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Advanced

Algebra I

CURRICULUM GUIDE

(Middle School)

Mathematics Curriculum Guide

Revised 2019. Available at www.rcps.us.

Roanoke County Public Schools does not discriminate with regard to race, color, national origin, sex, or handicapping condition in an educational and/or employment

policy or practice. Questions and/or complaints should be addressed to the Director of Administration at (540) 562-3900 ext. 10121 or the Director of Special Education

and Pupil Personnel Services at (540) 562-3900 ext. 10181.

Acknowledgements

The following people have made tremendous contributions to the completion of this curriculum guide and all are appreciated.

Dana Bryan

Cave Spring High

Ann Fajardo

Glenvar Middle

Emily Parisi

Cave Spring Middle

Carli Barnett

William Byrd Middle

Katie Warren

Cave Spring Middle

Roanoke County Public Schools Administration

Dr. Ken Nicely

Superintendent

James Soltis

Director of Secondary Instruction

Dr. Rebecca Eastwood

Director of Elementary Instruction

Terry Hartley

Mathematics Supervisor

Preface

This guide will assist the mathematics teacher in preparing students for the challenges of the twenty-first century. As established by the National Council of

Teachers of MathematicsPrinciples and Standards for School Mathematics, educational goals for students are changing. A comprehensive and coherent set of

mathematics standards for each and every student from prekindergarten through grade 12,Principles and Standards is the first set of rigorous, college and career

readiness standards for the 21st century. Students should have many and varied experiences in their mathematical training to help them learn to value mathematics,

become confident in their ability to do mathematics, become problem solvers, and learn to communicate and reason mathematically. This guide, along with the

available division resources, VDOE resources, professional literature, alternative assessment methods, and in-service activities will assist the mathematics teacher

in continuing to integrate these student goals into the curriculum.

i

Introduction/General Comments

This curriculum guide follows the 2016 Virginia Algebra I SOLs as adopted by the Virginia Department of Education. It is extremely important and required that the Sequence of Instruction and Pacing be followed as presented in this guide. Topic references from the textbook,Virginia Algebra I, (2019 edition) by Houghton-Mifflin-Harcourt are listed in this curriculum guide in the Resources sections.

Students will take three formative assessments during the year (dates to be determined annually). Each teacher-designed test will assess skill levels of the SOLs as presented in the Sequence of Instruction and Pacing and the formative assessment blueprint. The data collected from the formative assessments will help teachers determine students’ strengths and weaknesses, and inform instructional decisions.

The Mapping for Instruction is based on specified SOLs which are to be taught in the predetermined order. Note, some SOLs (or their parts) may be taught over multiple 9-week periods.

Refer to the Mathematics 2016 Standards of Learning Algebra I Curriculum Framework during every lesson. It is located at the back of this guide. This will provide valuable information for the teacher (Understanding the Standard) and desired goals for instruction (Essential Knowledge and Skills). Examples of teaching techniques and strategies, definitions, and recommended manipulatives are included in the Curriculum Framework and on the VDOE website under Mathematics Instructional Plans (MIPs) http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/mip/index.shtml.

Resources Overview

Resources for all SOLs

IXL

PowerSchool

BrainPop

HMH – Think Central

VDOE

Mathematics Instructional Plans (MIPs): http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/mip/index.shtml#a

Desmos: https://teacher.desmos.com/

Promethean Planet

Number Talks

Performance Tasks

RCPS Common Assessments (pretests, formative assessments, posttests)

get2math

mathbitsnotebook.com Algebra I

coolmath.com – algebra

mathisfun.com - algebra

Quizizz.com

Kahoot

Khan Academy

ii

Sequence of Instruction and Pacing

First Nine Weeks Second Nine Weeks Third Nine Weeks Fourth Nine Weeks

SOL Instructional Focus Blks SOL Instructional Focus Blks SOL Instructional Focus Blks SOL

Instructional

Focus

Blks

A.1ab Write algebraic expressions/equations Translate expressions and equations:

• Verbal to algebraic
• Algebraic to verbal Evaluate algebraic expressions 5

A.7abdef Analyze and investigate functions (is it a function?) Identify domain, range, zeros, and intercepts Determinef(x) for a value of x Represent relations and functions using verbal descriptions, tables, equations, and graphs Calculator use

A.4de Solve systems of linear equations algebraically and graphically Solve practical problems

