ALGEBRA (CreatedI 2014) Amherst County Public Schools

ALGEBRA I (Created 2014)

Amherst County Public Schools

The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students should learn. Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for each standard. The Curriculum Framework is divided into two columns: Essential Understandings and Essential Knowledge and Skills. The purpose of each column is explained below. The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.

Virginia Department of Education (http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/)

Textbook Overview Course Text: Algebra I, Holt McDougal, 2012

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/

Suggested Sequence of Instruction and Pacing

First Nine Weeks

SOL Chapter/Sections/Topic Time Frame (Tentative)

Pre-Requisite Skills Numbers / Number Sense 2 Days

A.1 Verbal Expressions 3 Days

A.1, A.4b, A.5b Properties, Simplifying Expressions 8 Days

A.4d Solving Equations 10 Days

A.5a Solving Inequalities 3 Days

A.4a Literal Equations 3 Days

A.4f, A.5c Word Problems 4 Days

A.4a Linear Equations (solving for y)* 3 Days

A.7b Graphing Point on Coordinate Plane/Domain and Range* 3 Days

Review/Testing 6-8 Days

45 Days

*Due to threat of inclement weather, linear equations (solving for y), graphing points, and domain and range should be covered in the first nine weeks, but will be assessed on the 2nd Nine Weeks.

Second Nine Weeks


A.7 Functions 3-4 Days

A.7 (e) Graphing Lines from a Table 4 Days

A.6 (a) Slope 4-5 Days

A.6 (a) Graphing Lines from Slope and Intercept 4 Days

A.6 (b) Writing the Equation of a Line 5 Days

A.8 Direct & Inverse Variation 3 Days

A.6 (a,b) Linear Inequalities 4 Days

A.4 (e) Systems of Equations, Intro and Solve by Graphing # 4 Days

A.4 (e) Systems of Equations by Substitution # 4 Days

Review and Testing 8 Days

45 Days

# = Because of typical inclement weather in the third nine weeks, these items will be presented in the 2nd nine weeks but tested in the 3rd.

Third Nine Weeks


A.4 (e) Systems of Equations by Elimination 6-7 Days

A.5 (d) Systems of Inequalities 4 Days

A.2 (a) Exponent Rules 10 Days

A.2 (b) Operations with Polynomials 10 Days

A.2 (c) Factoring numbers, expressions of the form x2 + bx + c 3 Days

Review / Testing 4-6 Days

(less total days because of typical inclement weather during this time) 40 Days

Fourth Nine Weeks


A.2 (c) Factoring Expression of the form ax2 + bx + c 5 days

A.3 Simplifying Square Roots and Cube Roots 4 – 6 days

A.4 (c) Quadratic Equations 5 – 7 days

A.9, A.10, A.11 Statistics 7 – 10 days

Practice SOL Exam (Most Recent Released Exam) 2 Days

Review for SOL Exam 7 - 10 Days

Remediation / Extra Topics as Determined by Teacher 5 - 8 Days

45 Days

First Nine Weeks Instruction

SOL Covered Textbook Chapter and Section

Resources Essential Questions / Skills Vocabulary

1.2, 1.3, 1.4, 1.5, 1.6

Glencoe Student Workbook Sec. 1-2

Rational number Integer All Real Numbers Order of Operations

A.1 The student will represent verbal quantitative situations algebraically

1.1 Glencoe Student Workbook Sec 1-1

Write the following verbal expression as algebraic. Write the following algebraic expression as verbal.

Expression Quantitative Representation Absolute value Variable

A.1 …and evaluate these expressions for given replacement values of the variables.

Glencoe Student Workbook Sec 1-5

What is the value of the following expression when…? Find the value of three more than twice a number when the number is 2.

Replacement value Square root Cube root

A.4 (b) The student will solve multistep linear and quadratic equations in two variables, including justifying steps used

1.7 Glencoe Student Workbook Sec 1-3

Name each property used to simplify the expression. Which property is shown from line 3 to

Associative Property Commutative Property Distributive Property



in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets

line 4? Name each property used to solve the equation. Simplify the Expression Which expression is in simplified form?

