 # Course Descriptions & Syllabi

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Areas of Study | | MATH119 syllabus

 COURSE NUMBER: MATH119 COURSE TITLE: Mathematics for Elementary Education II DIVISION: Sciences IAI CODE(S): M1 903 SEMESTER CREDIT HOURS: 3 CONTACT HOURS: 45 STUDENT ENGAGEMENT HOURS: 3 DELIVERY MODE: In-Person

COURSE DESCRIPTION:
The second of a two-course sequence (along with MATH 118). Together, these two courses are designed to help you develop the mathematical content knowledge necessary to effectively teach math at the elementary level. Emphasis is placed on structure, meaning, relationships, and types of thinking in elementary mathematics. This course focuses on measurement, geometry, statistics, and probability.

PREREQUISITES:
Grade of “C” or better in MATH118 (Mathematics for Elementary Education I) or equivalent.

NOTES: This course is not available for web registration.

STUDENT LEARNING OUTCOMES:
A student with at least 60% proficiency should be able to:
• Apply the use of all technology skills appropriate for the class, including the use of mathematical manipulatives
• Clearly demonstrate and explain the logical processes that lead one from an initial question (problem) to a correct answer (solution), using multiple modes of explanation (expressions, equations, charts, tables, diagrams)
• Convert between measurements (including 1-dimensional, 2-dimensional, and 3-dimensional aspects)
• Make predictions based on data
• Construct polygons and aspects of polygons given a compass and straightedge
• Prove why the sum of angles in a triangle is 180 degrees
• Use proper measurements for a given situation (including, but not limited to, units and differentiating between weight, volume, area, etc)
• Explain steps and solutions for mathematical concepts or processes, verbally and in writing, including
• Determining the area and perimeter of a given shape
• Determining the volume and surface area of solid (3D) shapes
• how geometric transformations affect images
• basic probability ideas
• Use all appropriate symbolic forms that elementary school students would encounter, verbally and in writing.
• Describe and explain basic geometry facts (including, but not limited to, angle calculation, definition of shapes, and circle properties)
• Explain how to determine the volume and surface area of solid (3D) shapes
• Explain how geometric transformations affect images
• Explain the criteria required for similar shapes/figures and then apply that to solving problems
• Evaluate basic statistical information, including performing calculations (examples: formulate good questions, sample information, centers of average, data distributions)
• Interpret data displays, including recognizing errors or misleading displays
• Create data displays
• Apply basic probability ideas to perform calculations and create solutions.
• Use appropriate mathematical terminology

TOPICAL OUTLINE:
• Geometry 4 hours
• Facts about angles to determine the value of unknown angles.
• Proofs of why the sum of angles in a triangle is 180°
• Definition of circles and spheres
• Using properties of circles to describe locations between points
• Definition of special quadrilaterals and various polygons
• Construction of polygons of given specifications using a compass and straightedge
• Measurement 6 hours
• Differences between measurements (weight, volume, area, etc)
• Using appropriate units for a given measurement
• Metric prefixes and converting between them
• Describing one, two, and three dimensional aspects of an object
• Precision with measurement reporting
• Converting measurements (one, two, and three dimensional)
• Area of Shapes 11 hours
• Describe the area of a general shape
• Determine and use the area formulas for a rectangle, a triangle, a circle, and a parallelogram
• Moving and additivity principles to determine area of shapes
• Determine areas of various polygons (other than the shapes listed above)
• Definition of pi
• Using grids to estimate the area of a shape
• Determine the perimeter of a shape
• Determine possible areas of a rectangle given a specific perimeter
• Prove the Pythagorean Theorem
• Use the Pythagorean Theorem to determine lengths/distances
• Volume and Surface area of solid shapes 6 hours
• Describe prisms, cylinders, pyramids, and cones
• Distinguish three dimensional objects from two dimensional shapes
• Determine the number of vertices, edges, and faces of a given type of prism or pyramid
• Visualize a shape from a pattern
• Create a pattern for prisms, cylinders, pyramids, and cones of specified dimensions
• Determine surface area of prisms, cylinders, pyramids, and cones
• Determine and use the volume formula for a prism and cylinder
• Determine the volume of an object by liquid displacement
• Motion and Changes 10 hours
• Determine the image of a shape after a translation, a reflection, or a rotation
• Determine the new coordinates of a point after a shape has been transformed across the x- or y-axis
• Determine the transformation applied given a “before and after” image
• Symmetries within a shape or design
• Define congruence
• Determine criteria for triangle congruencies
• Basic constructions with a straightedge and compass (perpendicular bisectors, bisecting an angle, etc)
• Define similar shapes
• Using similar shapes to solve applied problems
• Comparing areas/volumes of similar objects
• Statistics 6 days
• Formulating statistical questions
• Characteristics of good samples, sample sizes, random samples
• Using random samples to make predictions about a full population
• Make data displays
• Interpret information from data displays
• Recognize erroneous or misleading data displays
• Centers of data (mean, median, mode)
• Summarizing, describing, and comparing data distributions
• Probability 6 days
• Calculating probabilities in simple cases
• Applying empirical probability to make estimates
• Counting the number of outcomes (using multiplication)
• Calculating probabilities of compound events
• Calculating expected amounts
• Using fraction arithmetic to calculate probabilities

TEXTBOOK / SPECIAL MATERIALS:

Mathematics for Elementary Teachers. 5th Edition. Beckmann
Web access required
Compass, protractor, ruler

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

Students will be evaluated with homework, quizzes, chapter tests, instructional projects, and a comprehensive final examination.

 Tests Problem Sets Projects/Reflections Final Exam 50% 15% 15% 20%