Standardized Test Preparation and Tips for Success
Preparing Your Students for the Ohio Graduation Test
in Mathematics

This page includes information on:

• What is tested?

• How to Use this Resource with Six Steps to Success on the OGT in Math

Or, you may link immediately to Strand Resources:

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

What is Tested?

The Ohio Graduation Mathematics Achievement Test has 38 questions of which 32 are multiple-choice (4 responses), five are short-answer, and one is extended-response.  Each mathematics item assesses concepts and skills related to one of the five major areas of mathematics: Number, Number Sense and Operations; Measurement; Geometry and Spatial Sense; Patterns, Functions and Algebra; and Data Analysis and Probability.

Readers should note that Ohio administered the Ohio Graduation Tests (OGT) for the first time in spring 2003 in mathematics and reading.  Prior to this new exam, Ohio administered the 9th grade proficiency tests.  Ohio considers the OGT to be a measure of 10th grade standards.  The exam is designed to meet the testing requirements of the No Child Left Behind Act.  The graduating class of 2007 will be the first to have diplomas withheld for failure to pass the OGT (Gayler, Chudowsky, Kober, & Hamilton, 2003, p. 120).  

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How to Use this Resource

CT4ME has identified resources related to each benchmark of the Ohio Mathematics Academic Content Standards that students should have mastered by the end of the grades 8-10 program.  Students should be able to review on their own using the resources.   For each benchmark related to the five major areas tested, you will find Web resources by strand for reviewing the concept and practice problems.

You will also find links to online videos embedded within this resource.  The selected videos were posted by classroom teachers and professors who explain concepts and provide examples for problem solving.  Teachers, parents, and students should note that CT4ME has reviewed all of those for suitability and appropriateness for classroom use that are linked from this site.

New for 2008: Each strand also has a pdf test prep booklet with the resources CT4ME has identified for review of each benchmark.  Booklets are designed to be used with links provided at CT4ME.

Students can print the entire booklet, or just those pages for benchmarks they need to work on.  They can write their notes in the booklet next to each resource they used in their review.  As they review each benchmark, they complete a K-W-L chart answering the questions: What do you already know about that benchmark? What do you still want to know? What did you learn?  After using the resources provided for each benchmark, they reflect on their understanding and the questions they had and decide how they will find answers to any remaining questions.  They rate their overall belief about their level of mastery: still no or very little understanding (N), some to a great deal of progress (P), I’ve got it!--mastery (M).  Each booklet contains a page for students to add additional resources they used for test prep.

Test Prep Strand Booklets

The file size for each booklet is approximately 200 KB.

• Number, Number Sense and Operations (pdf)
• Measurement (pdf)
• Geometry and Spatial Sense (pdf)
• Patterns, Functions and Algebra (pdf)
• Data Analysis and Probability (pdf)

If needed, download Adobe Acrobat Reader, free software for viewing and printing PDF files.

Keep in mind that posting standards and benchmarks in your classroom and just reading them does not mean that students understand what mastery means.  For them to take responsibility, they must be able to self-assess and self-adjust their learning from standards that are broken down into meaningful components.  This is why students should use these booklets to accompany their test prep efforts.

Six Steps to Success 

1. This resource will be of most value to your students if they have clear knowledge of which benchmarks they have not yet mastered.  Post standards and benchmarks for mastery in your classroom and provide each student with a copy from which they can monitor their progress. 

   A diagnostic tool, such as Pro-Ohio, designed specifically for Ohio schools, or a formative assessment tool (screening, progress, and diagnostic), such as PASeries Mathematics and Algebra I from Pearson Education, will help educators identify specific areas of weakness that students might have, and will also help educators to tailor their classroom instruction to meet the needs of students.  The Northwest Evaluation Association's Measures of Academic Progress can also be used.  These are state-aligned computerized adaptive assessments that provide information about student achievement and growth. 

   While a diagnostic test with item analyses reveals weaknesses in concepts and content related to strands tested, teachers will still need to delve deeper into an analysis of why students missed certain questions.  At a second level, student literacy skills might have played a role in not answering a question correctly.  More on this below.

   Benchmarking tests should be given periodically, perhaps every nine weeks, to monitor progress in mastering objectives.  Such tests might be developed by districts.

    

2. Use the strand resources linked from this page, which correspond to weaknesses identified on your diagnostic test, or to generally review for the OGT.  Students  should use CT4ME's Strand Test Prep Booklets to record their progress and reflections on the resources provided.
    
