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To prepare for teaching mathematics, Mathematics for Elementary Teachers I students will:

- Understand the number system and the concept of place values.
- Analyze the structures and properties of the base ten and other numeral systems, including numeration systems of ancient cultures.
- Recognize decimal expansions.
- Use scientific notation in an appropriate context.
- Analyze procedures (e.g., rounding, regrouping) for estimation.
- Determine whether estimates are reasonable.
- Identify subsets of real numbers and their characteristics.

- Understand integers, fractions, decimals, percents, and mixed numbers.
- Understand the meaning and models of integers, fractions, decimals, percents, and mixed numbers and apply them to the solution of word problems.
- Analyze and convert among representations of numbers (e.g., graphic, numerical, symbolic, verbal).
- Use number lines.
- Compare, sort, order, and round numbers.
- Recognize equivalent representations of numbers (e.g., fractions, decimals, percents).

- Understand and apply principles of number theory.
- Identify prime and composite numbers and their characteristics.
- Find and use the prime factorization of a number.
- Demonstrate knowledge of the divisibility rules and why they work.
- Find the least common multiple (LCM) and the greatest common factor (GCF) of a set of numbers.
- Use the LCM and GCF to solve problems.

- Understand operations of numbers.
- Understand the meaning and models of operations on real and rational numbers.
- Analyze and justify standard and nonstandard computational algorithms and mental math techniques (e.g., by application of the arithmetic properties, such as commutativity, associativity and distributivity).
- Evaluate the validity of nonstandard or unfamiliar computational strategies.
- Recognize and analyze various representations (e.g., graphic, pictorial, verbal) of number operations.
- Recognize relationships among operations (e.g., addition and subtraction, addition and multiplication, multiplication and exponentiation).
- Identify and apply the arithmetic properties and the transitive properties of equality and inequality.
- Apply the order of operations.
- Apply the laws of exponents.
- Demonstrate fluency in arithmetic computation, including operations with fractions.
- Interpret the concept of absolute value.
- Apply appropriate strategies (e.g., proportional thinking, ratios) to estimate quantities in diverse contexts.
- Solve problems using arithmetic operations with various representations of numbers.