The Seven Objectives of the MTLE- Basic Math
I. Understand the principles of geometry
II. Apply principles of algebra to expressions and equations
III. Apply principles of algebra to linear and nonlinear functions
IV. Understand measurement concepts
V. Demonstrate knowledge of data, statistics, probability, and discrete math
VI. Understand mathematical processes and perspectives
VII. Understand numbers and the number system
Twenty-One Targets
I. Understand the principles of geometry (0015)
A. analyzing polygons using attributes of sides, angles, and parallel and perpendicular lines
B. analyzing three-dimensional figures using attributes of faces, edges, and vertices
C. applying geometrical transformations (e.g., translations, reflections, rotations) to geometric figures and using the concepts of symmetry, similarity, and congruence to solve problems
D. using coordinate geometry to analyze geometric figures
E. using algebraic methods (e.g., Pythagorean theorem, coordinate geometry) to solve mathematical and real-world problems
F. analyzing arguments and justifying conclusions based on geometric concepts
II. Apply principles of algebra to expressions and equations (0012)
A. analyzing and extending a variety of patterns
B. using the concepts of variable, equality, and equation to generate, interpret, and evaluate algebraic expressions based on verbal descriptions
C. manipulating algebraic expressions and solving equations using a variety of techniques (e.g., performing operations, simplifying, factoring)
D. applying algebraic principles to represent and solve word problems involving fractions, ratios, proportions, and percents
III. Apply principles of algebra to linear and nonlinear functions (0013)
A. distinguishing between relations and functions
B. translating between different representations (e.g., tables, verbal descriptions, equations, graphs) of linear and nonlinear functions
C. relating the characteristics of a linear equation (e.g., slope, intercepts) to its graph
D. selecting a linear equation that best models a real-world situation, and interpreting the slope and intercepts in the context of the problem
E. selecting a nonlinear function that best models a real-world situation
F. solving linear equations, systems of linear equations, and inequalities symbolically and graphically
G. analyzing the graph of a nonlinear function (e.g., quadratic, rational, exponential)
IV. Understand measurement concepts (0014)
A. estimating and calculating measurements using metric, customary, and nonstandard units, unit conversions, and dimensional analysis in real-world situations
B. applying formulas to calculate perimeter, circumference, length, area, surface area, volume, and angles for two- and three-dimensional figures in mathematical and real-world situations
C. estimating and calculating measurements indirectly using the Pythagorean theorem, ratios, proportions, and the principles of similarity and congruence
D. determining how the characteristics of geometric figures (e.g., area, volume) are affected by changes in their dimensions
E. solving a variety of measurement problems (e.g., time, temperature, rates of change)
V. Demonstrate knowledge of data, statistics, probability and discrete mathematics (0016)
A. using measures of central tendency (e.g., mean, median) and spread (e.g., range) to draw conclusions and make predictions from data
B. selecting appropriate ways to display data and statistical information (e.g., tables, circle graphs, histograms)
C. analyzing and drawing inferences from data presented in different formats (e.g., frequency distributions, percentiles, graphs)
D. calculating probabilities for simple, compound, independent, dependent, and conditional events described in various ways (e.g., word problems, tree diagrams, Venn diagrams)
E. identifying real-world applications of topics in discrete mathematics (e.g., graph theory, combinatorics, algorithms, iteration)
VI. Understand mathematical processes and perspectives (0017)
A. selecting an appropriate problem-solving strategy for a situation (e.g., estimation, drawing a picture, working backward, using manipulatives)
B. using mathematical reasoning and principles of logic to evaluate arguments (e.g., distinguishing between inductive and deductive reasoning, applying principles of logic, using counterexamples, evaluating informal proofs) and determining the reasonableness of solutions to problems
C. translating between verbal descriptions and mathematical language, notation, and symbols (e.g., function notation, set notation, order relations)
D. identifying connections between mathematical concepts, other academic disciplines, and technology
VII. Understand numbers and the number system (0011)
A. demonstrating knowledge of the properties of integers, rational and real numbers, and number operations
B. demonstrating fluency in computation, including operations on decimals, percents, fractions, and exponents
C. using number sense and different number representations to solve mathematical and real-world problems
