MAT156

Jane's Mathematics for Elementary Teachers I Mindmap

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MAT156 by Mind Map: 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

1.3. Equivalent Sets

1.4. Cardinal Numbers

1.5. Sets

1.5.1. AㅌB

1.6. Subsets

1.6.1. AㄷB

1.7. Set Intersection

1.7.1. A(opposite U)B

1.8. Set Union

1.8.1. AUB

1.9. Set Difference

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. Hindu-Arabic 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

2.3. Egyptian Numeration System

2.4. Babylonian Numeration System

2.5. Mayan Numeration System

2.6. Roman Numeration System

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

3.1. Inductive Reasoning

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...

3.5. Other Sequence

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. repeated Addition

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

5.3.5.4. Addition Subtraction

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

6.1. Addition Algorithm

6.1.1. manipulation

6.1.2. paper/pencil operation

6.1.3. regroup/trade problems

6.1.3.1. carrying

6.1.3.1.1. 1 37 + 28

6.1.4. Lattice Algorithm for Addition

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

6.3. Equal-Addition Algorithms

6.4. Understanding Addition and Subtractions in Bases Other than ten

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. Missing Addend

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. Addend

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. Addition Facts

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. Single x 2 digits

9.1.1. 12x4

9.1.2. 10+2 x 4

9.2. Two Digit Factors

9.2.1. 2 3 x 1 4

9.2.2. 9 2 2 3 0

9.3. Lattice Mult.

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

10.1. Each element of A is paired with exactly one element of B

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