ALGEBRA 1 · 2010. 12. 7. · 1.1 Write and evaluate a variable expression. 2 1.2 Evaluate expressions containing exponents. 1 Necessary though not specifically addressed by P.E.’s

1 Updated: Thursday, December 02, 2010

Mathematics Curricular Guide

ALGEBRA 1

2010-2011 SCHOOL YEAR

Pasco School District Algebra 1 2010 – 2011 School Year


MATHEMATICS SCOPE & SEQUENCE

Unit Title Dates Page 1. Connections to Algebra (Ch 1) ................................................................................................................................................. 3

2. Properties of Real Numbers (Ch 2) ........................................................................................................................................... 4

3. Solving & Graphing Linear Equations and Inequalities (Ch 3, 6) ............................................................................................... 5

4. Graphing Linear Equations and Functions (Ch 4) ...................................................................................................................... 7

5. Writing Linear Equations (Ch 5) ............................................................................................................................................... 9

6. Unit Six ................................................................................................................................................................................... 11

7. Systems of Linear Equations and Inequalities (Ch 7) .............................................................................................................. 12

8. Exponents and Exponential Functions (Ch 8) ......................................................................................................................... 13

9. Quadratic Equations and Functions (Ch 9) ............................................................................................................................. 15

10. Polynomials and Factoring (Ch 10) ......................................................................................................................................... 17

11. Rational Equations and Functions (Ch 11) .............................................................................................................................. 18

12. Unit Twelve ............................................................................................................................................................................ 19



Unit Name: Connections to Algebra (Ch 1) [Starting Date] [Ending Date]

Standard Lesson & objective Days Formative Assessments/

Assignments Alignment Notes

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.

1.1 Write and evaluate a variable expression.

2

1.2 Evaluate expressions containing exponents.

1 Necessary though not specifically addressed by P.E.’s.

1.3 Use the order of operations to evaluate algebraic expressions.


A1.1.A Select and justify functions and equations to model and solve problems.

1.5 Translate verbal phrases into algebraic expressions. Model and solve a real-life problem.

2

A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.

1.7 Identify a function and make an input-output table for a function.

2

Process Standards Addressed:

A1.8.A Analyze a problem situation and represent it mathematically.

A1.8.B Select and apply strategies to solve problems

A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem

A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.

A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others.

A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.

Assessment: (type)



Unit Name: Properties of Real Numbers (Ch 2) [Starting Date] [Ending Date]



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.

2.1 Graph and compare real numbers using a number line.

1

2.2 Addition of real numbers.

1

2.3 Subtract real numbers. 1

2.5 Multiply real numbers. 1 Necessary though not specifically addressed by P.E.’s.

2.6 Use the distributive property. Simplify by combing like terms.


2.7 Divide real numbers and use division to simplify algebraic expressions.




Assessment: (type)



Unit Name: Solving & Graphing Linear Equations and Inequalities (Ch 3, 6)

[Starting Date] [Ending Date]



A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.4.A Write and solve linear equations and inequalities in one variable.

3.1 Solve linear equations using addition and subtraction.

2

3.2 Solve linear equations using multiplication and division.

2

3.3 Solve multi-step equations.

2

3.4 Solve equations with variables on both sides of the equal sign.

2

3.5 Problem solving with linear equations.

2

A1.4.A Write and solve linear equations and inequalities in one variable.

3.6 Find exact and approximate solutions of equations that contain decimals.

1

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. A1.3.C Evaluate f(x) at a (i.e. f(a)) and solve for x in the equation f(x)=b. A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others.

3.7 Solve a formula for one of its variables. Rewrite an equation in function form.

2


6.1 Graph linear inequalities in one variable. Solve one step linear inequalities.

1






6.2 Solve multi-step linear inequalities.

2


6.3 Write, solve, and graph compound inequalities

2

A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. A1.6.B Make valid inferences and draw conclusions based on data.

6.6 Make and use a stem-and-leaf plot to put data in order. Find the mean, median, and mode of data.

3 Need to include reference on the spread of data (range, standard deviation).

A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. A1.6.B Make valid inferences and draw conclusions based on data.

