• Math Topics
• Common Core
• Initiatives
• Methodology
• Resources
• Projects
• Manipulatives
• Software
• Learning Support
• Standardized Test Prep
• Technology Integration
• Assisting Readers
• Professionalism
• Associations
• Journals
• News
• Professional Development
• Standards
• Educational Research
• CT4ME Publications

Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.

 

 

 

Standardized Test Preparation and
Tips for Success

Preparing Your Students for the
Ohio Graduation Test in Mathematics

Strand Resources:
Patterns, Functions, and Algebra

Other strand resources:

[ Number, Number Sense, and Operations ]   [ Measurement ]   [ Geometry and Spatial Sense ]   [ Patterns, Functions, and Algebra ]   [ Data Analysis and Probability ]   [ Mathematical Processes ]

What is Algebra? 

 

 

Benchmarks in Patterns, Functions, and Algebra

 

Benchmarks in this strand have been correlated to the Common Core State Standards (CCSS) for Mathematics for the Conceptual Category (CC), Domain (D), and Cluster (C).

NOTE: As a general resource for all Algebra benchmarks, students might consult the following resources:

• Algebra from Oswego City School District (NY) Regents Exam Prep Center.  Each sub-section includes lessons and interactive practice exercises. The algebra strand, in particular, addresses variables and expressions, equations and inequalities, patterns/functions/relations, trig functions (sine, cosine, tangent), and the Pythagorean theorem.

• HippoCampus, a project of the Monterey Institute for Technology and Education, provides multimedia content.  Select sections from the topics in the full online texts for Algebra 1A, 1B, or Elementary Algebra.  Each lesson includes multiple-choice assessments and an answer key.  "This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally."

 

A.  Generalize and explain patterns and sequences in order to find the next term and the n^th term.

CCSS: CC: Functions, D: Interpreting Functions, C: Understand the concept of a function and use function notation.

CCSS: CC: Functions, D: Build Functions, C: Build a function that models a relationship between two quantities.

Purplemath: Number Patterns finding the next number in a sequence, including common differences and recursions.

Glencoe Online Study Tools, Mathematics, Algebra I, 2005, multiple choice practice:

• Arithmetic Sequences

• Writing Equations from Patterns

Mathguide.com:

• Identifying arithmetic sequences

• Quizmaster for finding the formula for the general term in the arithmetic sequence (fill in and check answer).

Play video at YouTube.com:

• Recognizing Patterns: Review arithmetic, geometric, powers, inductive reasoning patterns

B.  Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

CCSS: CC: Functions, D: Interpreting Functions, C: Analyze functions using different representations.

CCSS: grade 8, D: Functions, C: Define, evaluate, and compare functions.

CCSS: grade 8, D: Functions, C: Use functions to model relationships between quantities.

Purplemath: Functions

Glencoe Online Study Tools, Mathematics, IMPACT Math, Course 3, multiple choice practice: Linear Relationships

Play video at YouTube.com:

• Introduction to Linear Functions illustrates the concept and how linear functions represent a constant rate of change.

C.  Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

CCSS: CC: Algebra, D: Reasoning with Equations and Inequalities, C: Represent and solve equations and inequalities graphically.

CCSS: CC: Functions, D: Interpreting Functions, C: Interpret functions that arise in applications in terms of the context, and C: Analyze functions using different representations.

CCSS: grade 8, D: Functions, C: Define, evaluate, and compare functions.

Purplemath: Translating Word Problems Keywords

Glencoe Online Study Tools, Mathematics, Algebra I, 2005, multiple choice practice: Writing Equations

D.  Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

CCSS: CC: Algebra, D: Creating Equations, C: Create equations that describe numbers or relationship.

CCSS: CC: Functions, D: Linear, Quadratic, and Exponential Models, C: Construct and compare linear, quadratic, and exponential models and solve problems.

CCSS: grade 8, D: Functions, C: Use functions to model relationships between quantities.

Mathguide.com: The quizmaster for each of the following is fill in and check answers:

• Add quadratic trinomials

• Subtract quadratic trinomials

• Multiply binomials with terms in the form ax + b

OnlineMathLearning.com: Types of Algebra Word Problems Among those are complete explanations and how to's for age, average, coin, consecutive integer, distance, fraction, geometry, interest, lever, mixture, number sequences, ratio, proportion, symbol, and work problems.

