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MTEL Elementary School Mathematics Test Breakdown

Number Sense, Operations and Data Analysis has six subareas with a total of 37 to 39 questions and counts 30percent of the final score.

1. Number Theory and Numeration Systems: properties and structure, place value, order relations, relationship between operations, factors and divisibility, prime and composite numbers, rational and irrational numbers, operations and their inverses, real number line, roots and powers, exponents, scientific notations, and theorems.
2. Integers: principles and operations; order and representation; identity and inverse elements; associative, cumulative and distributive properties; rounding and estimation; standard computational algorithms and their beginnings and development, operations and their inverses; integers; and algebra and solving problems using these concepts.
3. Fractions: principles, operations and representations; equivalent fractions; adding, subtracting, multiplying and dividing; comparison, ordering and estimation; placement on a number line; simplification, mixed and improper fractions; fractions and algebra; and solving problems using these concepts.
4. Decimals and Percents: principles, operations and representations; adding, subtracting, multiplying and dividing; ordering and placement on a number line; terminating and repeating; rounding and estimating; conversion between decimals, percents and fractions; decimals and algebra; and solving problems using these concepts.
5. Descriptive Statistics: collecting, organizing, reporting and analyzing data, tables, charts and graphs; measures of central tendency and dispersion; percentile scores; sampling techniques and methods for gathering and interpreting data; line of best fit; and inferences, interpolations and extrapolations from data.
6. Probability: fundamental principles, events and outcomes, permutations and combinations, calculating the probability of simple and compound events, simulations, geometry and probability, and models of real-world events.

Patterns, Relations and Algebra has five subareas with a total of 30 to 32 questions and counts 25percent of the final score.

1. Functions and Relations: patterns, properties and representations in numeric, geometric and tabular forms; change created by functions; iterative and recursive patterns; creating and interpreting graphs; and representations of relations.
2. Algebra: manipulation and simplification of expressions, equations and inequalities; variables; standard computational algorithms and algebra; direct and inverse relationships; solving equations; and inequalities and modeling situations using algebra.
3. Linear Relationships: properties, applications and functions; rate of change; direct variation; graphs, slopes and intersects of lines; finding the equation of a line; systems of linear equations and inequalities; and modeling and solving problems using these concepts.
4. Ratios and Proportions: properties and applications, relative and absolute relationships, direct variations, and writing and solving problems using these concepts.
5. Quadratic, Exponential, Polynomial and Rational Functions and Relations: properties and applications; methods of solving and roots of quadratic equations, graphs, exponential growth and decay; inverse variation; and modeling and solving problems using these concepts.

Geometry and Measurement has four subareas with a total of 30 to 32 questions and counts 25percent of the final score.

1. Measurement: principles, concepts and procedures; unit conversions; changing linear dimensions; measurement errors and rounding and solving problems involving length, perimeter, area, volume, mass, capacity, density, time, temperature, angles, rates of change, ratios and proportions; similar plane figures; and indirect measurements.

2. Euclidian Geometry: principles and properties and using them to prove theorems; axiomatic systems, terms and postulates; relationship between points, lines, angles and planes; proving triangles are congruent; characteristics of similar triangles; justification of geometric constructions; evaluating conjectures; and proving theorems.
3. Euclidian Geometry and Two and Three Dimensional Objects: applying and analyzing the relationship of triangles, quadrilaterals and other polygons; identifying plane figures, Pythagorean Theorem, right triangles and circles; composite shapes, cross sections and nets; and solving problems using common two- and three-dimensional objects.
4. Coordinate and Transformational Geometry: principles, properties, theorems and representations; distance, midpoint, slope and parallel and perpendicular lines; dilations, translations, rotations, reflections and glide-reflections; symmetry; tessellations,;transformations; and solving problems using these concepts.

MTEL Elementary School Mathematics Test Practice Questions