Equality Properties Identity Properties Inverse Properties Simplify Combine Like Terms

A.5 (b) The student will solve multistep linear inequalities in two variables, including justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;

What would be the next line if the Division Property of Inequality is used?

Division Property of Inequality

A.4 (d) The student will solve multistep linear and quadratic equations in two variables, including solving multistep linear equations algebraically and graphically

2-1, 2-2, 2-3, 2-4, 2-7

Glencoe Student Workbook Sec 2-2, 2-3, and 2-4

Find the solution to the equation. Which is the solution for…?

Solve Solution

A.5 (a) The student will solve multistep linear inequalities in two variables, including solving multistep linear

3-2, 3-3, 3-4, 3-5

Glencoe Student Workbook Sec 5-1, 5-2, and 5-3

Find the solution to the inequality. Which is the solution for…?

Inequality Linear Inequality



inequalities algebraically and graphically;

A.4 (a) The student will solve multistep linear and quadratic equations in two variables, including solving literal equations (formulas) for a given variable

2-5 Glencoe Workbook Sec 2-8

Solve the equation for ____. Rewrite the following formula in terms of ____.

Literal Formula

A.4 (f) The student will solve multistep linear and quadratic equations in two variables, including solving real-world problems involving equations and systems of equations.

2-1, 2-2, 2-3, 2-4, and 2-7

Glencoe Workbook Sec 2-2, 2-3, and 2-4 Teacher created materials

A.5 (c) The student will solve multistep linear inequalities in two variables, including solving real-world problems involving inequalities;

3-2, 3-3, 3-4, and 3-5

Glencoe Workbook Sec 5-1, 5-2, and 5-3



A.4 (a) The student will solve multistep linear and quadratic equations in two variables, including solving literal equations (formulas) for a given variable

Solving for 𝑦 Teacher created materials and Infinite Algebra Software.

Solve for y Put the equation into slope-intercept form.

Slope – Intercept Form

A.7 (b) The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including domain and range.

4-1 and 4-2 Glencoe Workbook Sec 1-6

What is the domain/range of the function? Given the domain x={….}, find the range of the function….

Domain Range Dependent variable Independent variable

Second Nine Weeks Instruction



A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically

4-3 Glencoe Workbook Sec 1-7 and 3-1

Which is/is not a function? Given f(x), find f(n).

Function Function notation

A.7 (e) The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including finding the values of a function for elements in its domain

4-4 Glencoe Workbook Sec 1-7 and 3-1

Graph the function using a table. Given the following domain, find the range to draw the line. Plot three points that would lie on the function y = …..

Table of values

A.6 (a) The student will graph linear equations and linear inequalities in two variables, including determining the

5-3 and 5-4 Glencoe Workbook Sec 3-3

Find the slope of the line. Which graph(s) have positive/negative/zero/undefined

Slope Rise over Run Rate of Change



slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined

slope(s) Given the slope m = a/b, which point would lie on the line with (x, y)

Change in y over Change in x Undefined slope Positive/negative slope

A.6 (a) The student will graph linear equations and linear inequalities in two variables, including determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined

Use the slope and y-intercept to graph the line…. Which line shows y = …… Which line has a slope of ____ and goes through the point (0, y)?

y-intercept

A.6 (b) The student will graph linear equations and linear inequalities in two variables, including writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

Write the equation of the line that goes through (x, y) and has a slope of m = -a/b. Write the equation of the line that contains the points (x1, y1) and (x2, y2)

Slope – intercept form Point – slope form



A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

A.6 (a, b) The student will graph linear equations and linear inequalities in two variables, including determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined and writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

Which graph has the correct region shaded? Graph the following inequality.

Dashed line greater than, less than Solid line greater/less than or equal to



A.4 (e) The student will solve multistep linear and quadratic equations in two variables, including solving systems of two linear equations in two variables algebraically and graphically

Find the solution to the system of equations by graphing them.

System of Equations Point of Intersection No Solution Infinite Solutions


Use substitution to find the solution to the system of equations

Third Nine Weeks Instruction




Use elimination to find the solution to the system of equations.