Purplemath: Translating Word Problems Applications

Play the video tutorials at the Ohio Resource Center for Mathematics, Science, and Reading:

• Mixture and Concentration Problems for setting up and solving mixture and concentration problems with science examples, video #16.

• Using Rates and Proportions for working with unit rates, ratios, and proportions, video #17.

Play videos at YouTube.com.  The presenter translates the word problem into the algebraic equation, discusses the problem, shows diagrams as needed, and presents the solution.  He is very detailed--excellent how-to videos.  Students: For a learning experience, pause the video after the problem is presented, then solve.  Use the video to check your solution method:

• Use perimeter of the rectangle.  Find dimensions of the rectangle.

• Sum of three consecutive odd integers.  Find the integers.

• Distance = Rate x Time (Airplanes traveling in opposite directions)

• Mixture (Salt solution)

• Coins (26 coins in your pocket consisting of dimes and quarters)

• Work (How much time does it take to complete the job if two people work together to paint a fence?)

• Investments (Use Interest =Principal x Rate: An investment consisted of stocks and bonds and earned interest in one year.  How much was invested in stocks? in bonds?)

E.  Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

CCSS: CC: Functions, D: Interpreting Functions, C: Interpret functions that arise in applications in terms of the context, and C: Analyze functions using different representations.

CCSS: CC: Functions, D: Build Functions, C: Build new functions from existing functions.

Purplemath: Graphing Overview

Shodor Interactivate, Virtual Manipulative: Function Flyer -- plot an algebraic function on the coordinate plane, and use sliders to manipulate the constants of the graphed function.

F.  Solve and graph linear equations and inequalities.

CCSS: CC: Algebra, D: Reasoning with Equations and Inequalities, C: Understand solving equations as a process of reasoning and explain the reasoning, C: Solve equations and inequalities in one variable, and C: Represent and solve equations and inequalities graphically.

CCSS: CC: Functions, D: Interpreting Functions, C: Analyze functions using different representations.

CCSS: CC: grade 8, D: Expressions and Equations, C: Analyze and solve linear equations and pairs of simultaneous linear equations.

Mathguide.com: Solve linear equations of the form ax + b =c; ax + b + cx + d; and ax + b = cx +d.  The page contains explanations and quizmaster for each type.  Fill in and check answers.

Purplemath:

• Graphing Linear Equations

• Graphing Linear Inequalities

The Math Page: Algebra, Section 32, Equation of a straight line, including graphing using intercepts, y = ax, and lines parallel to axes, explanations, plus problems with answers

Glencoe Online Study Tools, Mathematics, Algebra I, 2005, multiple choice practice:

• Graphing Linear Equations

• Graphing Inequalities

• Solve equations for a variable

• Solve multi-step equations

• Solving equations with variables on each side

• Solve multi-step inequalities, including those with variables on both sides

Glencoe Online Study Tools, IMPACT Mathematics, Course 3, multiple choice practice: Solve inequalities symbolically and graphically, including word problems

Shodor Interactivate:

• Algebra Quiz: Practice solving algebraic equations.  The quiz allows you to select the difficulty level, time limit and equation type. Choose to include one or more options: variable on both sides, distributive property, quadratic, one-step problems, and two-step problems.
• Graphit: Graph linear equations and inequalities.

Play videos at YouTube.com:

• Paired Data and the Rectangular Coordinate: graph linear equations using x- and y- intercepts; ordered pairs satisfying the equation.

• Solve and graph the linear inequality in one variable: Reviews rule for division by a negative integer when solving

• Graph inequalities in two variables

G.  Solve quadratic equations with real roots by graphing, formula and factoring.

CCSS: CC: Algebra, D: Seeing Structure in Expressions, C: Write expressions in equivalent forms to solve problems.

CCSS: CC: Algebra, D: Reasoning with Equations and Inequalities, C: Solve equations and inequalities in one variable.

CCSS: CC: Geometry, D: Expressing Geometric Properties with Equations, C: Translate between the geometric description and the equation of a conic section.

Mathguide.com:

• Solving quadratic equations with the formula.  Formula is presented.  Quizmaster presents the quadratic equation.  Fill in answers rounded to nearest tenth and check answers.

• Practice factoring quadratic trinomials with integer coefficients
  ax² + bx + c where a = 1 or a >1.  Fill in and check answers.

