equations. Point of intersection Systems of Equations 4.2.1 Introduction to Systems of Equations I can identify the point of intersection as the solution to the system of equations. (1 day) A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities I can write a system of linear equations to represent a problem situation. 4.2.2 Writing rules from Word Problems A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.1.C Solve I can write a system of linear equations to represent a problem situation. Page 165 Math Notes: Systems of Equations Vocabulary ( 1 day) I can graph a system of linear equations. I can interpret the meaning of the solution to a system of equations. 4.2.3 Solving Systems Algebraically Page 171 Math Notes: Solving a Linear Equation (1 day) I can solve a system of linear equations algebraically. I can interpret the meaning of the solution to a system of equations. I can write a system of linear equations to represent a problem situation. I can solve a system of linear equations algebraically. Linear Equal Values Method 4.2.4 Extending the Web to Other Linear Situations Page 176 Math Notes: The Equal Value Method (2 days) 14 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide problems that can be represented by a I can interpret the meaning of the system of two linear solution to a system of equations. equations or inequalities Assessment: Chapter Closure p. 179-185 (1 day) + Test (1 day) 15 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Simplifying and Solving Equations (Chapter 5 Multiplication & Proportion) STANDARD ELD Standard Performance Timeline: 11 days, 11/7-11/23 Benchmark #1 Test: 11/17 Lessons and Objectives Vocabulary A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A1.2.F Add, subtract, multiply and divide polynomials I can multiply two expressions (representing side lengths) to find an expression representing the total area of a rectangle. Product Sum counterexample I can multiply two expressions (representing side lengths) to find an expression representing the total area of a rectangle. Distributive Property A.1.2.E Use algebraic properties to factor and combine like terms in polynomials. A1.2.F Add, subtract, multiply and divide polynomials. I can multiply two expressions (representing side lengths) to find an expression representing the total area of a rectangle. A1.2.F Add, subtract, multiply and divide polynomials. A1.4.A Write and I can multiply two expressions (representing side lengths) to find an expression representing the total area of a rectangle. Formative Assessment Resources and Pacing 5.1.1 Exploring an Area Model Notes and Self Reflection Page 192 Math Notes: Multiplying Algebraic Expressions with Tiles (1 day) 5.1.2 Multiplying Binomials and the Distributive Property 5-14 (page 194) names process as distributive property (1 day) I can write algebraic expressions in equivalent forms using the distributive property. Generic rectangles 5.1.3 Using Generic Rectangles to Multiply Page 198 Math Notes: The Distributive Property (1 day) I can write algebraic expressions in equivalent forms using the distributive property. 5.1.4 Solving Equations with Multiplication Page 201 Math Notes: Checking a solution 16 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide solve linear equations and inequalities in one variable A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others. A.1.7.D Solve an equation involving several variables by expressing one variable in terms of the others. grade 7 PE (1 day) I can write algebraic expressions in equivalent forms using the distributive property. I can solve equations using the distributive property. I can write algebraic expressions in equivalent forms using the distributive property. I can solve equations using the distributive property. Linear equation Standard form Y=mx+b form Growth factor y-intercept 5.1.5 Working with Multi-Variable equations Page 205 Math Notes: Linear Equations (1 day) I can change an equation from standard form to y = mx +b form. I can solve an equation involving multiple variables for a variable. I can solve an equation involving multiple variables for a variable. grade 7 PE grade 7 PE 5.1.6 Solving Equations without Manipulatives (1 day) Rational numbers closed 5.2.1 Setting up and Solving Proportions 5.2.2 Practice with Proportions Optional section: not HS PEs Optional section: not HS PEs 5.2.3 Applying Page 214 Math Notes: Rational Numbers and Closure Optional section: not 17 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Proportions HS PEs Page 218 Math Notes: Using Generic Rectangles to Multiply Assessment: Chapter Closure p. 220-228 (1 day) + Test (1 day) Core Content: Systems of Linear Equations (Chapter 6) STANDARD ELD Standard Performance A1.4.A Write and solve linear equations and inequalities in one variable I can represent a problem situation with an equation and define what the variables represent. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. I can represent a problem situation with an equation and define what the variables represent. Timeline: 12 Days, 11/28-12/13 Lessons and Objectives Vocabulary Mathematical Sentences Let statement System of equations Formative Assessment Resources and Pacing 6.1.1 Mathematical Sentences Notes and Self Reflection Page 234 Math Notes: Mathematical Sentences (1 day) 6.1.2 Solving Word Problems by Writing Equations (1 day) I can write a system of equations to solve a word problem. I can write a system of equations to solve a word problem. 