algebra i - amherst.k12.va.us · pdf filethe 2009 mathematics standards of learning curriculum...
TRANSCRIPT
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
Suggested Sequence of Instruction and Pacing
First Nine Weeks SOL Chapter/Sections/Topic Time Frame (Tentative)
Prerequisite Skills Numbers / Number Sense 2 Days
A.1 Verbal Expressions 3 Days
A.1, A.4b, A.5b A.4b – Justify steps used in simplifying expressions and solving equations. [Moved to A.4a,b EKS] A.5b – Justify steps used in solving inequalities. [Moved to A.5a EKS]
Properties, Simplifying Expressions 8 Days
A.4d A.4d – [Moved to A.4a]
Solving Equations 10 Days
A.5a Solving Inequalities 3 Days
A.4a A.4a – [Moved to A.4c]
Literal Equations 3 Days
A.4f, A.5c A.4f – [Moved to A.4e]
Word Problems 4 Days
A.4a A.4a – [Moved to A.4c]
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
SOL Chapter/Sections/Topic Time Frame (Tentative)
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) A.6 – Graph linear equations [Moved to A.6c]
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) A.6 – Graph linear inequalities [Moved to A.5b]
Linear Inequalities 4 Days
A.4 (e) A.4e – [Moved to A.4d]
Systems of Equations, Intro and Solve by Graphing # 4 Days
A.4 (e) A.4e – [Moved to A.4d]
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
SOL Chapter/Sections/Topic Time Frame (Tentative)
A.4 (e) A.4e – [Moved to Systems of Equations by Elimination 6-7 Days
A.4d]
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
SOL Chapter/Sections/Topic Time Frame (Tentative)
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 © A.4c – [Moved to A.4b] A.4 EKS – Identify roots or zeros of a quadratic function by solving a
Quadratic Equations 5 – 7 days
related quadratic equation. [Moved to A.7c]
A.9, A.10, A.11 Delete A.9 – Interpret variation in real-world contexts and calculate and interpret standard deviation, and z-scores. [Included in AFDA.7 and AII.11]; calculate and interpret mean absolute deviation. A.10 – Compare and contrast multiple univariate data sets, using box-and-whisker plots. [Moved to 8.12] A.11 EKS – Design experiments and collect data to address specific, real-world questions. [Included in AFDA.8] A.11 – [Moved to A.9]
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 Additions: A.1a EKS – Translate between verbal quantitative situations algebraically with equations.
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. A.1 EKS – Evaluating algebraic expressions (clarified that expressions may contain absolute value, square roots, and cube roots without rationalizing denominators).
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 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 A.4 – Use of graphing calculators. [Moved to A.4 EKS] A.4a,b EKS – Apply properties of real numbers and properties of equality.
1.7 Glencoe Student Workbook Sec 1-3
Name each property used to simplify the expression. Which property is shown from line 3 to line 4? Name each property used to solve the equation. Simplify the Expression Which expression is in simplified form?
Associative Property Commutative Property Distributive Property 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; A.5b – Justify steps used in solving inequalities. [Moved to A.5a EKS]
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.4d – [Moved to A.4a] A.4a,b EKS – Apply properties of real numbers and properties of equality.
A.5 (a) The student will solve multistep linear inequalities in two variables, including solving multistep linear inequalities algebraically and graphically; Additions A.5 EKS – Determine and verify algebraic solutions using a graphing utility. A.5a EKS – Solving multi-step linear inequalities in one variable (clarified that solving would be algebraic and representing a solution would be graphical); apply properties of real numbers and properties of inequality. A.5b – Justify steps used in solving inequalities. [Moved to A.5a EKS]
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
A.4 (a) The student will solve multistep linear and quadratic equations in two variables, including solving literal equations (formulas) for a given variable A.4a – [Moved to A.4c] A.4a,b EKS – Apply properties of real numbers and properties of
2-5 Glencoe Workbook Sec 2-8
Solve the equation for ____. Rewrite the following formula in terms of ____.
Literal Formula
equality.
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. A.4f – [Moved to A.4e]
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; A.5c EKS – Determine if a coordinate pair is a solution of an inequality or system of 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 A.4a – [Moved to A.4c] A.4a,b EKS – Apply properties of real numbers and properties of equality.
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. Delete A.7 EKS – Detect patterns in data and represent arithmetic and geometric patterns algebraically. [Included in AFDA.1 and AII.5] Addition A.7 EKS – Investigate and analyze characteristics and multiple representations of linear and quadratic functions using a graphing utility. A.7a EKS – Determine whether a relation represented by a mapping is a function.
