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.