A.2bc Polynomials -Completely factor -quotients 7

A.5bcd Graph solution to two variable linear inequalities Solve a system of linear inequalities graphically

A.7b-f Analyze and investigate quadratic functions Identify domain, range, zeros, and intercepts Confirm factors Determinef(x) for a value of x Represent relations and functions using verbal descriptions, tables, equations, and graphs Calculator use

A.3ab Simplify square and cube roots (limited to perfect squares and cubes) (^2)

A.6abc Write and graph linear equations (include vertical and horizontal lines) Determine slope

A.2a Simplify monomials and ratios of monomial expressions using the laws of exponents

A.4b 8.9b

Solve quadratic equations algebraically Pythagorean Theorem

A.4ace

8.

8.

Solve multistep linear equations algebraically Solve multistep literal equations for one variable Solve practical problems Percentage Change Angle Relationships

A.8 Direct and inverse variation

A.3abc Simplify expressions including square and cube roots (not limited to perfect squares and cubes)

6

A.9 Find curve of best fit, make predictions, and solve practical problems

Mapping for Instruction - First Nine Weeks

SOLs

A.1 The student will a) represent verbal quantitative situations algebraically; and b) evaluate algebraic expressions for given replacement values of the variables.

A.3 The student will simplify a) square roots of whole numbers and monomial algebraic expressions; b) cube roots of integers; and

A.4 The student will solve a) multistep linear equations in one variable algebraically; c) literal equations for a specified variable; e) practical problems involving equations and systems of equations.

A.5 The student will a) solve multistep linear inequalities in one variable algebraically and represent the solution graphically; c) solve practical problems involving inequalities; and

8.4 The student will solve practical problems involving consumer applications.

8.5 The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.

SOL Instructional Focus Vocabulary Comments Blocks

A.1ab Write quantitative expressions/equations:

• Verbal to algebraic
• Algebraic to verbal Evaluate algebraic expressions:
• Apply order of operations
• Absolute value
• Square roots
• Cube roots Practical situations:
• Concrete, pictorial, symbolic, verbal

Algebraic, numerical, equation, expression, inequality, substitution, absolute value, square root, cube root, rational, irrational, integer, exponent, squared, cubed, parentheses, brackets, braces, order of operations, variable, coefficient, translation Symbols: abs value - | | , square root - √ cube root - √^3

A.3ab Simplify square and cube roots (limited to perfect squares and cubes)

Square root, cube root, perfect square, cubing, perfect cube, radical, inverse, consecutive

Simplify ONLY perfect squares and perfect cubes during this nine weeks.

Simplifying non-perfect radicals and expressions is taught in the third nine weeks within order of operations and replacement value problems.

A.4ace Apply properties to simplify expressions and solve multistep linear equations algebraically

Determine if there are one, infinite, zero solutions

Solve multistep literal equations for a specified variable

Solve practical problems involving equations

Determine reasonableness of solutions

Properties of real numbers: commutative, associative, distributive, identity, inverse

Properties of equality: addition, subtraction,

multiplication, division, reflexive, symmetric,

transitive, substitution

Multiplicative property of zero, zero product property, term, constant, coefficient, variable, like terms, substitution, literal equation, formula, solution, linear equation, and inverse operation, set notation

Practical problems involving systems of equations will be taught in the third nine weeks.

8.4 Compute the percent increase or decrease found in a practical situation

Percent decrease, percent increase, percent of change 1

8.5 Identify and describe angle relationships

Use angle pair relationships to determine the measure of unknown angles

Angles: vertical, adjacent, supplementary, complementary, nonadjacent, congruent, acute, right, obtuse; common ray, common vertex, intersecting lines, vertex

Students should be able to solve a multi-step equation for an unknown value of x that is part of an angle measure written as an algebraic expression.

A.5ac Apply properties to solve multistep linear inequalities algebraically

Graph solutions to inequalities

Determine if an ordered pair is a solution to a linear inequality

Solve practical problems

Properties of real numbers: commutative, associative, distributive, identity, inverse

Properties of inequality: addition, subtraction, multiplication, division, transitive, substitution Inequality, inverse operations, half-plane, set notation

Students should be able to determine and verify algebraic solutions using a graphing utility.

