Main Menu Units by Performance Expectation Units by Strand Units by Topic About the Capstone Course

Problem Solving, Decision Making, and Integration

Students will apply algebraic, geometric, and statistical concepts and the relationships among them to solve problems, model relations, and make decisions using data and situations within and outside of mathematics. To accomplish this goal, students will develop and enhance a repertoire of skills and strategies for solving a variety of problem types. The major goal of the mathematics performance expectations is for students to become competent mathematical problem solvers in contexts found in higher education coursework and postsecondary career or technical training.

  1. The student will solve practical problems involving rational numbers (including numbers in scientific notation), percents, ratios, and proportions.

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  3. The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.
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  5. The student will use pictorial representations, including computer software, constructions, and coordinate methods, and transformation.
    This will include

    a) investigating and using formulas for finding distance, midpoint, and slope;

    b) applying slope to verify and determine whether lines are parallel or perpendicular;

    c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

    d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

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  6. The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.

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  7. The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties
    of special right 
    triangles, and right triangle trigonometry.

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  8. The student will use formulas for surface area and volume of three-dimensional objects to solve real-world problems.

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  9. The student will use similar geometric objects in two- or three-dimensions to

    a) compare ratios between side lengths, perimeters, areas, and volumes;

    b) determine how changes in one or more dimensions of an object affect area and/or volume of the object;

    c) determine how changes in area and/or volume of an object affect one or more dimensions of the object; and

    d) solve real-world problems about similar geometric objects.

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  10. The student will compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.

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  11. The student will design and conduct an experiment/survey. Key concepts include
  12. a) sample size;

    b) sampling technique;

    c) controlling sources of bias and experimental error;

    d) data collection; and

    e) data analysis and reporting.

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  13. The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems,
    including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include Σ and an.
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  15. The student will use angles, arcs, chords, tangents, and secants to

    a) investigate, verify, and apply properties of circles;

    b) solve real-world problems involving properties of circles; and

    c) find arc lengths and areas of sectors in circles.

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