MAT 156 Math Instruction

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MAT 156 Math Instruction

Fractions

Vocabulary

Denominator

Numerator

Fraction

Part

Whole

Adding & Subtracting Fractions

1/2 + 1/2 = 1

Fraction Bars

Equivalent Fractions

3/4 = 6/8 = 12/16

Decimals to Fractions, etc.

Rounding Fractions

4 6/7 + 5 2/9 =

5 + 5 =

Fraction Diagrams

-3...-2...-1...0...1...2...3

3-D Example

2-D Parts of a Whole

Functions

Evaluate a Function

Arrow Diagram

Make a Table

f(x) = x+2

f(3) = (3) + 2

f(2) = (2) + 2

f(1) = (1) + 2

Graph

Equation

Ordered Pairs

Understanding Multiplication & Division

Long Division

Circle

B

Bring down

Check if less

Subtract

Multiply

Divide

Repeated Addition

3 x 4 = 3+3+3+3

Inverse Operations

Addition is the inverse of subtraction

Multiplication is the inverse of division

Venn Diagrams

Finding the nth Term

Number Sequences

Geometric

multiplication/division

an = a1r^n-1

Fibonacci

previous term + current term = next term in the sequence

1, 2, 3, 5, 8, 13...

Arithmetic

addition/subtraction

an = a1+(n-1)d

Understanding Addition and Subtraction

Manipulatives, then Paper & Pencil

number line

tens

doubles

take away models

counting blocks

fact families

counting back/on

Subtraction of Whole Numbers

Adding & Subtracting Integers

Equations

5 + (-6) = -1

Number Line

Chip Model

Least Common Multiple & Greatest Common Denominator

Prime Factorization

Ladder Method

Number Line

Intersection of Sets

40: 1, 2, 4, 5, 8, 10

32: 1, 2, 4, 8, 32

20: 1, 2, 4, 5, 20

Prime & Composite Numbers

Color Map

Subtopic

Factor Trees

Rainbow

Order of Operations

Properties

Closure

Identity

of Zero - addition/ multiplication

of One - addition/mulitiplication

Distributive

Commutative

Associative

S

Subtraction

A

Division

Multiplication

E

Exponents

P

Parenthesis

Simple Vocabulary

function

f(x)=x+2; (1,3)(2,4)(3,5)

Every domain (input, x) has exactly one range (output, y)

division

quotient

diviisor

dividend

multiplication

product

factors

subtraction

minuend

subtrend

difference/remainder

Addition

sum

addends

One-to-One Correspondences

Outfit example:

2 pants & 2 shirts = 6 possible outfits

Make a table or tree

Brown - brown/yellpw, brown/red, brown/green

Blue - blue/yellow. blue/red, blue/green

2 pants = blue, brown; 3 shirts = yellow, red, green

Numeration Systems

Chinese

Bases

Tally Marks

Arabic

Roman Numerals

M

= 1,000

D

= 500

C

= 100

L

= 50

X

= 10

V

= 5

I

= 1

Main topic

Sum of Sequential Numbers

Odd

S = 1+3+5+7...+101

Even

S = 2+4+6+8+...+100

Normal Sequence

S = 1+2+3+4+5...+100

S = 5,050

S = (100 x 101)/2

2S = 100 x 101

So there are 100 sums that equal 101

1+100=101, 2+99 =101, 3+98=101...

Polya's 4 Steps to Solve a Problem

Examples of Problem Solving Plans

indirect/direct resasoning

guess & check

identify a subgoal

make a table/diagram

working backwards (input/output problem)

equations

4 Steps

Look Back

Carry Out the Plan

Devise a Plan

Understand the Problem