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
SOL Covered Textbook Chapter and Section
Resources Essential Questions / Skills Vocabulary
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically Addition A.7 EKS – Investigate and analyze characteristics and multiple representations of linear and quadratic functions using a graphing utility. A.7a EKS – Determine whether a relation represented by a mapping is a function.
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.7 EKS – Investigate and analyze characteristics and multiple representations of linear and quadratic functions using a graphing utility. A.7a EKS – Determine whether a relation represented by a mapping is a function.
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 A.6 – Graph linear equations. [Moved to A.6c]
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(s) Given the slope m = a/b, which point would lie on the line with (x, y)
Slope Rise over Run Rate of Change 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 – Graph linear equations. [Moved to A.6c]
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. A.6 – Graph linear equations. [Moved to A.6c]
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
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
graph of the line, two points on the line, or the slope and a point on the line.
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 A.4e – [Moved to A.4d]
Find the solution to the system of equations by graphing them.
System of Equations Point of Intersection No Solution Infinite Solutions
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 A.4e – [Moved to A.4d]
Use substitution to find the solution to the system of equations
Third Nine Weeks Instruction
SOL Covered Textbook Chapter and Section
Resources Essential Questions / Skills Vocabulary
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 A.4e – [Moved to A.4d]
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 A.5d – Solving systems of inequalities (clarified that solutions to systems of inequalities should be represented graphically).
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 Delete A.2 EKS – Identify prime polynomials. A.2c EKS – Factoring binomials or trinomials limited to one variable (two variables included in Algebra II) and limit the leading coefficient to be an integer with no more than four factors after factoring out a greatest common factor. A.2 EKS – Use x-intercepts to determine and confirm factors. [Moved to A.7c,d EKS]
Factor completely. Find all of the factors of ________.
Fourth Nine Weeks Instruction
SOL Covered Textbook Chapter and Section
Resources Essential Questions / Skills Vocabulary
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 Delete A.2 EKS – Identify prime polynomials. A.2c EKS – Factoring binomials or trinomials limited to one variable (two variables included in Algebra II) and limit the leading coefficient to be an integer with no more than four factors after factoring out a greatest common factor.
Factor completely. Find all of the factors of ________.
Greatest Common Factor
A.2 EKS – Use x-intercepts to determine and confirm factors. [Moved to A.7c,d EKS]
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. Addition A.3b – Simplify cube roots of all integers (previously limited to whole numbers). A.3c EKS – Simplify numerical expressions containing square or cube roots and add, subtract, and multiply two monomial radical expressions limited to a numerical radicand.
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 A.4c – [Moved to A.4b] A.4a,b EKS – Apply properties of real numbers and properties of equality. A.4b – Solving quadratic
Find the solution(s) for the equation…
Quadratic Equation Roots Zeros Solutions x-intercepts Vertex
equations (clarified that both rational and irrational solutions to quadratics will be included).
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 Delete A.9 – Interpret variation in real-world contexts and calculate and interpret standard deviation, and z-scores [Included in AFDA.7 and AII.11]; calculate and interpret mean absolute deviation.
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 Delete A.10 – Compare and contrast multiple univariate data sets, using box-and-whisker plots. [Moved to 8.12]
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 median/IQR/…?
Interquartile range Minimum Value Lower Quartile Median Upper Quartile 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.
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
Mathematical models will include linear and quadratic functions Delete A.11 EKS – Design experiments and collect data to address specific, real-world questions. [Included in AFDA.8] A.11 – [Moved to A.9] A.9 – Determine the equation of best fit (clarified to be performed with the use of a graphing utility).
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
A.2 The student will perform operations on polynomials, including b) adding, subtracting, multiplying, and dividing polynomials
A.2 The student will perform operations on polynomials, including 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;
A.4 The student will solve multistep linear and quadratic equations in two variables, including 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
A.4 The student will solve multistep linear and quadratic equations in two variables, including c) solving quadratic equations algebraically and graphically
A.4 The student will solve multistep linear and quadratic equations in two variables, including d) solving multistep linear equations algebraically and graphically;
A.4 The student will solve multistep linear and quadratic equations in two variables, including e) solving systems of two linear equations in two variables algebraically and graphically;
A.4 The student will solve multistep linear and quadratic equations in two variables, including 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
A.5 The student will solve multistep linear inequalities in two variables, including 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
A.5 The student will solve multistep linear inequalities in two variables, including c) solving real-world problems involving inequalities
A.5 The student will solve multistep linear inequalities in two variables, including 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
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including b) domain and range;
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including c) zeros of a function;
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including d) x- and y-intercepts;
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including e) finding the values of a function for elements in its domain;
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including 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