Students should be familiar with the use of set notation to express solutions. 8

Remediation, Review, Assessment 10

Total blocks 45

• Find measures of complementary, supplementary, vertical, and adjacent angles

A.5ac HMH 61-66, 67-74, 259-

Virginia SOL Success 258A-258C

Khan Academy: Solving Inequalities Math Bits Notebook: Solving Inequalities Quizizz: Solving Inequalities Quizlet: Solving Inequalities

See MIPs: A.5ac - Lemonade Stand: Solving Practical Problems Using Linear Inequalities in One Variable (Word) / PDF Version A.5a - Solving Linear Inequalities in One Variable (Word) / PDF Version

Mapping for Instruction - Second Nine Weeks

SOLs

A.6 The student will a) determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line; b) write 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; and c) graph linear equations in two variables.

A.7 The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; b) domain and range; d) intercepts; e) values of a function for elements in its domain; and f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.

***** Quadratic functions and A.7c w ill be covered in the 4th^ nine w eek s.

A.8 The student, given a data set or practical situation, 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.

SOL Instructional Focus Vocabulary Comments Blocks

A.7abdef Analyze and investigate functions (general overview)

Determine whether a relation is a function (from set of ordered pairs, mapping, table, or graph)

Identify domain, range, zeros, and intercepts

Determine f(x ) for a value of x in domain

Represent relations and functions using verbal descriptions, tables, equations, and graphs

Given one representation, students should represent the relation in another form

Calculator use

Relation, function, function family, linear, transformation, domain, range, input, output, independent variable, dependent variable, function notationf(x), x-intercept, y-intercept, set notation, Symbols: Example of set notation – {y : y > 3} Empty set or null set – ∅, {^ }

The terms solutions, roots, and zeros (A.7c) will be taught explicitly in the 4 th^ nine-weeks, but teachers can consider teaching them in the context of linear functions.

Resources – Second Nine Weeks

SOL Textbook Links Supplemental Materials

A.7abdef HMH 97-106, 107-112, 113-120, 165-172, 173-178, 179-188, 195-202, 203-212, 213-220, 221-228, 229-238, 245-250, 251-258, 697-708, 709-716, 717-728, 735-744, 745-

Virginia SOL Success 120A-120C

Identifying functions https://quizizz.com/admin/quiz/57e9e59af3e215a43b64bc

Desmos Activity: Explore Domain and Range of Graphs

https://teacher.desmos.com/activitybuilder/custom/5953f7bc 02399f3cd

Domain and range https://www.quia.com/cb/79585.html

Evaluate functions https://quizlet.com/188872547/function- notation-practice-flash-cards/

Describe transformations

https://teacher.desmos.com/activitybuilder/custom/5beeffea3d 1b0c5a36db5fLinear Transformations Practice Activity

https://drive.google.com/file/d/1DMCcSeQxkynj5w6xWXThDCbYG _vuQXKr/preview

See MIPs: A.7abef - Functions 1: Investigating Relations and Functions (Word) / PDF Version A.7aef- Square Patios (Word) / PDF Version A.7bcd - Functions 2: Exploring Quadratic Functions (Word) / PDF Version A.7cd - Quadratic Connections (Word) / PDF Version A.7cd - Solving Linear Equations Using Functions with Desmos (Word) / PDF Version

Multiple representation of functions http://www.esc4.net/users/0236/camt/r4camt_linear_repre sentations_ds.pdf

A.6abc HMH 113-120, 165-172, 173-178, 179-188, 195-202, 203-212, 213-220, 221-228, 229-238, 245-

Virginia SOL Success 212A-212C, 220A-220C

Slope

Desmos Activity: Put the Point on the Line

https://teacher.desmos.com/activitybuilder/custom/57f3dd9dcf3c 849008d

https://mathbitsnotebook.com/Algebra1/LinearEquations/LERefre shSlope.html

https://www.geogebra.org/m/CCqSxRkK

http://www.crctlessons.com/slope-game.html

See MIPs: A.6a - Slippery Slope (Word) / PDF Version A.6abc - Slope-2-Slope with Desmos (Word) / PDF Version A.6ab - Writing Equations of Lines (Word) / PDF Version A.6c - Rate of Change of Practical Situations (Word) / PDF Version A.6c - Transformation Investigation (Word) / PDF Version

Slope-intercept form

Desmos Activity: Slope-Intercept Stars

https://teacher.desmos.com/activitybuilder/custom/5831bb9627e 495f1053a113e

Desmos activity: Writing the Equation of a Line https://teacher.desmos.com/activitybuilder/custom/ 358ae

