MTE 280 Concepts

Honelako gehiago

Long Division

by Drew Lodermeier

Matric

by NORGADILAH SHAARI

Elements, Compounds and Mixtures

by Batbold Enkhlin

Elementary MathematicsmMAT156 FALL2012

by Laura Jaramillo

MTE 280 Concepts

Week 4

Multiplication Algorithms

1. American Standard
2. Expanded Notation

10

23=20+3

x14=10+4

+100 +90+2

200 +30+0

=300+20+2

=322

3.Place Value

Division Algorithims

1. American Standard Algorithm ( long division)
2. Place Value Explicit (use pictures/diagrams)
3. Alternating Algorithm (boxes example)

Week 2

Expanded Notation

Expanded Notation

Convert 375 to expanded notation

375= 300+70+5

= (3x100)+(7x10)+(5x1)

=(3x10^2)+(7x10^1)+(5x10^0)

Base-5

Convert 212base 5

ex 212base5=(2x5^2)+(1x5^1)+(2x5^0)

=(2x25)+5+2

=50+5+2

=57

Convert 31 to a base 5

31=111^5

Numeration Systems & Bases

Base-10:

ones 10^0

tens 10^1

hundreds 10^2

thousands 10^3

Base-5:

ones 5^0

fives 5^1

25s 5^2

125s 5^3

Ex: Base 9---> 12

1 group of 9s, 3 groups of 1s

=13base9

Week 5

Subtraction Algorithms

1. American Standard
2. European/Mexican
3. Reverse Indian
4. Left to Right
5. Expanded Notation
6. Integer Subtraction

Addition Algorithims

1. American Standard (right to left)

576

+279

=855

2.Partial Sums

3.Partial Sums with Place Values

4.Left to Right

576

+279

=700

+140

+15

=855

5.Lattice

6.Expanded Notation

Week 3

Properties of Addition, Subtraction, and Multiplication

Addition Properties

Identity Property:

a+0=a

ex: 4+0=4

Commutative Property:

a+b=b+a

4+3=3+4

Associative Property:

(a+b)+c=a+(b+c)

(2+3)+5=2+(3+5)

Subtraction Properties

Comparison: neither subtraction or addition

Missing Addend:

3+_x_=7

Multiplication Properties

Identity Property:

ax1=a

ax0=0

Commutative Property

AxB=BxA

Associative Property:

(axb)xC=ax(bxc)

Distributive Property

ax(b+c)=

3x7=3x(5+2)=(3x5)+(3x2)

Other Base Systems

Base-3:

ones 3^0

threes 3^1

nines 3^2

27s 3^3

1212base3=(1x3^3)+(2x3^2)+(1x3^1)+(2x3^0)

=(1x27)+(2x9)+3+2

=27+18+3+2

=50

Base-8:

ones 8^0

eights 8^1

64s 8^2

Week 1

G. Polya Steps

G. Polya Steps

1. Understand the Problem-make sure you know how to solve
2. Devise a Plan- decide on different strategies
3. Carry out Plan-implement strategy solve
4. Look Back at Problem and Check- check if answer is reasonable

Problem Solving

G. Polya Steps

Devise Plan

-What problem solving strategy are you going to use?

-guess and check/trial and error

-draw a picture

-make a table

Carrying out plan

-easier than devising plan

-be patient and persistent

-try a different strategy if one doesn't work

Look back and Check

-Does answer make sense?

-Did you answer all the questions?

-Could you have solved it differently?