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 Dependent Variable

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# Math Standards

1 = 4-yr
2 = 2-yr
3 = K12
4 = other

CONTENT components
Step 1. Assign the rating of “5” to the four components most important to include on the CRMT.
Step 2. Assign the rating of “1” to the four components least important to include.
Step 3. Based on these anchors, assign ratings 2, 3, and 4 to all other components.
 IMPORTANCE LEAST IMPORTANT somewhat moderately very MOST IMPORTANT 1 2 3 4 5

NOTE: Italic text = extra expectations

Standard 4: Number Sense -- The student accurately describes and applies concepts and procedures related
to real and complex numbers.

(2) 4.1. Understand the concept of real numbers.

4.1.a. Explain the meaning of the square root of a number, including why negative numbers have no real square
roots.
4.1.b. Describe a situation that requires an irrational number and provide an example of an irrational number.
4.1.c. Apply the definition for negative integer exponents of real numbers.
4.1.d. Represent real numbers with rational exponents.
4.1.e. Compare and order real numbers without a calculator using relationships between integers, and the
effects of radicals and rational exponents on those relationships.

(3) 4.2. Accurately and efficiently compute with real numbers in all forms, including rational exponents and scientific
notation.

4.2.a. Complete multi-step computations using the order of operations and the properties of operations
(associative, commutative, distributive, etc.) in situations involving combinations of real numbers.
4.2.b. Recognize and justify the need for an exact answer in a given situation.
4.2.c. Select and justify appropriate strategies and tools to compute the answer in a problem.

(4) 4.3. Apply estimation strategies using real numbers.

4.3.a. Recognize and justify the sufficiency of estimating or approximating the result of a calculation involving
real numbers.
4.3.b. Use estimation to predict or verify the reasonableness of calculated results.

(5) 4.4. Understand the concept of complex numbers and perform computations with complex numbers.

4.4.a. Add, subtract, multiply, and divide complex numbers; express in standard form and explain the properties
(i.e., why useful; when used).
4.4.b. Describe a situation that requires a complex number (include an algebraic example and a graphical
example).

Standard 5: Geometry -- The student makes hypotheses, models situations, draws conclusions, and supports
claims using geometric concepts and procedures.

(6) 5.1. Make and test conjectures about 2-D figures (polygons and circles) and 3-D figures (spheres, right prisms and
pyramids, right circular cylinders and cones), or figures constructed from these shapes.

5.1.a. Use physical, symbolic, and technological models to explore conjectures.

(7) 5.2. Represent the relevant features of a physical situation using 2-D figures with and without a coordinate system.

5.2.a. Use basic 2-D figures such as circles or polygons to represent objects essential to a situation.
5.2.b. Include additional line segments to represent important known or unknown distances.
5.2.c. Introduce a coordinate system when useful for describing the position of objects in a situation.

(8) 5.3. Use properties of and relationships between 2-D or 3-D figures to draw and justify conclusions about a situation
represented with such figures with or without a coordinate system.

5.3.a. Inductively generate a conjecture and deductively support it.
5.3.b. Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in
problem-solving situations.
5.3.c. Distinguish between area and perimeter of 2-D figures, surface area, and volume of 3-D figures.
5.3.d. Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons.
5.3.e. Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to
compute unknown distances.
5.3.f. Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders,
right prisms, right pyramids, and right cones.
5.3.g. Graph ellipses and hyperbolas whose axes are parallel to the x and y axes, and demonstrate
understanding of the relationship between their standard algebraic form and their graphical characteristics.

(9) 5.4. Recognize and apply the basic right triangle trigonometric relationships (sine, cosine, and tangent) to solve
problems.

5.4.a. Use sine, cosine or tangent to find unknown distances and angles.
5.4.b. Use the inverse of sine, cosine, or tangent to find the measure of a missing angle.
5.4.c. Understand the relationship of cotangent, secant, and cosecant to basic right-triangle ratios.
5.4.d. Use Law of Cosines and Law of Sines to solve problems.

Standard 6: Probability and Statistics -- The student accurately describes and applies concepts and
procedures from probability and statistics to analyze data.

(10) 6.1. Use empirical/ experimental and theoretical probability to investigate, represent, solve, and interpret the solutions
to problems involving uncertainty (probability) or counting techniques.

6.1.a. Describe and apply the concepts of complementary, mutually exclusive, independent, and compound
events.
6.1.b. Describe and apply procedures for computing and comparing theoretical probabilities and
empirical/experimental results.
6.1.c. Describe and apply procedures for counting techniques such as the Fundamental Counting Principle,
permutations, and combinations.

(11) 6.2. Develop informative tables, plots, and graphic displays to accurately represent and study data.

6.2.a. Use and interpret pie charts, bar graphs, histograms, box-and-whisker plots, scatter plots, stem and leaf,
and line graphs.
6.2.b. Analyze data displays to evaluate the reasonableness of claims, reports, studies, and conclusions.
6.2.c. Justify the use of appropriate graphical displays to accurately represent and study data.
6.2.d. Determine trends, predicted values and possible causes of skewed and clustered distributions.

(12) 6.3. Develop and evaluate inferences and predictions that are based on data.

6.3.a. Use measures of central tendency (mean, median, mode) and spread (range, quartiles) to summarize
data, draw inferences, make predictions, and justify conclusions.
6.3.b. Develop and conduct an investigation drawing appropriate conclusions through the use of statistical
measures of center, frequency, and spread, combined with graphical displays.

(13) 6.4. Create and evaluate the suitability of linear models for a data set.

6.4.a. Create, select, and justify an appropriate linear model for a given set of data.
6.4.b. Use reasonable models to make predictions and justify conclusions.
6.4.c. Recognize when arguments based on data confuse correlation with causation.