MATH105

Demonstrate effective pedagogy in elementary math education using manipulatives, modeling and problem solving strategies to help build connections to new knowledge.

Demonstrate proficiency in basic math skills with a 90% or better on timed competency exams; Multiplication, Division, Sign Numbers, Fractions, Decimals and Geometry.

Demonstrate conceptual understanding thru assessments, participation, discussion and engagement.

Demonstrate problem solving and critical thinking skills.

(Problem Solving) - Analyze and make sense of problems; look and extract key entry points; implement varying strategies; preserve and arrive at correct solution(s). Students will be able to analyze givens, constraints, relationships and goals, make conjectures, devise a plan and check solution(s). Student will be able to apply and demonstrate Polya's problem solving strategy to both simple and complex problem. Conceptualize and solve problem(s), construct drawings, create tables, model algorithms and identify, find and complete patterns.

(Sets and Reasoning) - Sort and classify according to attribute. Create sets; identify and list elements of a set; understand and find the union, intersection, complement or combination there. of using set notation, lists, written descriptions and/or Venn Diagrams. Illustrate and construct Venn Diagrams to represent given information. Understand and use stated assumptions, definitions and deductive reasoning to analyze, discuss, construct viable arguments and critique the reasoning of others. Write and identify conditional statements in the form of If P then Q. Make conjectures and use deductive reasoning to determine the validity of a conclusion based on its premises.

(Whole Numbers) - Represent a whole number using both base five and base ten pieces. Decipher ancient numeration systems and models for numeration. Use model algorithms to perform operation of addition, subtraction, multiplication, division on base five numerals and with base five pieces. Student will be able to compute operations using mental calculation and approximation.

(Number Theory) - Define, identify and list odd, even, prime and composite numbers. Determine whether a number is prime with the Prime Number Test algorithm and find all the prime numbers between 1-100 using the Sieve of Eratosthenes. Determine the divisibility of a number using divisibility tests without carrying out the division. Find the Greatest Common Factor and Least Common Multiple using prime factorization algorithms, specifically Factor Trees, Factor Ladders and Multiple listings.

(Integers and Fractions) - Define an integer and fraction, its origin and need. Identify the describe the parts of an addition, subtraction, multiplication and division (fraction) problem with correct terminology. Define a proper fraction, improper fraction and mixed number and give examples. Covert mixed numbers to improper fractions and an improper fractions to mixed numbers. Demonstrate the concept of integers and show operation on integers using the Chip Model, Number Line and Fraction Bars. Demonstrate the concept of fractions and operations on fractions using Part to Whole Concept, Fraction-Quoitent Concept and Ratio concept. Define and explain the meaning of PEMDAS. Solve/calculate an expression and equation using PEMDAS. Calculate using mental calculations and approximations.

(Decimal: Rational and Irrational Numbers)- Define a Rational and Irrational Number. State place value of each digit of a decimal. Show place value with Base Ten pieces and Decimal Squares. Perform operations, mental calculations and approximations on decimals. Convert a number from standard notation to Scientific Notation. Calculate percent using A = P and proportion method. Convert between a fraction, decimal and percent. Solve using the Pythagorean Theorem. Calculate the square and cube root of a number and how irrational numbers relate to roots. Perform operations on rational and irrational numbers.

(Algebra) - Define a variable, expression, equation and inequality, give examples of each. Use Algebra as a problem solving strategy. Locate and graph coordinates. Find the slope given a set of coordinates, a line or an equation. Define and graph a linear equation. Solve a system of equations by Elimination and Graphing. Determine the number of solutions to a system (one, zero or infinitely many), type of equations (dependent, independent), type of system (inconsistent, consistent) and what the system looks like graphically.

(Geometry) Use the fundamentals of geometry to classify regions, curves, polygons and figures and calculate angle measures.

(Measurement) - Distinguish between one, two and three dimensions. Use correct formulas to calculate perimeter, area, surface area and volume and give correct units.