# 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
• 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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