MTE 280 (2)

MTE 280

Week 5: Algorithms

Thursday: Exam 1

Tuesday: Add.,Sub.,Mult.,Div.

Addition algorithms

1. American Standard

• right to left
• No reference to place value
• This is the last step

1. Partial sums

• add the partial sums with Use of columns
• No reference to place value
• Right to left

1. Add place value to partial sums

• talk about the Values being added
• Right to left
• Reference to place value with columns

1. Left to right

• solve the equation from left to right using place values

1. expanded notation

• use expanded notation and knowledge of place values to solve equation

1. Lattice Method

• The numbers are written in columns to find the final sum

Subtraction algorithms

1. American Standard

• Left to right

1. reverse Indian

• left to right
• No reference to place value

1. left to right

• add place value
• Adjust numbers for borrowing

1. expanded notation

• use expanded notation and knowledge of place values to solve the equation

1. integer sub algorithm

• using integers , Positive and negative numbers
• use place values

Multiplication algorithms

1. American Standard
2. Place value
3. Expanded notation
4. lattice Method

Week 4:

Thursday: Algorithms

Division:

there are three different signs to division

There is a divisor quotient dividend, and remainder

Long division algorithm:

Teach this when students can explain what they are doing with the method of place values with manipulative. you turn the remaining hundreds into tens and turn the remaining 10’s into 1’s

And alternative algorithm you can use is by asking yourself how many boxes can fit into the number given

Tuesday: Operations

Additional meaning and properties

Identity: a+o=a *When I add zero to any number, the number does not change

Commulative: a+b=b+a *The order does not matter

Associative: (a+b)+c = a+(b+c) * the way you group does not matter

Subraction:

1. take away 4-3=1
2. comparison
3. missing addend

as adults, we subtract, as kids, we add

Multiplication

3x4: 3 groups of 4

3 and 4 are factors ,12 is the product

repeated addition:

telling time

SKIP counting

Cartesian product: combining groups

Properties:

1. identity ax1=a when I multiply by one, the identity does not change
2. Commutative: Order axb=bxa The order in which I multiply does not matter
3. Associative: grouping (axb)xc=ax(bxc) The way we group the problems is not matter
4. zero: Any number multiplied by zero equals zero
5. distributive: When I multiply a number by the sum of two other numbers, it is the same as multiplying the number by each addend

Week 3:

Thursday: Numeration Systems

Continuation numeration systems

base-2:

ones-2^0

twos-2^1

fours-2^2

eights-2^3

sixteens-2^4

digits: 0,1

practice: 1111 base 2= (1x2^3)+(1x2^2)+(1x2^1)+(1x2^0)=15

1. 43 base 3 > 25 base 5
2. 4 base 5 = 4 base 6
3. 111 base 2 = 7
4. 100 base 2 < 18 base 9

Tuesday: Numeration Systems

Continuing numeration systems

base-3:

ones- 3^0

threes-3^1

nines-3^2

27’s-3^3

practice:

1222 base 3= ((1x3^3)+(2x3^2)+(2x3^1)+(2x3^0)=53

Base 5 Digits Used: 0, 1, 2, 3, 4 Expanded: ones 5^01 1 1 base 5 fives5^1| | ones 25s 5^2 l fives

125s

5^3 25s

111 base 5: (1×5^2) + (1 x511) + (1 x510)

111 base 5: (1 x 25) + (1 x 5) + (1 x 1)

111 base 5:25 + 5 + 1 = 31

1023 base 5: (1 x 513) + (0 x 5^2) + (2 x 511) + (3 x 510)

1023 base 5: (1 x 125) + (0 x 25) + (2 x 5) + (3 x 1)

1023 base 5: 125 + 0 + 10 + 3 = 138

Use Manipulatives to help you

XX XX XX XX

XX XX XX XX

XX X

Week 2

Thursday: Numeration Systems

Numeration Systems: A way of recording quantity

Base-10 system/decimal system

Numbers get value from the place they sit

• 1-10 relationship between places
• 1-10 relationship is always there

Digits used in Base-10: 0,1,2,3,4,5,6,7,8,9

Expanded Notation: 375

300+70+5=375 =(3x100)+(7x10)+(5x1)= (3x10^2)+(7x10^1)+(5x10^0)

Example:

1078 = 1000 + 0 + 70 + 8

1078 = (1 x 1000) + (0 x 100) + (7 x 10) + (8 x 1)

1078= (1 x 1013) + (0x10^2) + (7×1011) + (8 x 1010)

Base-5:

ones- 5^0

fives- 5^1

25’s- 5^2

125’s- 5^3

digits used in base-5: 0,1,2,3,4

Base-10:

ones- 10^0

tens- 10^1

100’s- 10^2

1000’s- 10^3

practice:

111 base 5: (1×5^2) + (1 x511) + (1 x510)

111 base 5: (1 x 25) + (1 x 5) + (1 x 1)

111 base 5:25 + 5 + 1 = 31

1023 base 5: (1 x 513) + (0 x 5^2) + (2 x 511) + (3 x 510)

1023 base 5: (1 x 125) + (0 x 25) + (2 x 5) + (3 x 1)

1023 base 5: 125 + 0 + 10 + 3 = 138

practice: 375. 25

Related to Money:

• 3 $100 bills
• 7 $10 bills
• 5 $1 bills
• 2 dimes
• 5 pennies (1/10 of a dime)

Tuesday: Problem Solving

Problem Solving:

George Polya “How to Solve it”

1. understand
2. Devise plan
3. Carry out
4. Look back

Use children in practice problem as manipulatives and act the problem out

one person cancels out every time

find patterns

make combinations

organize info to find patterns

Week 1

Thursday: Problem Solving

Problems Solving:

1. understand
2. devise plan
3. implement plan

Practice Problems: Time and Manipulatives

1. look back and ask if it is reasonable
2. work backwards

Tuesday: Intro to MTE 280