The Math Page: Algebra, Section 36, Solve Quadratic Equations by graphing, formula, factoring, explanations, plus problems with answers

Purplemath: Solving Quadratic Equations

Edmonton Public Schools (CA), Jim Reed, Math 9: Interactive Quadratic Formula and Sum/Product Method

Glencoe Online Study Tools, Mathematics, IMPACT Math, Course 3, multiple choice practice:

• Quadratic Formula Use

• Solve Quadratics by Factoring

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice: Solving Quadratic Equations by Graphing

Play videos at YouTube.com:

• Solve a simple Quadratic Equation with no linear term (solve by square root method)

• Solve Quadratics by Factoring #1(common factor is present)

• Solve Quadratics by Factoring #2 (reminder to set equation =0 as a first step)

• The Quadratic Formula: How to solve a quadratic equation using the formula

Play videos at Blip.tv [Note, while completing the square is one method for solving the quadratic equation, it is not one that is expected for mastery on this benchmark]:

• GCSE Maths Tutor no.3 completing the square part 1 --how to solve quadratics by completing the square method

• GCSE Maths Tutor no.4 completing the square part 2 --common examples of the use of completing the square for the solution of quadratic equations

H.  Solve systems of linear equations involving two variables graphically and symbolically.

CCSS: CC: Algebra, D: Reasoning with Equations and Inequalities, C: Solve systems of equations, and C: Represent and solve equations and inequalities graphically.

CCSS: CC: grade 8, D: Expressions and Equations, C: Analyze and solve linear equations and pairs of simultaneous linear equations.

Mathguide.com: Solve systems of linear equations with addition, multiplication/addition, and substitution.  Lesson and then quizmaster.  Fill in and check answers.

Purplemath: Systems of Linear Equations

The Math Page: Algebra, Section 33, Simultaneous Linear Equations,  explanations for graphical, addition, substitution methods, plus problems with answers

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice:

• Graphing Systems of Equations

• Graphing Systems of Linear Inequalities

Glencoe Online Study Tools, IMPACT Mathematics, Course 3, multiple choice practice: Solve symbolically Systems of Linear Equations

Systems of Linear Equations drill by Elias Saab and Daniel Saab.  Enter the ordered pair for the answer.  Feedback tells correct answer, but not the complete details to solution.  Select from five levels of difficulty with either two, three, or four variables in the problem.

Play videos at YouTube.com:

• Solve Systems of Linear Equations by Substitution

• Solve Systems of Linear Equations by Elimination (Part 1: you can add or subtract at step 1)

• Solve Systems of Linear Equations by Elimination  (Part 2: first find a common multiple for one variable in both equations, then add or subtract)

• Solve Systems of Linear Equations by Graphing

I.  Model and solve problem situations involving direct and inverse variation.

Purplemath: Direct, Joint, and Inverse Variation

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice:

• Slope and Direct Variation

• Inverse Variation

Play videos at YouTube.com for solving algebra word problems.  The presenter translates the word problem into the algebraic equation, discusses the problem, shows diagrams as needed, and presents the solution.  He is very detailed--excellent how-to videos.  Students: For a learning experience, pause the video after the problem is presented, then solve.  Use the video to check your solution method:

• Direct Variation (Application to wages earned)

• Inverse Variation (F varies inversely with the square of M)

• Direct and Inverse Variation in same problem (P varies directly with X and inversely with Y)

J.  Describe and interpret rates of change from graphical and numerical data. (Includes: Compute and interpret slope, midpoint, and distance given a set of ordered pairs.)

CCSS: CC: Functions, D: Interpreting Functions, C: Interpret functions that arise in applications in terms of the context.

Purplemath: Meaning of Slope and Y-Intercept

Glencoe Online Study Tools, Algebra I, 2005, multiple choice practice: Slope

AlgebraLab.org: Algebra I: Distance and Midpoint Formulas.  Study aids with examples and practice problems (short answer and T/F).  Given two ordered pairs, determine length of a segment and midpoint.  Given three ordered pairs, determine if the vertices form a right triangle.

References

 

Back to top

 

See other strand resources:

[ Number, Number Sense, and Operations ]   [ Measurement ]   [ Geometry and Spatial Sense ]   [ Patterns, Functions, and Algebra ]   [ Data Analysis and Probability ]   [ Mathematical Processes ]

See related pages: [ Standardized Test Preparation and Tips for Success (first  page)]  [ OGT Introduction ]