Linear equation card sort https://mrshclassblog.wikispaces.com/file/view/linear+sort +and+match+game.pdf

Stained Glass Graphing project http://staff.tamhigh.org/wetzel/Stained-Glass- Project%20project.pdf

https://www.geogebra.org/m/Evp3A9DK

http://www.math.com/school/subject2/lessons/S2U4L2GL.html

https://books.quia.com/rr/379720.html

https://www.geogebra.org/m/fnY6ptWQ

http://www.math.com/school/subject2/lessons/S2U4L3GL.html

https://www.geogebra.org/m/Spq9uhju

https://www.varsitytutors.com/assets/vt-hotmath- legacy/hotmath_help/games/kp/kp_hotmath_nosound.swf

https://www.thatquiz.org/tq/practice.html?algebra Point-slope https://www.geogebra.org/m/qknBFn8Q Standard form https://www.quia.com/rr/49074.html Parallel/perpendicular lines

Desmos Activity: Parallel and Perpendicular Lines https://teacher.desmos.com/activitybuilder/custom/560199005b be23c0628ebcf

https://www.geogebra.org/m/waXDEZEm

https://www.quia.com/ba/109264.html

Parallel, perpendicular or neither activity https://learning.arpdc.ab.ca/pluginfile.php/24966/mod_pag e/content/30/Parallel_Perpendicular_Neither_Activity.pdf

A.8 Virginia SOL Success 374A-374F Desmos Activity: Direct Variation https://teacher.desmos.com/activitybuilder/custom/5a71ff07c0c 170a94ef611f

Thatquiz- direct and inverse variation https://www.thatquiz.org/tq/practicetest?5xjblmy190l

See MIPS: A.8 - Direct Variation (Word) / PDF Version A.8 - Inverse Variation (Word) / PDF Version

https://www.teacherspayteachers.com/Product/Direct- Inverse-Variation-Equations-Card-Sort-461450 (free resource)

A.2a Use the laws of exponents to simplify:

• Monomial expressions
• Ratios of monomial expressions (in which exponents are integers)

Monomial, ratio, negative exponent, zero exponent, product of powers, power of a power, power of a product 6

A.3abc Simplify square roots

Express principal square root of a monomial algebraic expression (where variables are assumed to have positive value) in simplest form Simplify cube roots Simplify expressions containing square or cube roots Add, subtract, and multiply two monomial radical expressions

Square root, simplest form, cube root, radical expression, principal square root Symbols: square root - √ ; cube root - 3 √

Perfect squares and perfect cubes were taught in the first nine weeks. This lesson highlights simplifying radicals into simplest radical form. This includes numbers and variables. 6

A.2b Polynomials:

• Add, subtract, multiply polynomials
• Model operations with polynomials using concrete objects, pictorial representations, and symbols

Polynomial, degree of a polynomial, prime polynomial, factorization, leading coefficient, like terms, GCF

Long or synthetic division is not required but students may benefit from experience with these methods.

8.10 Solve area and perimeter problems, including practical problems, involving composite plane figures.

Perimeter, area, subdivide Subdivide plane figures into triangles, rectangles, squares, trapezoids, parallelograms, and semicircles. Reinforce SOL A.2abc skills by using polygons with algebraic expressions for side lengths

Remediation, Review, Assessment 12 Total blocks 45

Resources – Third Nine Weeks

SOL Textbook Links Supplemental Materials

A.4de HMH

5-10, 45-54, 55-60, 251-258, 387- 394, 395-404, 405-412, 413-422, 429-440, 447-454, 751-758, 771- 780, 781-790, 791-800, 807-814, 815-826, 827-834, 835-

Virginia SOL Success 10A-10C, 54A-54B

Solve by graphing

Desmos Activity: Systems of Two Linear Equations https://teacher.desmos.com/activitybuilder/custom/ 07d7306ef115e7053a142a

Desmos Activity: Solutions to Systems of Linear Equations https://teacher.desmos.com/activitybuilder/custom/ 4a325345d9115d

See MIPs: A.4de - Road Trip: Applying Systems of Linear Equations (Word) / PDF Version A.4de - Spring Fling Carnival: Applying Systems of Linear Equations (Word) /PDF Version

Solve by substitution

Solve systems by substitution https://www.quia.com/ba/119379.html Solve by elimination

