Jun 06, 2023
MATH 130 - Elements of Mathematics I: Mathematical Reasoning and Number Systems
An examination of mathematical reasoning, problem solving, and sets. Topics include concepts and processes involving numeration systems, whole numbers, number theory, integers, and rational numbers. Intended for elementary education majors. PRE- or COREQUISITE(S): Appropriate score on mathematics assessment test, a grade of C or better in MATH 050 , or concurrent enrollment in MATH 030 , or consent of department. Assessment Level(s): ENGL 101 /ENGL 011 or AELW 940 /ELAI 990 , READ 120 or AELR 930 /ELAR 980 . Four hours each week.
4 semester hours
Upon course completion, a student will be able to:
- Communicate mathematical ideas effectively using appropriate vocabulary and grammar.
- Demonstrate the intricacy of counting, including the distinction between counting as a list of numbers in order and counting to determine a number of objects.
- Illustrate how the base-ten place value system relies on repeated bundling in groups of ten using varied representations.
- Explain how efficient base-ten computation methods for addition, subtraction, multiplication, and division rely on decomposing numbers represented in base ten according to the base-ten units represented by their digits and applying (often informally) properties of operations to decompose a calculation into parts.
- Use drawings or manipulative materials to reveal and explain the rationale behind computation methods for whole numbers and decimals.
- Extend the base-ten system to decimals, view decimals as address systems on number lines, and explain the rationale for decimal computation methods.
- Explain and apply the standard arithmetic algorithms as well as alternate algorithms for whole number operations.
- Represent fractions on a number line and as numbers using area, set models, and lengths.
- Recognize that addition, subtraction, multiplication, and division problem types and associated meanings for the operations extend from whole numbers to fractions.
- Apply reasoning to compare numbers in base ten and fractions.
- Explain the rationale for defining and representing equivalent fractions and procedures for adding, subtracting, multiplying, and dividing fractions.
- Employ pictorial models to represent fractions, equivalent fractions, and arithmetic with fractions.
- Write, classify and solve application problems using addition, subtraction, multiplication, and division, and illustrate the meanings of the operations illustrated by these problem types.
- Demonstrate the teaching/learning paths for single-digit addition and associated subtraction as well as single-digit multiplication and associated division, including the use of properties of operations.
- Demonstrate, apply, and explain basic concepts of number theory.
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