Middle School Math

• Name of Test: Middle School Education: Mathematics - Grades 5-9 (012)

  • 2 Hours and 45 min (includes 15min tutorial)

  • 80 multiple-choice questions

  • Average time per question: 1 minute 48 seconds

  • Passing score: 220 out of 300 points

  • You are not penalized for wrong answers--so if you are stuck, go ahead and guess

  • Fee: $73

  • Takes ~18 days to get score (to see score schedule, clear here then click “view score report dates")

  • Online Scientific Calculator and Formulas page is provided

  • Website

Copy and paste this framework into your study guide document. Highlight areas of least confidence red, medium confidence orange, and most confidence green.

Number and Operations - 19%

• Understand Numbers

  • Analyze the relationships between the subsets of the real numbers.

  • Understand the role of place value in any number system.

  • Analyze the use of estimation in a variety of situations.

  • Translate between different representations of numbers.

  • Apply number-theory concepts (e.g., divisibility rules, prime factorization, greatest common factors) in problem-solving situations.

• Understand Operations

  • Analyze relational and operational properties (e.g., multiplication and

  • division of fractions).

  • Analyze a variety of conventional and alternative algorithms.

  • Solve a variety of real-life and mathematical problems involving integers, fractions, and decimals, including exponents.

  • Solve a variety of real-life and mathematical problems involving ratios, proportions, unit rates, and percents.

Algebra and Functions - 36%

• Understand patterns, relations, and functions

  • Analyze patterns and relationships.

  • Analyze the properties of relations and functions in multiple representations (e.g., tables, graphs, equations, words).

  • Analyze direct and inverse proportional relationships.

  • Determine the effects of transformations on the graph of a function or relation.

• Understand algebraic techniques and applications

  • Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor).

  • Solve linear and nonlinear equations and inequalities.

  • Create algebraic expressions or equations that describe numbers or relationships.

• Understand linear relations and applications

  • Analyze the relationship between a linear equation or inequality and its representations

  • Solve systems of linear inequalities or equations with a variety of methods

  • Interpret the meaning of the slope and the y-intercept in various contexts

  • Analyze a variety of real-life and mathematical problems involving linear equations, systems, and inequalities

• Understand nonlinear relations and concepts of calculus

  • Analyze relationships between multiple representations of a nonlinear equation (e.g., quadratic, polynomial, exponential) or inequality.

  • Solve a variety of real-life and mathematical problems involving nonlinear equations and inequalities.

  • Demonstrate knowledge of the concepts of limit, continuity, and rate of change as they relate to function behavior.

  • Demonstrate knowledge of sequences and series and of recursive definitions.

  • Demonstrate knowledge of how concepts of calculus can be used to solve problems in real-life situations.

Measurement and Geometry - 27%

• Understand measurement principles, procedures, and applications

  • Reason quantitatively and use units and unit conversions to solve problems.

  • Calculate or estimate measures of lengths, areas, and volumes.

  • Apply the concepts of similarity, scale factors, and proportional reasoning to solve indirect measurement problems.

  • Analyze precision, accuracy, and rounding in measurements and computed quantities

• Understand Euclidean geometry in two and three dimensions

  • Analyze properties of points, lines, planes, and angles.

  • Use the properties of triangles, quadrilaterals, and other polygons and circles to solve problems.

  • Apply principles of similarity and congruence.

  • Understand and apply the Pythagorean theorem and its converse.

  • Visualize relationships between two-dimensional and three dimensional figures.

  • Analyze geometric arguments using deductive reasoning.

• Understand coordinate and transformational geometry

  • Analyze two- and three-dimensional figures using coordinate systems.

  • Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.

  • Analyze transformations of figures in the coordinate plane.

  • Analyze figures in terms of symmetry and tessellations of the plane

Statistics and Probability - 18%

• Understand principles and techniques of statistics

  • Analyze the effects of bias and sampling techniques.

  • Use appropriate formats for organizing and displaying data.

  • Analyze univariate and bivariate data in a variety of representations.

  • Make inferences and justify conclusions from data presented in a variety of representations (e.g., scatter plots).

  • Analyze the use of measures of central tendency and spread.

• Understand principles of probability and techniques for determining probability

  • Determine probabilities of simple and compound events.

  • Use counting principles (e.g., permutations, combinations) to calculate probabilities and solve problems.

  • Use a variety of visual representations to calculate probabilities.

  • Demonstrate knowledge of methods for simulating probabilities.

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Official MOCA test questions from the MOCA test developer:

• Free Sample Questions: http://www.mo.nesinc.com/Content/STUDYGUIDE/MO_SG_SRI_012.htm

• ***$29.95 The official full MOCA practice test.***

  • If you can only purchase one study resource, this is the one to pick. Though you can only take it twice, you can review the questions and answers anytime within 120 days of purchasing

Digital Materials the test development companies that make the MOCA and other content area tests:

• $24.99 NES Study Guide (select “Middle Grades Mathematics”)

  • The study guide portion does not have much study content (mostly it’s a list of possible topics), but there are lots of practice questions and the best part is that you can look up practice questions by topic

• $29.95 A practice test from NES which has a similar framework to the MOCA test: full NES practice test

Resources from online study sites:

• Free Practice Test (diagnostic, too): 240 Tutoring practice test

  • You can see your overall score without an account, but to see the diagnostic report you need to create a free account.

  • $39.99 They offer a monthly membership for study materials (materials, flashcards, quizzes, practice test)

• Free: Look up specific topics at https://www.khanacademy.org/

• Study.com membership $60 a month: Study.com math materials

• Free: Practice test made by SLU that mirrors types of questions and topics that will be found on the official test.

Print resources:

• ***Mometrix study book, created by a study guide company and aligns with the MOCA framework. Includes content by category and a practice test. The content can tend to be more surface level but it is a great resource, overall. An essential study resource.***

  • Free copy in SLU Pius library: MS Math 012

  • Free to borrow, SLU SOE has a couple copies, contact karissa.sywulka@slu.edu to see if one is available

  • $39.99-$72.99 Purchase your own through Mometrix or Amazon

• Free books at Pius library

  • There are teacher edition math textbooks that you can use to study specific topics. Ask Martha Allen for assistance.

• • Pius link if you want to request from interlibrary loan a colorful middle school math review book