First Nine Weeks - Anderson School District Five€¦ · Web viewGCF Color by Number 12 / 6 Review 1 / 0.5 Test 1 / 0.5 Unit 10: Quadratic Graphing (Daily -8 days; A/B - 4 days)

Algebra 1 CP – Curriculum Pacing Guide – 2012-2013

SOUTH CAROLINA ACADEMIC STANDARDS FOR MATHEMATICSThe mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes.Standard EA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.IndicatorsEA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.EA-1.2 Connect algebra with other branches of mathematics.EA-1.3 Apply algebraic methods to solve problems in real-world contexts.EA-1.4 Judge the reasonableness of mathematical solutions.

EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

COMMON CORE STATE STANDARDS FOR MATHEMATICSIndicatorsA-SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.A-SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A-SSE-2 Use the structure of an expression to identify ways to rewrite it.

F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F-5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Anderson School District Five Page 1 Copyright July 1, 2012

Algebra 1 CP – Curriculum Pacing Guide – 2012-2013


Algebra 1 CP – Curriculum Pacing Guide – 2012-2013First Nine Weeks

Unit 1: Essential Algebra Skills (Daily- 9 days; A/B- 5 days)

Indicator Essential Tasks Activities Resources DaysDaily/AB

SC EA-2.1

CCSSN-RN.3

Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Be able to classify and give examples of integers, rational numbers, irrational numbers, whole, and natural numbers.

Review with bellringer daily or weekly.

Real numbers Venn diagram

Identify the Real Numbers Order of Operation Practice

Sheet

2 / 1

SCEA-2.6

Carry out a procedure to evaluate an expression by substituting a value for the variable.

Be able to write expressions and evaluate. Be able to substitute values for one or more variables. Review Order of Operations (PEMDAS).

Expression Bingo Substitute using Literal

Equations

SC EA-2.5

CCSSN-RN.3

Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Be able to recognize and apply commutative, associative, and distributive properties.

Properties Quiz Integers and Like Terms Expression and Property

Jeopardy

2 / 1

Quiz 1 / 0.5



Unit 1: Essential Algebra Skills (Daily- 9 days; A/B- 5 days)


SC EA 2.7

CCSSA-

APR.1

Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

Understand that polynomials form a system analogous to the integers, namely they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Be able to add and subtract polynomial expressions and combine like terms.

Hands on Equations Kit Integers and Like Terms Combining Like Terms

Matching

2 / 1

SCEA-2.9

Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication)

Be able to add and subtract matrices of size no larger than 3 x 3 and multiply matrix by a scalar.

Matrix Activity Matrices Fill In Matrices Fill In Completed

(Answers)

1 / 0.5

SCEA-2.10

Represent applied problems by using matrices.

Be able to distinguish relevant from irrelevant data. Be able to represent data using matrices and understand the meaning of columns and rows in the applied situation.

Unit Test 1 / 1



Unit 2: Solving Linear Equations (Daily- 20 days; A/B- 10 days)


SC EA 4.7

CCSSA-REI.1

CCSSA-REI.3

Carry out procedures to solve linear equations for one variable algebraically

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Use inverse operations to solve linear equations involving one step, two steps, distributive property, variables on both sides, fractional coefficients, decimals and the collecting of like terms. Solve linear equations that result in one solution, no solution or infinitely many.

Equation Frames Equation Bingo Equation Jeopardy Equation Word Problems Distributive Equations Fractions and Decimals –

One Step Equations Solving Equations Review Problem Solving Equations Sums and Consecutive

Integers Word Problems

12 / 6

SCEA-3.8

Apply proportional reasoning to solve problems

Be able to solve proportional equations and use proportional reasoning to solve problems in applied situations, including similar figures.

Proportions Problems Introduction Proportion

Problems 2 / 1

SC EA- 3.7

CCSSA-

CED.4

Carry out a procedure to solve literal equations for a specified variable.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Be able to use inverse operations to solve literal equations for a specified variable that may involve multiple steps.

Literal Equation Manipulative

Substituting and Simplifying Literal Equations 2 / 1

SCEA-2.4

Use dimensional analysis to convert units of measure within a system.

