MTH 116W - Mathematics for Elementary Teachers II

1. Demonstrate agility in solving mathematical or statistical problems with the use of a graphing calculator or technology.
        A. Use a graphing calculator for computation, graphing (linear, quadratic,cubic, exponential, statistical graphs) and data analysis.
2. Demonstrate agility in solving mathematical or statistical problems without the use of a graphing calculator or technology.
   1. Solve computation, graphing (linear, quadratic, cubic, exponential, statistical graphs) and data analysis problems without the use of a graphing calculator or technology. 
3. Solve non-routine problems using a variety of problem-solving strategies.
   1. Use strategies such as: look for a pattern, make a list, use a variable, draw a diagram, direct and indirect reasoning, properties of numbers, symmetry, etc.
4. Demonstrate an understanding of concepts related to a function.
   1. Define and recognize functions, relations, domain, range, and codomain.
   2. Use the vertical line test for functions.
   3. Provide multiple representations of a function.
   4. Construct and interpret graphs:linear, quadratic, exponential, cubic, and step functions.
5. Demonstrate an understanding of the properties of integers.
   1. Use the number line and the chip model to justify properties of integers.
   2. Explain why division by zero is undefined.
6. Demonstrate an understanding of rational exponents.
   1. Use rational exponents.
   2. Explain exponential notation.
   3. Justify the rules for exponents, including the zero exponent.
7. Demonstrate an understanding of statistical concepts.
   1. Graph and interpret:circle graphs, stem and leaf plots, line plots, bar graphs, histograms, boxplots.
   2. Recognize outliers in graphs.
   3. Determine an appropriate graphical model for a given set of data.
   4. Use measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation).
   5. Use z-scores and normal distributions.
8. Demonstrate an understanding of elementary probability.
   1. List the sample space of an experiment.
   2. Distinguish between experimental and theoretical probability.
   3. Apply the addition and multiplication rules of probability; use a tree diagram.
   4. Apply Pascal's triangle to a binomial experiment.
9. Demonstrate an understanding of geometry and measurement.
   1. Describe and use properties of polygons.
   2. Explain the minimum characteristics needed to describe a type of triangle or quadrilateral.
   3. Solve problems using reflection and rotation symmetry.
   4. Solve problems involving regular polygons, tessellations, and circles.
   5. Use the vocabulary of geometry including, but not limited to, points, lines (parallel, intersecting, skew), planes, rays, adjacent angles, alternate interior angles, vertex angles, interior angles, and exterior angles.
   6. Derive the rule for the sum of the interior angles of a triangle.
   7. Solve problems using the properties of the angles (central, vertex, exterior) of a regular polygon; discuss relationships among the angles.
   8. Identify the regular polygons that can form tessellations of a plane.
   9. Identify properties of polyhedra; justify Euler’s formula for polyhedra.
   10. Identify properties of cones, cylinders, and spheres.
   11. Solve problems involving perimeter, area, and volume.
10. Communicate effectively about mathematics and statistics.
    1. Use writing to communicate an understanding of the concepts listed in items #1-8 above.