MAT1153

Essential Elements in Mathematics I

MAT 1153. Essential Elements in Mathematics I. (3-0) 3 Credit Hours. (TCCN = MATH 1350)

Prerequisite: MAT 1023 or MAT 1073. Numeration systems; properties of the systems of whole numbers, integers, rational numbers, and real numbers; problem solving; logic. May not be applied toward a major in mathematics. (Credit cannot be earned for both MAT 1153 and MAT 1143.) Generally offered: Fall, Spring, Summer. Course Fees: LRS1 $45; MFSM $30; STSI $21.

Date	Section	Topic	Prerequsite Skills	Student Learning Outcome
Example	Example	Problem Solving Introduction	Example	Explore and discuss multiple forms of representation, including concrete models, pictures, diagrams, tables, and graphs Explore mathematical reasoning from various points of view and a variety of appropriate strategies in problem solving
Example	Example	Patterns	Example	Recognize and generalize arithmetic, geometric and other numerical sequences
Example	Example	Sets	Example	Operate on sets using the following: union, intersection, complements, & set difference
Example	Example	Number Systems, Base 10, 5 and 2	Example	Understand the structure and use different number systems Use different models to represent and compare Whole numbers Use Base ten blocks to give different representations of any Whole number
Example	Example	Base 10, Base 2 & Base 5	Example	Use and compare different base numerical systems
Example	Example	Whole numbers addition models and properties	Example	Use different models to represent addition of Whole numbers (number line, sets…) Understand and master basic addition facts (counting on, doubles, make ten…) Understand and use models to justify the different properties of addition of whole numbers using models
Example	Example	Whole numbers subtraction models and properties	Example	Use different models to represent subtraction of Whole numbers (number line, sets…) Understand and use models to justify the different properties of subtraction of whole numbers using models
Example	Example	Addition Algorithms	Example	Use Base 10 blocks to develop the standard algorithm for addition of large whole numbers Use alternative algorithms (Expanded, left-to-right, lattice…)
Example	Example	Subtraction Algorithms	Example	Use Base 10 blocks to develop the standard algorithm for subtraction of large whole numbers Use alternative algorithms (Equal addends, Left to right…)
Example	Example	Cognitive Guided Instruction	Example	Recognize the different structures of basic addition and subtraction problems types Classify problem types differentiating between action (Join/Separate) and non-action (Compare/part-part-whole) problem types
Example	Example	Whole numbers multiplication models and properties	Example	Use different models to represent multiplication of Whole numbers (repeated addition, area model, cartesian product…) Understand the meaning of multiplication and structure of multiplication (number of groups x number of units per group = total number of units) Understand and justify the different properties of multiplication of whole numbers using models
Example	Example	Whole numbers division models and properties	Example	Use different models to represent division of Whole numbers (set model, repeated subtraction, missing factor model…) Understand and justify the different properties of division of whole numbers using models Understand the relationship between the four basic operations (addition, subtraction, multiplication and division)
Example	Example	Multiplication Algorithms	Example	Use Base 10 blocks to develop the standard algorithm for multiplication of large whole numbers Use alternative algorithms (Expanded, lattice, repeated addition…)
Example	Example	Division Algorithms	Example	Use Base 10 blocks to develop the standard algorithm for division of large whole numbers Use alternative algorithms (Expanded, short, repeated subtraction…)
Example	Example	Exponents	Example	Example
Example	Example	Number Theory	Example	Example
Example	Example	Divisibility	Example	Example
Example	Example	Divisibility Tests	Example	Example
Example	Example	Prime Numbers	Example	Use number-theory arguments to find whether a number is prime or composite
Example	Example	LCM & GCD	Example	Example
Example	Example	Addition and subtraction of integers	Example	Use different models to represent, compare, add and subtract integer numbers (chip/charge model, number line...) Understand and justify the different properties of addition and subtraction of integer numbers using models
Example	Example	Multiplication and division of integers	Example	Use different models to represent multiplication and division of integer numbers Understand and justify the different properties of multiplication and division of integer numbers using models
Example	Example	Fractions meaning and models	Example	Example
Example	Example	Equivalents Fractions	Example	Example
Example	Example	Addition and subtraction of fractions	Example	Use different models to represent addition of Rational numbers (number line, area model…) Add and Subtract fractions using multiple strategies
Example	Example	Multiplication and division of fractions	Example	Use different models to represent multiplication and division of Rational numbers (number line, area model…) Multiply and Divide fractions using multiple strategies
Example	Example	Real Numbers (Rational vs. Irrational Numbers)	Example	Describe and apply real number concepts such as rational and irrational numbers and their decimal representations
Example	Example	Models and basic operation with decimals	Example	Work flexibly with decimals and use basic operations to solve problems, compare and order decimal numbers, and find their locations on a number line
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