# MTH 127 : Mathematics for Elementary School Teachers I

This course develops understanding of the mathematical content of number and operations at the deep level required for successful elementary school teaching in ways that are meaningful to pre-service elementary teachers. Topics include: place value and arithmetic models; mental math; algorithms; prealgebra; factors and prime numbers; fractions and decimals; ratio; percentage and rates; integers; and elementary number theory. Prerequisite: Intermediate Algebra Competency. Three lecture hours per week.
Gen. Ed. Competencies Met: Quantitative and Symbolic Reasoning.

## Course Outcomes

- Apply the properties of closure, commutativity, associativity, and identity to addition and multiplication of whole numbers.
- Represent subtraction of whole numbers using the take-away and missing addend approaches.
- Construct the addition and multiplication facts table for any base from 2 through 10 and read it “backwards” to find subtraction and division facts respectively.
- Perform all arithmetic operations in bases 2 through 12.
- Describe “less than” and “greater than” with whole numbers using the operation of addition.
- Describe multiplication of whole numbers using repeated addition and rectangular array approaches.
- Represent division of whole numbers using the missing factors and repeated subtraction.
- Explain division problems involving zero.
- Explain whole number exponents using repeated multiplication.

- Use the sieve of Eratosthenes to find prime numbers.

- State and apply the fundamental theorem of arithmetic.

- Apply tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.

- Find the prime factorization of a number to find all of its factors.

- Find the Greatest Common Factor and Least Common Multiple of any given pair of numbers using the prime factorization method.

- Determine equality of fractions.

- Express a fraction in the simplest form.

- Perform any arithmetic operation on rational numbers and integers, providing rationale for your computations.

- Solve applied problems involving ratios, proportions, and percents.

- Change any fraction to its decimal form and vice versa.

- Define and apply the distributive property of multiplication over addition.