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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:

• 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.

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.

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.

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 YouTube videos from the Ohio Resource Center Tutorials for High School Mathematics:

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

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

Play videos from Khan Academy:

• Age Word Problems

• Mixture Problems 1 (Coffee mixture) posted at YouTube

• Mixture Problems 2 (Salt solution)

• Mixture Problems 3 (Sugar solution)

• Sums of consecutive integers.  Find the integers.

• Rectangle area and perimeter word problems

Play videos at YouTube.com

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

• Coins (coins consisting of dimes and nickels)

• Rate of Work Problems (How much time does it take to complete the job if two people or things work together?)

• Investments (Use Interest =Principal x Rate: Money was invested, part at one rate and part at another rate.  The total interest in one year is provided.  How much was invested at each rate?)

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.

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.

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.

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.

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

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, B: Interpret functions that arise in applications in terms of the context.

 

 

References

*Note 2017: The current academic content standards for mathematics are now available at http://education.ohio.gov/Topics/Learning-in-Ohio/Mathematics

 

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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 ]