Be able to set up and solve unit conversion problems using unit analysis. Be able to recall conversion

2 /1



Unit 2: Solving Linear Equations (Daily- 20 days; A/B- 10 days)


factors listed in support document.

Review 1 / 0.5

Test 1 / 0.5



Unit 3: Inequalities (Daily- 5 days; A/B- 2.5 days)


SC EA-4.8

CCSSA-REI.3

Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Be able to solve linear inequalities involving one step, two steps, distributive property, variables on both sides, fractional coefficients, decimals and the collecting of like terms. Be able to graph inequalities on a number line.

Graphing Inequalities Nutrition Activity

2 / 1

SC EA- 5.12

CCSSA-

CED.1

Analyze given information to write a linear inequality in one variable that models a given problem situation.

Create equations an inequalities in one variable and use them to solve problems.

Be able to assign a variable, assign restrictions to the variable, and solve an inequality.

2 / 1

Test 1 / 0.5




Algebra 1 CP – Curriculum Pacing Guide – 2012-2013Second Nine Weeks

Unit 4: Functions (Daily- 11 days; A/B- 5 days)


SC EA -3.1

CCSSF-IF.1

CCSS8.F-1

Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Be able to classify a set of ordered pairs in a table, or mapping, as a function or not a function. Be able to use the vertical line test to classify the graph as a function or not a function.

Guess My Rule Function Bridge Function Flow Chart What’s Your Function

Card Game

2 / 1

Quiz 1 / 0.5SC

EA-3.2

CCSSF-IF.2

Use function notation to represent functional relationships.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Be able to use function notation to represent functions given as an equation, graph, or described in words.

Function Web Linear Function

Application Problems

1 / 0.5





SC EA-3.3

CCSSF-IF.2

Carry out a procedure to evaluate a function for a given element in the domain.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Be able to substitute a given value for the independent variable and use the order of operations to evaluate the function for the given element.

Function Notation

1 / 0.5

SC EA -3.4

CCSSF-IF.5

Analyze the graph of a continuous function to determine the domain and range of the function.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Be able to determine and describe the set of x- and y- coordinates using words or mathematical expressions to specify the domain and range of a continuous function.

1 / 0.5

SC EA-3.5

CCSSF-IF.7b

CCSSF-IF.7a

CCSSF-BF.3

Carry out a procedure to graph parent functions (including).Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

Identify the effect on the graph of replacing f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic

Be able to graph parent functions.

Be able to understand how the value of slope affects the steepness and direction of the line. Be able to understand how the value of the y-intercept affects where the line crosses the y-axis.

Algebra Aerobics Transformations Linear Function

Project

2 / 1





expressions for them.

EA 3.6 Classify a variation as either direct or inverse.Be able to understand and classify a variation as inverse or direct.

Direct Variation Practice

Test 1 / 0.5



Unit 5: Writing and Graphing Linear Equations – Part 1 (Daily- 15 days; A/B- 8 days)


SC EA-5.1

CCSSF-IF-7a

Carry out a procedure to graph a line when given the equation of the line.

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Review plotting points. Be able to graph a given equation by making a table and identifying rate of change.

Cookie Cutter Activity Create a Foldable for

Equations of Lines Ski Slope Design 2 / 1

SC EA-5.6

CCSSF-IF.6

Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Be able to find the slope of a line from a table and graph. Be able to find the slope of a line from two points using the formulas for slope.

Linear Function Application Problems

Spaghetti Linear Lab

2 / 1

SC EA-5.7

CCSSS-ID.7

F-IF.6

F-LE.1b

Apply the concept of slope as a rate of change to solve problems.

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Be able to identify and use slope as a rate of change in applied problems.

2 / 1





SC EA-4.1

CCSS8.F-4

Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Be able to find the slope of a line from a graph or table. Be able to recognize and use the slope intercept form of a linear equation.

2 / 1

SC EA-5.3

CCSSF-IF.7a

Carry out a procedure to graph the line with a given slope and a y-intercept.


Be able to use the slope intercept form of a line to identify and plot the y-intercept and use slope to plot additional points of a line. Be able to graph and recognize horizontal and vertical lines.

