MTE 280 Concepts

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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?