3. As many students rely on their teacher to provide all the techniques for completing math assignments, you might provide students with tips for Reading a Math Textbook, suggested by Cynthia Arem of Pima Community College:
   • Slow down, every word counts
   • Reread for mastery
   • Do not skim illustrative material
   • Use a glossary to clarify terms (e.g., Math.com Glossary)
   • Write as you read--work out examples, compare
   • Use 3 x 5 cards with formulas, key vocabulary, properties, examples, and facts
   • Test yourself, write or say aloud important points
   • Use other math books as reference
   • Read your lesson before and after class

    

4. Review problem solving strategies (noted at MathCounts.org).  Provide students with problems that use those strategies, which generally fall into the following categories:

    

   Problem Solving Strategies
   Compute or simplify	Use a formula	Make a model
   Make a table, list, or chart	Guess, check, and revise	Determine if problem requires a single-step or multiple-steps to solve
   Solve a simpler case or work backwards	Look for a pattern	Write an equation
   Eliminate possible solutions and/or extra information	Draw a picture or diagram	Use logical reasoning

   Emphasize that often there is more than one way to solve a problem.  Examine the practice problems at Port Angeles (WA).  All of the problems at this site, which are separated into strands and strategies, are designed to help students learn to write in mathematics, which is an essential skill for the short answer and extended response questions on the OGT:

   • Math Practice Problems  to Teach Strategies for the High School
   • Math Practice Problems to Teach Strategies for Eighth Grade
    

   Writing helps students to make sense of mathematics and helps them to identify what they know or don't know.  As students tackle problems, stress George Polya's (author of "How to Solve It") problem solving steps:  The four steps are:

   • understanding the problem,
   • devising a plan,
   • carrying out the plan, and
   • looking back.

   If students do not know the meaning of words within test items, they cannot complete the problems successfully.  Encourage students to use correct mathematical vocabulary in discussion and in their writing.  Be sure students understand key action words typical of short answer and extended response questions, such as determine, identify, compare, contrast, explain, analyze, describe.  Such words are not typical of everyday speech.  Also note specialized math terminology used within the questions posed.  Ask students to define these in their own words.  You might be amazed at how many students have difficulty with the key action words and math vocabulary.  An analysis of the requisite language needed to complete a problem is at the root of student performance.

    

5. Next, students should review techniques for taking multiple choice and essay tests and how to deal with anxiety, such as those provided by Southwestern University: Preparation for a Successful Exam Day or at Study Guides and Strategies: Multiple Choice Tests.  Students need to know about the mechanics of test taking, such as distracters, adhering to time limits, working with bubble sheets, reading and following test directions, and using deductive thinking to eliminate incorrect answers.  They might begin their essays using graphic organizers to plan, write on every other line, which leaves room for revision when the response is reread. 

6. When students feel confident that they have mastered the objectives, they should take a few practice tests, such as:

• the online Sample Ohio Graduation Test in Mathematics developed by Holt, Rinehart, and Winston.  Other grade level tests are also available.
• the OGT Practice tests  located at the new portal for Ohio Statewide Testing, launched June 29, 2007.  The OGT Student Site also contains questions from recent tests, which are grouped by strands.  The benchmark associated with the question is presented. 
• sample tests released from other states. Links to these are available on CT4ME's Standardized Test Preparation page.

After all this preparation, remind students to get a good rest the night before and to eat a good breakfast on test day.  These strategies have given them the confidence they need to do well.

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Strand Resources

• Number, Number Sense and Operations
• Measurement
• Geometry and Spatial Sense
• Patterns, Functions and Algebra
• Data Analysis and Probability
• Mathematical Processes listed below are embedded in OGT questions, as they are in many states across the country.  Some states, such as California, have released test questions by strands and have also produced documents with selected questions from those strands involving mathematical reasoning. In Ohio, the video series What's the Problem, funded by eTech|Ohio,  targets critical thinking and problem solving and is listed below.

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Mathematical Processes

A.  Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.

B.  Apply mathematical knowledge and skills routinely in other content areas and practical situations.

C.  Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.

D.  Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.

E.  Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.

F.  Use precise mathematical language and notations to represent problem situations and mathematical ideas.

G.  Write clearly and coherently about mathematical thinking and ideas.

H.  Locate and interpret mathematical information accurately, and communicate ideas, processes and solutions in a complete and easily understood manner.

Mathematical Reasoning Resources

What's the Problem? --Reality Math for the Ohio Graduation Test is an intervention resource project funded by eTech|Ohio and produced by Ohio University students at the WOUB Center for Public Media.  This free series of eight 10-12 minute videos focuses on the uses of mathematics in the real world through parodies of different television reality shows.  The episodes are linked to grades 8-10 benchmarks in the Ohio Content Standards for Math (critical thinking/problem solving across the curriculum).  CT4ME is featured among the Teacher's Resources for these episodes.  Also see the complete teacher guide.

California (CAHSEE) Released Test Questions (Complete the section on mathematical reasoning and answers). 

References:

Gayler, K., Chudowsky, N., Kober, N., & Hamilton, M. (2003, August). State high school exit exams put to the test. Washington, D.C.: Center on Education Policy. Available under section: High School Exit Exams at http://www.cep-dc.org/ 

Ohio Mathematics Academic Content Standards. Available: http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=333&Content=13794 

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See strand resources:

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

See other pages of the section on Math Web Resources and Standardized Test Preparation: 

[ Standardized Test Preparation and Tips for Success (first  page)] 
[ Math Resources ] and [ Math Manipulatives ]