MAE3270 Module 10 - Lecture 2

Chapter 1: Inputs and Outputs

  • Introduction to inputs and outputs

  • Mapping consists of 3 components:

    • Set of input numbers

    • Rule for manipulating the numbers

    • Output numbers as the resulting pattern

  • Mapping is sometimes called a functional relationship

  • Input is said to be a function of the output

  • Three scenarios:

    • Given input and rule, find output

    • Given input and output, find rule

    • Given output and rule, find input

Order of Operations

  • Utilize BIMDAS: Brackets, Indices, Multiplication, Division, Addition, Subtraction

  • Calculate number sentences following the order of operations

  • Perform operations in the following order:

    • Brackets

    • Indices

    • Multiplication and Division (from left to right)

    • Addition and Subtraction (from left to right)

  • Division and multiplication have equal rank

  • Addition and subtraction have equal rank

Chapter 2: Variables Representing Numbers

  • Introduction to variables as a way of representing numbers using letters

    • Create algebraic expressions and evaluate them by substituting given values

    • Extend and apply laws and properties of arithmetic to algebraic terms and expressions

  • Working with linear and nonlinear relationships

    • Plotting points on the Cartesian plane

    • Solving simple linear equations

    • Investigating, interpreting, and analyzing graphs

  • Avoid the fruit salad approach

    • Example: 3a + 5b cannot be grouped together as 3 apples and 5 bananas

    • a and b can represent any number

    • Example: a = 3, b = 5, 3a + 5b = 9 + 25 = 34

  • Developing the idea of a variable

    • X being a variable is more sophisticated and powerful than representing an unknown number

    • Plenty of opportunities for students to use letters as algebraic symbols representing variables

  • Linking algebra and geometry

    • Using the Cartesian plane with XY coordinates

    • Number before the comma refers to the x-axis, number after the comma refers to the y-axis

    • Cartesian plane can be thought of as 2 number lines joined at right angles

    • Origin is the point in the middle with coordinate 0

  • Summary of algebraic thinking

    • Recognize, describe, and continue patterns

    • Use algebra to express generality, equality, and inequality

    • Describe linear and nonlinear relationships