# Mathematics for Elementary Teachers II

MTH 116W## Course Description

Prerequisite: MTH 115 or MTH 110 with a grade of "C" or better. Investigates problem solving, statistical charts and graphs, geometric figures and properties, and measurement systems including metric. Reviews fractions, decimals, percents, real numbers, their operations and properties. Reviews algebra of lines and equations. Includes a variety of learning styles using manipulatives, calculators and computer application. The National Council of Teachers of Mathematics Standards are incorporated. (45-0)

## Outcomes and Objectives

### Solve problems using various problem solving strategies.

#### Objectives:

- Define, illustrate, and utilize various problem solving strategies.

### Investigate elementary logic.

#### Objectives:

- Examine and utilize truth tables and deductive (direct) reasoning.

### Students will develop their skills in elementary probability.

#### Objectives:

- State and apply the definitions of experiment, event, outcome, and sample space.
- Explain what is meant by the probability of an event and distinguish between experimental and theoretical probability.
- Compute probabilities for events with equally likely outcomes.
- Use a tree diagram to represent the outcomes in a sample space.
- Draw Pascal’s triangle and be able to apply it in a binomial experiment.

### Students will develop their skills in geometry.

#### Objectives:

- Give analytical descriptions of various types of triangles.
- List several properties common to various types of triangles and quadrilaterals.
- Illustrate reflection and rotation symmetry of polygons, regular n-gons, and other shapes.
- Define and identify properties of points, rays, lines, planes, line segments and angles.
- Describe a) the interior of an angle; b) adjacent angles and ; c) how to measure an angle with a protractor.
- Explain and use the corresponding angles property, the alternate interior angles property and derive the angle sum in a triangle property.
- Determine the measures of central angles, vertex angles, and exterior angles in regular polygons and discuss the relationships among their measures.
- Describe and analyze tessellations with regular polygons.
- Identify the regular polygons that form tessellations of the plane.
- Define, compare and contrast parallel, intersecting, perpendicular and skew lines in space.
- Sketch or build and identify properties of polyhedra.
- Discover Euler’s formula for polyhedra.
- Sketch and identify properties of cones; cylinders; and spheres.

### Students will describe and perform conversions in various systems of measurement.

#### Objectives:

- State the three steps of the measurement process.
- Describe what is meant by informal measurement using non-standard units.
- Work with English system of measurement.
- Work with the Metric System
- Convert between Celsius and Fahrenheit systems of measurement.

### Communicate effectively about mathematics.

#### Objectives:

- Perform writing tasks to promote learning.

### Use technology appropriately to do mathematics.

#### Objectives:

- Define, explain, and utilize the terminology and resources necessary for the world wide web.
- Use and review software packages established for use in the elementary classroom for mathematics.
- Utilize a spreadsheet to perform calculations and to represent data in a statistical manner.
- Utilize the graphing calculator for graphing and data analysis.

### Examine the integration of mathematics and other curricula in the classroom.

#### Objectives:

- Investigate and utilize the literature available for easily integrating mathematics and literature at the K-8 level.
- Design integrated activities.

### Students will develop their skills with the calculator.

#### Objectives:

- Graph linear and quadratic functions with the calculator.

### Students will define, recognize, and understand concepts related to function.

#### Objectives:

- State the definition, the domain, range and codomain of a function.
- Describe the concept of function and represent functions in several ways.
- Construct and interpret graphs: linear, quadratic, exponential, cubic, and step functions.
- Apply the vertical line test to determine if a graph is the graph of a function.

### Students will develop their skill with handling exponents and integers.

#### Objectives:

- Explain the relationship between mulitiplication and exponentiation.
- Explain the meaning of a zero exponent.
- State the definition of rational exponent.
- State and apply properties of rational exponents.
- Represent integers with the chip (or changed ion) mode 1

### Students can solve a variety of equations and inequalities.

#### Objectives:

- State and apply the definitions of the following terms: equation, inequality, variables, solution, solution set.

### Students will develop their skills in using and graphing statisitics.

#### Objectives:

- Identify, give an example and interpret the following types of graphs: line plots, stem and leaf plots, pictographs, bar graphs, double bar graphs, frequency polygons, histograms, line graphs, circle graphs, box and whisker plots, double broken line graphs.
- Identify clusters and gaps (if they exist) on stem and leaf plots.
- Calculate the lower quaritle, upper quartile, the interquartile (IQR), and any outliers for a box and whisker plot.
- Discuss in writing how you would determine for all types of data collections the appropriate graph and be able to take the given date sets and graph using an appropriate graph.
- Describe and give examples of how graphs can be deceptive.
- Define and determine the following measures of central tenancy for given data: mode, median, and mean.

### Develop data analysis skills.

#### Objectives:

- Analyze data using statistical graphs.
- Examine measure of central tendency (mode, median, mean, variance, and standard deviation).
- Illustrate and compare the above measures by hand and using technology.