Using slope-intercept form to graph

Equations Graphs Card Match Game

Stained Glass Activity 1 / 0.5

Quiz 1 / 0.5





SCEA-4.2

CCSS8.F-4

SC EA-5.4

CCSSF-IF.7a

Carry out a procedure to write an equation of a line with a given slope passing through a given point.


Carry out a procedure to graph the line with a given slope passing through a given point.


Be able to write the equation of a line in slope intercept form and point-slope form given the slope and one point.

Be able to plot a point and use the slope to determine additional points. Be able to graph a line using slope intercept form and point-slope form.

2 / 1

SC EA-4.3

CCSS8.F-4

Carry out a procedure to write an equation of a line passing through two given points

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it

Be able to find the slope of a line given two points and write the equation of a line in slope intercept form or point-slope form.

2 / 1





models, and in terms of its graph or a table of values.

Review and Test 1 / 0.5





SC EA-4.6

CCSS8.F-4

Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).


Be able to write the equation of a line in standard form. Be able to use algebraic techniques to translate linear equations from one form to another. (standard, point-slope, slope-intercept)

4 / 2

SC EA-5.5

CCSSS-ID-7

Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Be able to recognize the x and y-intercepts as the points where a line intersects each axis and recognize the x and y-intercepts from a table of values. Be able to substitute zero for x or y to find the y or x- intercept.

2 / 1

SCEA-5.8

Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.

Be able to know the relationship between the slopes of parallel and perpendicular lines. It is not essential for students to write the equation of these lines at this time.

Parallel and Perpendicular Race

2 / 1





SC EA-5.9

CCSSA-

CED.2

Analyze given information to write a linear function that models a given problem situation

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Be able to recognize a linear relationship from a word problem. Be able to assign variables and write the linear equation for the applied problem.

1 / 0.5

SCEA-5.10

Analyze given information to determine the domain and range of a linear function in a problem situation.

Be able to determine the domain and range within an applied problem. Be able to specify between continuous and non-continuous domains.

1 / 0.5

SC EA-4.4

CCSSS-ID.6c

SC EA 4.5

CCSSS-ID.6a

CCSS8.SP-3

Use a procedure to write an equation of a trend line from a given scatterplot.

Fit a linear function for a scatter plot that suggests a linear association.

Analyze a scatterplot to make predictions.

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

Use the equation of a linear model to

Be able to graph a scatter plot and recognize the correlation of the data. Be able to write an equation of a trend line.

Be able to use the concept of slope as a rate of change to make predictions. Be able to determine the meaning of the slope, y-intercept, and coordinates in a contextual problem. Be able to determine which axis represents the independent and dependent variables.

Bucket Brigade Tying Knots

2 / 1





solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Review 1 / 0.5

Test 1 / 0.5




Algebra 1 CP – Curriculum Pacing Guide – 2012-2013Third Nine Weeks

Unit 7: Systems of Equations (Daily - 10 days; A/B - 5 days)


SC EA-4.9

CCSSA-REI.5

CCSSA-REI.6

CCSS8.EE-8a

CCSS8.EE-8b

Carry out a procedure to solve systems of two linear equations graphically.

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Be able to determine the point of intersection of the graph of the two linear equations. Be able to graphically recognize and understand when a system has exactly one solution (consistent and independent), infinitely many solutions (consistent and dependent) or no solution (inconsistent).

Carnegie Investigation Graphing Systems

PowerPoint

2 / 1





SC EA-4.10

CCSSA-REI.5

CCSSA-REI.6

CCSS8.EE-8a

CCSS8.EE-8b

Carry out a procedure to solve systems of two linear equations algebraically.

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Be able to apply the substitution and elimination method to solve a system.Be able to algebraically recognize and understand when a system has exactly one solution (consistent and independent), infinitely many solutions (consistent and dependent) or no solution (inconsistent).

System Worksheets Fund Raiser Activity Game Memory Systems of

Equations

4 / 2





SC EA-5.11

CCSSA-

CED.3

CCSS8.EE-8c

Analyze given information to write a system of linear equations that models a given problem situation

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Be able to write a system of linear equations given two linear relationships between two variables.

