MAT156

Jane's Mathematics for Elementary Teachers I Mindmap

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MAT156

1. Chapter 2.2,2.3- Sets

1.1. Language of Set

1.1.1. set is understood to be any collection of object

1.2. One-to-one Correspondence

1.2.1. same number of elements

1.5.1. AㅌB

1.6.1. AㄷB

1.7. Set Intersection

1.7.1. A(opposite U)B

1.8.1. AUB

1.9.1. A-B

1.10. Properties of Set Operations

1.10.1. Associative Property

1.10.2. Distributive Property

2. Chapter 2.1- Numeration System

2.1.1. Flat=100

2.1.2. Long=10

2.1.3. Unit=1

2.2. Tally Numeration System

2.2.1. I, II, III, IIII, IIIII

2.6.1. I=1

2.6.2. V=5

2.6.3. X=10

2.6.4. L=50

2.6.5. C=100

2.6.6. D=500

2.6.7. M=1000

2.7. Base System

2.7.1. Base Five Numbers

2.7.1.1. ex) one two three base five

2.7.1.2. 124 five

2.7.1.2.1. (1x5^2)+(2x5^1)+(4x5^0)

2.7.1.2.2. 25+10+4

2.7.1.2.3. 39

3. Chapter 1.2- Explorations with Patterns

3.2. Arithmetic Sequence

3.2.1. an=a1+(n-1)d

3.3. Geometric Sequence

3.3.1. an=a1xr^n-1

3.4. Fibonacci Sequence

3.4.1. 1,1,2,3,5,8,13,21...

4. Chapter 1.1- Problem Solving

4.1. 4-Step Problem Solving

4.1.1. 1. Understand the problem

4.1.2. 2. Devising a plan

4.1.3. Carrying out the paln

4.1.4. Looking back

4.2. Gauss's approach

4.2.1. 1+2+3+...+999

4.2.1.1. 999+1=1000, 998+2=1000,...

4.2.1.2. 999 sums of 1000= 999x1000

4.2.1.3. divide by 2=499500

4.2.2. 1+3+5+...+103

4.2.2.1. 103+1=2n

4.2.2.2. n=52

4.2.2.3. 52x104/2

4.2.2.4. 2704

4.2.3. 33+34+35+...+120

4.2.3.1. 120+33=153

4.2.3.2. 120-33+1=88

4.2.3.3. divide 88 by 2=44

4.2.3.4. 44x153=6732

5. Chapter 3.3- Multiplication and Division of Whole Numbers

5.1. Mult. of Whole #

5.1.1.1. 3+3+3+3=12

5.1.2. The Array and Area

5.1.2.1. ㅁㅁㅁ ㅁㅁㅁ ㅁㅁㅁ

5.1.3. Cartesian-Production

5.1.3.1. AXB A,B =factor AXB =product

5.2. Property

5.2.1. cont.

5.2.2. Zero Mult.

5.2.2.1. ax0=0

5.2.3. Distributive

5.2.3.1. a(b+c)=ab+ac

5.3. Rules

5.3.1. Dividen/Divisor=quotient

5.3.2. n/0=undefined

5.3.3. 0/n=0

5.3.4. 0/0=undefined

5.3.5. PEMDAS

5.3.5.1. Parenthesis

5.3.5.2. Exponents

5.3.5.3. Multiplication Division

6. Chapter 3.2- Argorithms for Whole-Number Addition and Subtraction

6.1.1. manipulation

6.1.2. paper/pencil operation

6.1.3.1. carrying

6.1.3.1.1. 1 37 + 28

6.1.4.1. 3 5 6 + 5 6 7 0/1/1/ 8/1/3

6.1.4.2. 9 2 3

6.2. Subtraction Algorithms

6.2.1. base-ten

6.2.2. remove take-away

7. Chapter 3.1- Subtraction of Whole Numbers

7.1. Inverse Operation

7.1.1. Subtractions is inverse operation of addition

7.2. Models

7.2.1. Take-away

7.2.1.1. take away 3 blocks from 8

7.2.2.1. 3+___=8

7.2.3. Comparison

7.2.3.1. Me 3 blocks You 8 blocks

7.2.4. Number Line

8. Chapter 3.1- Addition of Whole Numbers

8.1. Set Model

8.1.1. Set A {a,b,c}

8.1.2. Set B {d,e}

8.1.3. A+B={a,b,c,d,e}

8.1.4. n(A)+n(B)=3+2=5

8.1.5.1. 1+2

8.1.6. Sum

8.1.6.1. =3

8.2. Number Line (Measurement) Model

8.2.1. Always start at ZERO

8.3. Ordering Whole Numbers

8.3.1. Greater than and Less than

8.4. Properties

8.4.1. Closure Property

8.4.1.1. If a and b are WHOLE NUMBERS, then a+b is a WHOLE NUMBER

8.4.1.2. 3+4=7

8.4.2. Commutative Property

8.4.2.1. a+b=b+a

8.4.2.2. ex) 1+2=2+1 3=3

8.4.3. Associative Property

8.4.3.1. (a+b)+c=a+(b+c)

8.4.3.2. ex) (1+2)+3=1+(2+3) 3+3=1+5 6=6

8.4.4. Identity Property

8.4.4.1. a+0=a

8.4.4.2. ex) 1+0=1

8.5.1. Counting On

8.5.1.1. 3+4=3,4,5,6,7

8.5.2. Doubles

8.5.2.1. 3+4 3+3=6 +1 Double +1

8.5.3. Making 10

8.5.3.1. 8+5 (8+2)+3 10+3

8.5.4. Counting Back

8.5.4.1. 9+7 (10-1)=7

8.5.5. Inductive Reasoning

8.5.5.1. Method of making generalizations based on observations and patterns

9. Chapter 3.4- Algorithms for Whole Number Multiplication and Division

9.1.1. 12x4

9.1.2. 10+2 x 4

9.2.1. 2 3 x 1 4

9.2.2. 9 2 2 3 0

9.4. DMSCB

9.4.1. Divide

9.4.2. Multply

9.4.3. Subtract

9.4.4. Check

9.4.5. Bring Down

10. Chapter 4.3- Functions

10.2. Input Output

10.2.1. What goes in

10.2.1.1. Horizontal

10.2.2. What comes out

10.2.2.1. Vertical

10.3. Function as Equation

10.3.1. f(0)=0+3=3

10.3.2. Domain Range

10.3.2.1. f(0)

10.3.2.2. 3

10.4. Table and Ordered Pair

10.4.1. 0 1 1 3 2 5 3 7

10.4.2. (0,1) (1,3) (2,5) (3,7)

10.5. Every Function is a Relation

10.5.1. not every relation is a function