6.1.3 Solving Problems by Writing Equations (1 day) 18 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities I can solve a system of equations using the substitution method. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. I can solve a system of equations by looking at the intersection point on a graph. 6.2.2 Making Connections: Systems, Solutions, and Graphs I can write a system of equations to solve a word problem. (1 day) A.1.1.C Solve problems that can be represented by a system of two linear equations or substitution method 6.2.1 Solving Systems of Equations Using substitution (1 day) Further guidance is given for 6-43 Page 248 Math Notes: The substitution Method I can interpret the meaning of a solution of system of equations. I can represent a systems of equations with Algebra tiles and solve using the Elimination Method. I can write a system of equations to solve a word problem. I can write a system of equations to solve a word problem. I can multiply both sides of an equation by a numbers to use the elimination method. I can determine which method is most efficient to solve a system of equations. Elimination Method Point of intersection Coincide Solution Solution to the system of equation System of Linear Equations Infinite solutions 6.2.3 Solving Systems Using Elimination Page 252 Math Notes: Systems of Linear Equations Coefficients constants 6.2.4 More Elimination (1 day) Page 255 Math Notes: Coefficients and Constants 6.2.5 Choosing a Strategy to Solve Systems Page 258 Math Notes: Intersection, Parallel, and coincide Plane Intersect Parallel coincide (1 day) 19 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide inequalities A.1.4.D Write and solve systems of two linear equations and inequalities in two variables. A.1.8.A Analyze a problem situation and represent it mathematically. A.1.8.B Select and apply strategies to solve problems. A.1.8.C Evaluate a solution for reasonableness, verify its accuracy and interpret the solution in the context of the original problem. A.1.8.D Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve a specific problem. A.1.8.E Read and interpret diagrams, graphs and text containing the symbols, language and conventions of mathematics. A.1.8.G Synthesize information to draw conclusions and evaluate the Opportunity to review all standards listed above 6.3.1 Pulling it all Together Page 264 Math Notes: Elimination (1-3 days) Reviews content from Chapters 1 through 6 and helps students make connections Could use questions as PAWS course work samples, peer teach, etc. 20 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide arguments and conclusions of others. Assessment: Timeline: 17 Days, Finish by 1/20 End of 1st Semester Finals Week: 1/23-1/27 Core Content: Linear Relationships (Chapter 7) STANDARD ELD Standard Performance Lessons and Objectives Vocabulary A.1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. I can describe how changes in the parameters of a linear function affect the rules, graphs and tables. A.1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. I can draw a line to fit a linear pattern of data. A.1.4.C Identify and interpret the slope and intercepts of a linear function, I can use the graph to find the slope of a linear equation. Formative Assessment Resources and Pacing Notes and Self Reflection 7.1.1 y=mx+b Trend line (EOC uses line that fits the data) 7.1.2 Using Equations to make Predictions Page 279 Math Note: Trend Line Slope Slope triangles Delta x (x) Delta y (y) 7.1.3 Measuring Steepness: An Introduction to Slope page 283 Math Notes: Introduction to Slope I can use an equation and graph to make and justify predictions. 21 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide including equations for parallel and perpendicular lines. Lattice points A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A.1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. I can use the graph to find the slope of a linear equation. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. I can find the slope of a line between two points without using the graph. Positive slope Negative slope 7.1.4 Comparing x and y Page 287 Math Notes: More Solving Systems by Elimination Slope Delta x (x) Delta y (y) Horizontal line Vertical line Slope ratio 7.1.5 More on Slope Page 291 Math Notes: Slope of a line I can use slope information to graph a line. I can identify parallel lines by comparing slopes. Math note gives slope of 0 and undefined slope 22 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A.1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. I can predict how a graph will change based on its slope and yintercept. A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. I can graph a linear equation given word problem. 7.2.3 Rates of Change Page 301 X and Y intercepts A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two I can write an equation given slope and one point on that line. 7.3.1 Finding an equation given slope and one point Further guidance is given in problems 7-80 through 81 I can interpret the meaning of slope and y-intercept in word problems. Y=mx+b form Slope y-intercept slope-intercept form 7.2.1 Equation of a Line in Context 7-53 to 55 require a CBL 7.2.2 Slope as a Measurement of Rate 7-63 requires CBL Page 298 Math Notes: Writing the equation of a line from a graph 7-82 students write equation algebraically 23 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide points on the line, and translate between forms of linear equations. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. without table or graph given slope and a point A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. I can write an equation for a line given its slope and a point on the line. A.1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. I can write an equation for a line given two points on the line. Parallel lines Perpendicular lines Opposite reciprocals 7.3.2 Slopes of Parallel and Perpendicular Lines I can write an equation for a parallel or perpendicular line. I can find the equation a line that fits a linear set of data and use the line to make predictions. Page 308 Math Note: Parallel and Perpendicular 7-93 students have to change from standard form to slopeintercept form 7.3.3 Finding the Equation of a Line through Two Points 7-104 needs graphing calculator; remind students that units can be millions 24 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. A.1.4.B Write and I can write the equation of a line graph an equation for from a graph. a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A.1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. Assessment: Chapter Closure page 317-324 (1 day) + Test (1 day) 7.3.4 Applying y=mx+b to Find Equations from Graphs Check student understanding on graphing calculator knowledge. Core Content: Quadratics (Chapter 8) STANDARD A.1.5.C Solve ELD Standard Performance Page 314 Math Notes: Point-Slope Form of a Line (first and only mention of this; may need additional practice) Timeline: 17 days, 1/31-2/24 Benchmark #2: 2/23 Lessons and Objectives Vocabulary I can rewrite a quadratic equation factoring Formative Assessment Resources and Pacing 8.1.1 Introduction to Notes and Self Reflection Page 329 Math Notes 25 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. in factored form. A.1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A.1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A.1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A.1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. A.1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among I can rewrite a quadratic equation in factored form. factor (ed) reversing generic rectangles quadratic monomial binomial trinomial product sum factoring quadratics (1 day) 8.1.2 Factoring with generic rectangles contain new vocabulary to describe algebraic expressions Page 332 Math Notes contain diagonals of generic rectangles (1 day) I can rewrite a quadratic equation in factored form. standard form 8.1.3 Factoring with special cases Page 335 Math Notes on Standard Form of a Quadratic (1 day) I can rewrite a quadratic equation in factored form. Factored completely Common factor 8.1.4 Factoring Completely Page 338 Math Notes: Factoring Quadratic Expressions (1 day) I can describe characteristics of a parabola given a graph, table and equation. Symmetry vertex 8.2.1 Investigating a parabola Page 342 Math Notes: Symmetry (1 day) I can describe characteristics of a parabola given a graph, table and equation. I can solve a problem represented by a quadratic. Quadratic web x-intercepts roots 8.2.2 Multiple representations of quadratics (1 day) 26 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide the representations. A1.1.D Solve problems that can be represented by quadratic functions and equations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the xintercepts as solutions to a quadratic equation. A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the xintercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. I can identify and interpret the xintercepts and vertex of a parabola. I can sketch the graph of a quadratic using its intercepts. I can find the x-intercepts and yintercept of a parabola by factoring. Root Quadratic equation Zero Product Property 8.2.3 Zero Product Property Page 349 Math Notes: Zero Product Property (1 day) 27 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide A1.1.D Solve problems that can be represented by quadratic functions and equations. A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the xintercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A.1.1.D Solve problems that can be represented by quadratic functions and equations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and I can factor and solve quadratic equations. I can write the quadratic equation given a table. 8.2.4 Solving Quadratic Equations by Factoring 8-79 previews inequality symbols (1 day) I can sketch the graph of a quadratic given the equation. I can match a quadratic graphs to its rule. 8.2.5 Completing the Quadratic Web (1 day) 28 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide interpret the xintercepts as solutions to a quadratic equation. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret solution in the context of the original problem. A.1.1.D Solve problems that can be represented by quadratic functions and equations. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. I can use the quadratic formula to solve quadratic equations. A.1.1.D Solve problems that can be represented by quadratic functions I can use the quadratic formula to solve quadratic equations. roots Quadratic formula Standard form 8.3.1 Introduction to the Quadratic Formula (1 day) I can determine the number of solutions for a quadratic. Zero Product property Quadratic Formula I can solve quadratic equations that are not in standard form. I can choose a strategy that is 8.3.2 More Solving Quadratic Equations Page 358 Math Notes: Deriving the Quadratic Formula. (Students will not have to derive the formula on EOC.) Page 361 Math Notes: Solving a Quadratic Equation (1 day) Zero Product property Quadratic Formula Simplified Irrational number 8.3.3 Choosing a Strategy (1 day) Page 365 Math Notes: Simplifying Square Roots (may need more support and 29 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide and equations. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. more efficient to solve a quadratic equation. Real numbers practice) Assessment: Chapter Closure page 367 to 372 (1 day) + Test (1 day) 30 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Inequalities (Chapter 9) STANDARD A1.4.A Write and solve linear equations and inequalities in one variable. A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.4.D Write and solve systems of two ELD Standard Performance Timeline: 11 Days, 2/27-3/13 Lessons and Objectives Vocabulary I can represent a solution to a one variable inequality on a number line. Formative Assessment Notes and Self Reflection 9.1.1 Solving linear, one-variable inequalities Page 377 Math Notes: Inequality Symbols and directions I can solve a one-variable inequality. 9.1.2 More Solving Inequalities Page 386 Math Notes: Solving One-Variable Inequalities I can write and solve an inequality to solve an application problem. 9.2.1 Graphing twovariable inequalities. I can graph two-variable linear inequalities. 9.2.2 Graphing Linear and Non-Linear inequalities. 9.2.3 Introduction to Absolute Value I can evaluate expressions involving the absolute value operation. Inequality Boundary point Resources and Pacing Absolute value Page 389 Math Notes: Definition of Absolute Value I can create a table and graph for a linear inequality that includes an absolute value operation. I can identify the region on a coordinate plane that represents 9.3.1 Systems of Inequalities Page 393 Math Notes: Graphing Inequalities 31 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide linear equations and inequalities in two variables. the solution set to a system of linear inequalities. A1.4.D Test item specs: students understand the solution set to a system of inequalities is a region of the coordinate plane when the lines are graphed in the same coordinate plane.” I can write and graph a system of linear inequalities to represent and solve an application problem. with Two Variables 9.3.2 More Systems of Inequalities 9.3.3 Applying Inequalities to Solve Problems A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. Assessment: Chapter Closure page 401 to 404 (1 day) + Test (1 day) 32 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Simplifying and Solving (Chapter 10) STANDARD ELD Standard Performance Timeline: 16 Days, 3/14-4/13 Lessons and Objectives Vocabulary A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures. I can simplify algebraic expressions and fractions. A1.8.D Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve specific problems. I can solve an equation with algebraic fractions. A1.8.B Select and apply strategies to solve problems. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. A1.4.A Test item specs: Write and solve linear equations and inequalities including the absolute I can identify the excluded values for a rational expression. (What values for the variable will make the denominator zero in a fraction.) Algebraic fractions Rational expressions Equivalent expressions Equivalent equations Fraction Busters Method Rewriting Looking inside Undoing I can use different approaches to solve a one-variable equation. I can determine the number of solutions and find the solutions to an absolute value equation. I can determine the number of solutions and find the solutions for a quadratic equation in perfect square form. I can express solutions in exact or approximate forms. Perfect square form Exact approximate Formative Assessment Resources and Pacing 10.1.1 Simplifying Expressions 10.1.2 Multiplying and Dividing Rational Expressions. 10.1.3 Solving by Rewriting Notes and Self Reflection Page 410 Math Notes: Multiplicative Identity Property Page 413 Math Notes: Rewriting Rational Expressions 10.1.4 Fraction Busters Page 419 Math Notes: Solving equations with algebraic fractions 10.2.1 Multiple Methods for Solving Equations Page 424 Math Notes: Methods to Solve One Variable Equations 10.2.2 Determining the Number of Solutions Page 427 Math Notes: Perfect square form of a Quadratic 10.2.3 More Solving and an Application Page 430 Math Notes: Solving Absolute Value Equations 10.2.4 Solving Inequalities with Absolute Value 10.2.5 Solving 33 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide value of an expression. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures. I can change a quadratic equation from standard form to perfect square form by using a method called “completing the square”. I can solve an equation in perfect square form. I can apply the laws of exponents to simplify and evaluate expressions. (Laws of Exponents include: Power of a Product, Product of Powers, Quotient of Powers, Power of a Quotient , Zero power, negative exponents) I can rewrite an expression with a fractional exponent as the equivalent square or cube root. Completing the square Standard form Perfect Square form Absolute Value and Quadratic Inequalities 10.3.1 Completing the Square Page 438 Math Notes: Forms of a Quadratic Equation 10.3.2 More Completing the square Exponent Fractional Exponents Square root Cube root Scientific notation Standard form for numbers Base Exponent Laws of exponents 10.4.1 Simplifying Exponential Expressions 10.4.2 Zero and Negative Exponents 10.4.3 Fractional Exponents and Scientific Notation Page 444 Math Notes: Completing the Square Page 448 Math Notes: Inductive and Deductive Reasoning Page 452 Math Notes: Laws of Exponents I can translate between standard form and scientific notation for real numbers. A1.2.A Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line. Test Item Specs: real numbers include scientific notation, exponents and roots. Assessment: Chapter Closure page 454 to 457 (1 day) + Test (1 day) 34 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Core Content: Functions and Relations (Chapter 11) STANDARD A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A.1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b. A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic ELD Standard Performance Timeline: 12 Days, 4/16-5/1 Lessons and Objectives Vocabulary I can describe the graph of a function. I can determine input and output values for a relation. I can determine if a relation is a function. I can determine domain and range for a function. I can identify and describe connections between the rules, tables and graphs of functions. I can describe how changing the values (parameters) of an equation affect the graph. Formative Assessment Resources and Pacing Notes and Self Reflection 11.1.1 Describing a graph. relation inputs outputs f(x) is read “f of x” function function notation domain range asymptote independent variable dependent variable all real numbers 11.1.2 Relation Machines parameters (not in text) 11.1.6 Transformation of a function. Page 473 Math Notes: Relations and Functions 11.1.3 Functions 11.1.4 Domain and Range 11.1.5 Investigating a New Relation 35 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide expressions that involve variables. A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the xintercepts as solutions to a quadratic equation. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A1.4.D Write and solve systems of two linear equations and inequalities in two variables. A1.4.D Test Specs: Solve symbolic problems using a variety of methods (addition, subtraction, substitution) and I can identify the x and y intercepts for a function. I can identify the point(s) of intersection as the solution(s) for a system of equations. Intercept Intersect Intersection 11.2.1 Intercepts and Intersections 11.2.2 Pulling it all together I can solve a system of equations algebraically. 36 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide understand that the solution to a system of equations is given by the coordinates of the intersection. A1.3.A Determine I can identify a relation given clues whether a relationship about its symbolic expression, is a function and graph, and table. identify the domain, range, roots, and I can identify the domain and independent and range of a function. dependent variables. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Assessment: Chapter Closure page 490 to 493 (1 day) + Test (1 day) Core Content: Exponential Functions (UNIT 5 from Core-Plus Course 1) STANDARD A1.1.E Solve problems that can be represented by exponential functions and equations. A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of ELD Standard Lessons and Objectives Performance Vocabulary I can solve problems involving exponential growth or decay. 11.3.1 Relation Treasure Hunt Timeline: 13 Days, 5/2-5/18 3rd Benchmark: 5/24 Formative Assessment Resources and Pacing Notes and Self Reflection *Properties of Exponents reviews/extends material presented in CPM Chapter 10. I can accurately sketch a graph of an exponential function. I can describe how changes in the starting value (a) and growth/decay rate (b) affect the graph of an exponential 37 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide exponents to simplify and evaluate exponential expressions A1.3.B Represent an exponential function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.7.A Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions. A1.7.B Find and approximate solutions to exponential equations. function. I can explain how the starting value (a) and growth/decay rate (b) are found from a table of values for an exponential function. I can write a NOW-NEXT rule and an equation of the form 𝑦 = 𝑎𝑏 𝑥 for exponential functions I can use a table, graph or equation to approximate solutions to an exponential problem situation. I can use and apply properties of exponents to simplify expressions: Products of Powers Power of a Power Powers of Products Power of a Fraction Quotients of Powers Zero Power Negative Exponents Fractional Exponents I can rewrite square roots in least radical form. Assessment: To do… Need to finish Exponential Unit to identify pacing using the Core-Plus Unit 5 materials. 38 Burlington-Edison Revised August 2011 Algebra 1 Daily Learning Guide Still need a Supplemental Unit to address standards A1.6A-E: Data/Distributions (Core-Plus??) Where to fit in A1.7.C?? - Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence. Need to do a thorough Gap Analysis – what standards are missing/incomplete? 39 Burlington-Edison Revised August 2011