Systems short response System word problems Systems Trashketball

2 / 1

Review 1 / 0.5

Test 1 / 0.5



Unit 8: Laws of Exponents (Daily – 20 days; A/B - 10 days)


EA-2.2 Apply the laws of exponents and roots to solve problems

Be able to evaluate and simplify expressions using the laws of exponents.

6 / 3

EA-2.3Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

Be able to carry out a procedure to multiply and divide numbers written in scientific notation.

2 / 1

SC EA-2.7

CCSSA-APR-

1

Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

Understand that polynomials form a system analogous to the integers, namely they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Be able to add, subtract, and/or multiply polynomial expressions. Be able to divide a polynomial by a monomial.

Write polynomials in standard form, naming by degree and number of terms.

Polynomial Bullseye Mix and Match Polynomials Matching Polynomials

Algebra Tiles

6 / 3

EA-2.2 Apply the laws of exponents and roots to solve problems.

Simplify rational expressions containing integers including Pythagorean Theorem.

Exponent Bingo4 / 2

Review 1 / 0.5

Test 1 / 0.5



Unit 9: Factoring (Daily - 14 days; A/B - 7 days)


SC EA-2.8

CCSSA-

SSE.1a

A-SSE.1b

A-SSE.2

Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Use the structure of an expression to identify ways to rewrite it.

Be able recognize greatest common factors. Be able to factor quadratic trinomials by using difference of squares, trial-and-error method, or another suitable method.

Jeopardy Factor Review Factor Dominoes GCF Color by Number

12 / 6

Review 1 / 0.5

Test 1 / 0.5


Algebra 1 CP – Curriculum Pacing Guide – 2012-2013Fourth Nine Weeks

Unit 10: Quadratic Graphing (Daily -8 days; A/B - 4 days)


SCEA-5.2

Graph linear and quadratic functions and show intercepts, maxima, and minima. Axis of Symmetry

x = -b/2a 4 / 2

SC EA-6.1

CCSSF-BF.3

Analyze the effects of changing the leading coefficient a on the graph of

Identify the effect on the graph of replacingf(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Be able to determine the graphical effect of changing the sign and magnitude of the leading coefficient (y = ax2).

Transformations with Functions PowerPoint

Transformation PowerPoint

1 / 0.5

SC EA-6.2

CCSSF-BF.3

Analyze the effects of changing the constant c on the graph of .

Identify the effect on the graph of replacing f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Be able to determine the graphical effect of increasing or decreasing the constant (y = ax2 + c).

1 / 0.5

Review 1 / 0.5



Unit 10: Quadratic Graphing (Daily -8 days; A/B - 4 days)


Test 1 / 0.5



Unit 11: Quadratics and Factoring (Daily - 12 days; A/B – 6 days)


SC EA-6.4

CCSSA-

SSE.3a

A-REI-4b

Carry out a procedure to solve quadratic equations by factoring.

Factor a quadratic expression to reveal the zeros of the function it defines.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Be able to put a quadratic equation in

form and solve using factoring.

2 / 1

SCEA-6.3

CCSSF-IF.7a

Analyze the graph of a quadratic function to determine its equation.


Be able to associate the features of a graph with the lead coefficient or constant tem of equation. Be able to associate the x-intercepts of the graph with the factored form of the equation.

2 / 1

SCEA-6.5

CCSSF-IF-7a

Carry out a graphic procedure to approximate the solutions of quadratic equations.


Be able to graph a quadratic function and estimate the zeros from the graph.

2 / 1



Unit 11: Quadratics and Factoring (Daily - 12 days; A/B – 6 days)


EA-6.6Analyze given information to determine the domain of a quadratic function in a problem situation.

Be able to determine the meaningful domain of a quadratic function for an applied problem (may require finding the zeros of a quadratic function).

2 / 1

Application of Quadratics

Chutes and Ladders Review for Quadratics

Golf Ball Toss Hole in Bottle

Quadratics Pass the Ball Activity Quadratic Project

2 / 1

Review 1 / 0.5

Test 1 / 0.5


Documents

First Nine Weeks - Anderson School District Five€¦ · Web viewGCF Color by Number 12 / 6 Review 1 / 0.5 Test 1 / 0.5 Unit 10: Quadratic Graphing (Daily -8 days; A/B - 4 days)