A.5 (d) The student will solve multistep linear inequalities in two variables, including solving systems of inequalities

Find the solution to the system of inequalities. Shade the region that contains the solutions to the system of inequalities.

A.2 (a) The student will perform operations on polynomials, including applying the laws of exponents to perform operations on expressions;

Simplify the expression. Which is equivalent to….?

Multiplication Rule Division Rule Power Rule Negative Exponent

A.2 (b) The student will perform operations on polynomials, including adding, subtracting, multiplying, and dividing polynomials

Which is the (sum/difference/ product/quotient) of ______ and ______?

Monomial Polynomial Binomial Trinomial



FOIL Difference of Squares Perfect Square Trinomial

A.2 (c) The student will perform operations on polynomials, including factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations

Factor completely. Find all of the factors of ________.

Fourth Nine Weeks Instruction



A.2 (c) The student will perform operations on polynomials, including factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations

Factor completely. Find all of the factors of ________.

Greatest Common Factor

A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.

Which is the simplified form of ______? Find the simplest form of…..

Simplest radical form Simplified Cube Root



A.4 (c) The student will solve multistep linear and quadratic equations in two variables, including solving quadratic equations algebraically and graphically

Find the solution(s) for the equation…

Quadratic Equation Roots Zeros Solutions x-intercepts Vertex

A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores

Find the mean/variance/standard deviation/mean absolute deviation for the following set of data. Which data set is the most varied? Which person did better relative to their own class?

Mean Standard deviation Variance Mean Absolute Deviation z-score Standardize

A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots

Which group has a smallest/largest median/IQR/range/lower quartile/upper quartile? If the point (x) were added to the data set, what would happen to the

Interquartile range Minimum Value Lower Quartile Median Upper Quartile



median/IQR/…? Maximum Value Range

A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions

Find the line or curve of best fit using the calculator. Use your line/curve to estimate the value of y when given some x.

Line of Best Fit Curve of Best Fit Predict Estimate

Instructional Example Questions

A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

A.2 The student will perform operations on polynomials, including

a) applying the laws of exponents to perform operations on expressions


b) adding, subtracting, multiplying, and dividing polynomials


c) factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for

confirming algebraic factorizations.

A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form

A.4 The student will solve multistep linear and quadratic equations in two variables, including

a) solving literal equations (formulas) for a given variable;


b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and

its subsets


c) solving quadratic equations algebraically and graphically


d) solving multistep linear equations algebraically and graphically;


e) solving systems of two linear equations in two variables algebraically and graphically;


f) solving real-world problems involving equations and systems of equations

A.5 The student will solve multistep linear inequalities in two variables, including

a) solving multistep linear inequalities algebraically and graphically


b) justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets


c) solving real-world problems involving inequalities


d) solving systems of inequalities

A.6 The student will graph linear equations and linear inequalities in two variables, including

a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and

will be positive, negative, zero, or undefined

A.6 The student will graph linear equations and linear inequalities in two variables, including

b) writing the equation of a line when given the graph of the line, two points on the line, or the

slope and a point on the line

Write the equation of the line for each example.

A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including

a) determining whether a relation is a function


b) domain and range;


c) zeros of a function;


d) x- and y-intercepts;


e) finding the values of a function for elements in its domain;


f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic

A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct

variation algebraically and graphically and an inverse variation algebraically

A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-

scores

A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots

A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using

mathematical models. Mathematical models will include linear and quadratic functions

Additional Instructional Resources

http://www.corealgebra1.com/

http://www.glencoe.com/sites/virginia/teacher/mathematics/index.html

http://teachers.henrico.k12.va.us/math/hcpsalgebra1/solreview.htm

http://teachers.henrico.k12.va.us/math/hcpsalgebra1/modules.html

http://www.corealgebra1.com/

http://www.glencoe.com/sites/virginia/teacher/mathematics/index.html

http://teachers.henrico.k12.va.us/math/hcpsalgebra1/solreview.htm

http://teachers.henrico.k12.va.us/math/hcpsalgebra1/modules.html

Documents

ALGEBRA (CreatedI 2014) Amherst County Public Schools