6.7 Draw a box-and-whisker plot to organize real-life data. Read and interpret a box-and-whisker plot of real-life data.

3

Process Standards Addressed: A1.8.A Analyze a problem situation and represent it mathematically.



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 a

specific problem.


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.

Assessment: (type)



Unit Name: Graphing Linear Equations and Functions (Ch 4)




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. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.

4.1 Plot points in a coordinate plane. Draw a scatter plot and make predictions about real-life situations.

2 Emphasize use and interpretation of scatter plots.

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. 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.

4.2 Graphing a linear equation. Graph horizontal and vertical lines.

2

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. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

4.3 Find the intercepts of the graph of a linear equation. Use the intercepts to make a quick graph of a linear equation.

2

A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

4.4 Find the slope of a line using two of its points. Interpret slope as a rate of change in real-life situations.

2 Use geometry text 3.6 & 3.7 to address parallel and perpendicular

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. 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.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a

4.5 Write linear equations that represent direct variation. Use a ratio to write an equation for direct variation.

2



linear expression affect their graphs and the relationships they represent.



A1.4.B Write and graph an equation for a line given the slope and y-intercept, the slope and a point on the line, or two points on the line and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

4.6 Graph a linear equation in slope-intercept form. Graph and interpret equations in slope-intercept form that model real-life situations.

2

A1.3.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. A1.3.C Evaluate f(x) at a (i.e. f(a)) and solve for x in the equation f(x)=b.

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.

4.8 Define and identify functions and relations. Determine the difference between a function and a relation using the vertical line test and Input/output tables. Evaluate functions.

2 A1.7.C needs much more support than the book currently offers.






specific problem.




Assessment: (type)



Unit Name: Writing Linear Equations (Ch 5) [Starting Date] [Ending Date]



A1.4.B Write and graph an equation for a line given the slope and y-intercept, the slope and a point on the line, or two points on the line and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. 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.

5.1 Use slope-intercept form to write the equation of a line. Model real-life situation with a linear function.

2 More emphasis changing parameters (see 23-25).

A1.4.B Write and graph an equation for a line given the slope and y-intercept, the slope and a point on the line, or two points on the line and translate between forms of linear equations.

5.2 Use slope and any point on a line to write an equation of the line.

2


5.3 Write an equation of a line given two points on the line.

2

A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. 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. A1.6.E Describe the correlation of data in scatter plots in terms of strong or weak and positive or negative.

5.4 Find a linear equation that approximates a set of data points. Determine whether there is a positive or negative correlation in a set of real-life data.

3 Introduce the terms independent variables and dependent variables






5.5 Use point-slope form to write an equation of a line. Use point-slope form to model a real-life situation.

2


5.6 Write a linear equation in standard form. Use the standard form of an equation to model real-life situations.

2

A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent 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.

5.7 Determine whether a linear model is appropriate. Use a linear model to make a real-life prediction.

2





specific problem.




Assessment: (type)



Unit Name: Unit Six [Starting Date] [Ending Date]



A1.4.A Write and solve linear equations and inequalities in one variable.

6.4 Solve absolute-value equations. Solve absolute-value inequalities.

2

A1.6.C Describe how linear transformations affect the center and spread of univariate data.

1 MCAT/Leadership Team developed activities to meet this P.E.






specific problem.



Assessment: (type)



Unit Name: Systems of Linear Equations and Inequalities (Ch 7)




A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities A1.4.D Write and solve systems of two linear equations and inequalities in two variables

7.1 Solve a system of linear equations by graphing. Model a real-life problem using a linear system.

2


7.2 Use substitution to solve a linear system. Model a real-life situation using a linear system.

2


7.3 Use linear combinations to solve a system of linear equations. Model a real-life problem using a system of linear equations.

2


7.4 Choose the best method to solve a system of linear equations. Model real-life problems using a linear system.

2


7.5 Identify how many solutions a linear system has. Model real-life problems using a linear system.

2


7.6 Solve a system of linear inequalities by graphing. Use a system of linear inequalities to model a real-life situation.

