May 29, 2023
MATH 131 - Elements of Mathematics II: Geometry and Algebra
This course covers proportions, percents, and real numbers; basic geometry that includes congruence, similarity, symmetry, and transformations; measurement and coordinate geometry; and algebra emphasizing multiple representations. Intended for elementary education majors, this course is also suitable for parents of school-age children. PREREQUISITE(S): A grade of C or better in MATH 130 or consent of department. Four hours each week.
4 semester hours
Upon course completion, a student will be able to:
- Reason about how quantities vary together in a proportional relationship, using tables, double number lines, and strip diagrams as supports.
- Distinguish proportional relationships from other relationships, such as additive relationships and inversely proportional relationships.
- Employ different methods for solving problems involving proportions and percents.
- Employ procedures for mental computation and estimation of percents.
- Use unit rates to solve problems and to formulate equations for proportional relationships.
- Use pictorial models to represent proportions and percents.
- Illustrate the connection between fractions and division, and how fractions, ratios, and rates are connected via unit rates.
- Recognize algebraic reasoning in elementary mathematics.
- Apply processes of reasoning to identify, solve, manipulate, and/or evaluate expressions, equations, and systems of equations.
- Translate among multiple representations of a function.
- Recognize various representations and change patterns of linear and non-linear functions.
- Solve problems with tables, graphs, and equations.
- Find and describe patterns including finding the nth term of a sequence.
- Explain, apply, and connect the general principles of measurement, the process of iterations, and the central role of units
- Explain area and volume and give rationales for area and volume formulas that can be obtained by finitely many compositions and decompositions of unit squares or unit cubes.
- Explain common metric benchmarks for length, mass, and capacity and make conversions within the metric system.
- Develop basic area formulas and the Pythagorean Theorem in a deductive sequence and use these formulas to compute area and length.
- Describe, compare, classify, and draw plane and space figures.
- Explain the relationship among the formulas for the volume of prisms, cylinders, pyramids, and cones.
- Use nets to explain how to find the surface area of prisms and cylinders.
- Reason about proportional relationships and similarity.
- Perform rigid motions and relate them to congruence, symmetry, and similarity.
- Explain the sum of angle measures in a polygon and compute the measures of specific angles.
- Perform basic compass constructions and explain why they work.
- Use technology to study plane figures.
- Interpret statements that use geometric terminology.
- Prove or disprove conjectures about geometric shapes.
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