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Mathematics Competencies Tested on the MTLE

The MTLE Mathematics Subtest test covers five major skill areas with each skill area addressing a number of sub-skills. An outline showing these skill areas and their major sub-skills is shown below.

0001 Understand number properties and number operations.

• Demonstrate knowledge of place value and the relative magnitude of numbers.
• Use addition, subtraction, multiplication, and division of whole numbers in multidigit computations.
• Identify equivalent ways of representing integers, fractions, decimals, and percents, including the use of exponents and scientific notation.
• Apply operations with positive and negative integers, fractions, decimals, and percents.
• Solve word problems involving integers, fractions, decimals, percents, ratios, and proportions.

0002 Understand fundamental principles of algebra.

• Evaluate algebraic expressions by substituting numbers for variables.
• Solve linear algebraic equations and inequalities in one variable.
• Identify equivalent algebraic expressions.
• Graph ordered pairs and number relationships presented in tabular or symbolic form.
• Identify the linear equation that best represents data presented in tabular or graphic form.

0003 Understand measurement principles and geometry concepts.

• Identify a measurement or measurement unit needed to solve a problem.
• Convert units within and between standard and metric measurement systems.
• Solve problems involving lines, line segments, and angles.
• Analyze fundamental properties of triangles, quadrilaterals, and circles.
• Solve problems involving the length, perimeter, and area of basic shapes and the surface area and volume of rectangular solids.
• Solve real-world problems involving basic measurement and geometric concepts, including the Pythagorean theorem.

0004 Understand probability and statistics.

• Calculate the probability of a given outcome.
• Analyze information presented in tables, line graphs, scatter plots, pictographs, bar graphs, histograms, and pie charts.
• Recognize the appropriate graphic representation of data.
• Compute and interpret the mean, median, and mode of data.
• Demonstrate knowledge of the concepts of range, standard deviation, and spread.
• Recognize appropriate and inappropriate uses of basic statistics.

0005 Understand problem solving, reasoning, and mathematical communication.

• Estimate the solution to a given problem.
• Evaluate the reasonableness of a solution to a given computation or problem.
• Use algorithms (i.e., a set of instructions) to perform a given calculation or solve a given problem.
• Use inductive reasoning to identify missing terms in numerical and graphical patterns.
• Use deductive reasoning to draw conclusions and evaluate arguments.
• Translate between written English and mathematical terminology, concepts, and notation.

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