2





specific problem.

Assessment: (type)



Unit Name: Exponents and Exponential Functions (Ch 8)




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

8.1 Use properties of exponents to multiply exponential expressions.

2 Use story problems to emphasize interpretation.

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 A1.7.A Sketch the graph for an exponential function of the form 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 exponential equations

8.2 Evaluate powers that have zero and negative exponents. Graph exponential functions.

2

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 exponents to simplify and evaluate exponential expressions

8.3 Use the division property of exponents to evaluate powers and simplify expressions.

2

A1.1.E Solve problems that can be represented by exponential functions and equations A1.7.A Sketch the graph for an exponential function of the form 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

8.5 Write and use models for exponential growth. Graph models for exponential growth.

2 Emphasize the effects of changing parameters.





A1.1.E Solve problems that can be represented by exponential functions and equations A1.7.A Sketch the graph for an exponential function of the form 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

8.6 Write and use models for exponential decay. Graph models for exponential decay.

2 Emphasize the effects of changing parameters.





specific problem.


Assessment: (type)



Unit Name: Quadratic Equations and Functions (Ch 9)




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

9.1 Evaluate and approximate square roots. Solve a quadratic equation by finding square roots.

2

A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula

9.2 Use properties of radicals to simplify radicals. Use quadratic equations to model real life problems.

2

A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. 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 x-intercepts as solutions to a quadratic equation

9.3 Sketch the graph of a quadratic function.

3

A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. 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 x-intercepts as solutions to a quadratic equation

9.4 Solve a quadratic equation graphically.

2

A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A1.1.D Solve problems that can be represented by quadratic functions and equations A1.5.D Solve quadratic equations that have real roots by

9.5 Use the quadratic formula to solve a quadratic equation. Use quadratic models in real-life settings.

2



completing the square and by using the quadratic formula





specific problem.




Assessment: (type)



Unit Name: Polynomials and Factoring (Ch 10) [Starting Date] [Ending Date]



A1.2.E Use algebraic properties to factor and combine like terms in polynomials A1.2.F Add, subtract, multiply, and divide polynomials

10.1 Add and subtract polynomials.

1


10.2 Multiply polynomials 2


10.3 Multiplying special polynomials.

1

A1.5.C Solve quadratic equations that can be factored as (ax+b)(cx+d) where a, b, c, and d are integers

10.4 Solve polynomial equations that are already factored.

2

A1.2.E Use algebraic properties to factor and combine like terms in polynomials

10.5 Factor a quadratic expression in the form

2

A1.2.E Use algebraic properties to factor and combine like terms in polynomials A1.5.C Solve quadratic equations that can be factored as (ax+b)(cx+d) where a, b, c, and d are integers

10.6 Factor a quadratic expression in the form

2


10.7 Use special product patterns to factor polynomials. Solve quadratic equations by factoring.

2


10.8 Use the distributive property to factor a polynomial. Solve polynomial equations by factoring.

2




specific problem.

Assessment: (type)



Unit Name: Rational Equations and Functions (Ch 11)




A1.2.F Add, subtract, multiply, and divide polynomials

11.4 Simplifying rational expressions (in preparation for 11.7)

2

11.5 Multiply and divide rational expressions (in preparation for 11.7)

2

A1.2.F Add, subtract, multiply, and divide polynomials

11.7 Divide polynomials. 2



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 a specific problem.

Assessment: (type)



Unit Name: Unit Twelve [Starting Date] [Ending Date]



A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula 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 x-intercepts as solutions to a quadratic equation

12.4 Solving quadratic equations that have real roots by completing the square.

2 Introduce vertex form. See #77-79 for examples.

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.

2 See chapter 11 in McDougall-Littell Algebra 2 curriculum. Geometry Chapter 1 and worksheets.





specific problem.



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.

Assessment: (type)

Documents

ALGEBRA 1 · 2010. 12. 7. · 1.1 Write and evaluate a variable expression. 2 1.2 Evaluate expressions containing exponents. 1 Necessary though not specifically addressed by P.E.’s