Solve systems by elimination https://www.quia.com/rr/514985.html

Solve system using any method http://www.crctlessons.com/systems-of-equations- game.html

A.5bd

HMH

Desmos Activity: Inequalities in Two Variables https://teacher.desmos.com/activitybuilder/custom/ 7ce3e3a2374e9f05f8f47e

Desmos Activity: Graphing Linear Inequalities https://teacher.desmos.com/activitybuilder/custom/ d76f128fa0cb4106af57cc

Desmos Activity: Systems of Linear Inequalities https://teacher.desmos.com/activitybuilder/custom/ 67249eaba26aa2125b60d

https://www.thatquiz.org/tq-0/math/algebra/

See MIPs: A.5b - Represent the Solution of a Linear Inequality in Two Variables Graphically Scavenger Hunt with Desmos (Word) / PDF Version A.5d - Graphing Systems of Linear Inequalities in Two Variables with Desmos (Word) / PDF Version

A.2a

HMH

Virginia SOL Success 501A-501D, 510A-510D

https://www.mathsisfun.com/algebra/exponent-laws.html

http://www.coolmath.com/prealgebra/13-intro-to-exponents/05- exponent-rules-rule-4-01-

See MIPs: A.2a - Laws of Exponents (Word) / PDF Version A.2a - Operations with Expressions Written in Scientific Notation (Word) / PDF Version

Mapping for Instruction - Fourth Nine Weeks

SOLs

A.2 The student will perform operations on polynomials, including b) adding, subtracting, multiplying, and dividing polynomials; and c) factoring completely first- and second-degree binomials and trinomials in one variable.

A.4 The student will solve b) quadratic equations in one variable algebraically;

A.7 The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including b) domain and range; c) zeros; d) intercepts; e) values of a function for elements in its domain; and f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.

A.9 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions. 8.9 The student will b) apply the Pythagorean Theorem 8.12 The student will a) represent numerical data in boxplots; b) make observations and inferences about data represented in boxplots; and c) compare and analyze two data sets using boxplots.

SOL Instructional Focus Vocabulary Comments Blocks

A.2bc Polynomials:

• divide polynomials
• Completely factor first- and second- degree binomials and trinomials
• Model operations with polynomials using concrete objects, pictorial representations, and symbols
• Use a graphing calculator to factor and verify factorizations of polynomials

Polynomial, degree of a polynomial, prime polynomial, factorization, leading coefficient, like terms, GCF

Long or synthetic division is not required but students may benefit from experience with these methods.

7

A.7bcdef Analyze and investigate quadratic functions

Identify domain, range, zeros, and intercepts

Confirm factors using x intercepts

Determine f(x ) for a value of x

Represent relations and functions using verbal descriptions, tables, equations, and graphs

Quadratic function, domain, range, zero of a function, solution, root, function notationf(x), x- intercept, y-intercept, set notation, empty set, null set, ∅

Many function vocabulary terms were introduced during the second nine- weeks; review them here in the context of quadratic functions.

2

Investigate and analyze functions with a graphing calculator

A.4b Solve quadratic equations algebraically:

• factoring
• quadratic formula

Quadratic equation, quadratic formula, solution, rational, irrational, properties of equality, factoring

Solutions may be rational or irrational. 6

8.9b Apply Pythagorean Theorem

• Determine if a triangle is a right triangle
• Determine the measure of a side given two sides in a right triangle
• Solve practical problems using Pythagorean Theorem

Pythagorean Theorem 1

A.9 Determine a curve of best fit with a graphing calculator

Make predictions using data, scatter plots, or curve of best fit

Solve practical problems

Evaluate the reasonableness of the model of a practical situations

Scatterplot, positive correlation, negative correlation, no correlation, transformational graphing, linear, quadratic

Include both linear and quadratic curves of best fit.

SOL Review 12

Rationalizing the Denominator (Enrichment) Recommend this lesson after the Algebra I SOL test.

8.12abc

Boxplots (box-and-whisker plot):

**- Display data

• Make observations and inferences
• Compare data of 2 boxplots**

boxplot (box-and-whisker plot), median, range, lower extreme (minimum), upper extreme (maximum), lower quartile, upper quartile, quartile, interquartile range (IQR), five number summary, inference

Recommend this lesson after the Algebra I SOL test.

Remediation, Review, Assessment 9 Total blocks 45