Emphasis on Place Value, place of digit determines exponent

Expanded Notation: 375=300+70+5, hundreds, tens, ones

Helpful to think of it as dollars/coins

Bases 5,3,2 (computers/binary)

Important to think of digits as individual numbers

Digit cannot be larger than base

Youtube Video: https://www.youtube.com/watch?v=wtrrr15mbvQ

Three different symbols: division sign, fraction, and vinculum

Three parts to division sentence: answer=quotient, inside vinculum=dividend, outside vinculum= divisor

Using Cookies (Circles) for Smaller #'s

Long Division: Hardest for elementary level; start with visuals

Using Boxes & Magnets: Best for visual learners, emphasis on PV

Standard: Cookie Boxes Analogy, adding the amount of boxes as you go through the problem to get final answer

3 main methods of solving a multiplication problem: memorization, repeated addition, skip counting

Number lines* help determine which digit goes where in a multiplication sentence (*tip, use numberline on floor for students to jump over in classroom)

Clock is a good example of multiplying by 5's to count time

Arrays are best for visual learners (color each amount/digit from multiplication sentence)

Commutative: Order of numbers will not change answer

Identity: # multiplied by 1 will stay the same

Zero: # multiplied by 0 is 0

Assocative: any numbers in the sentence can be grouped, it will not change the answer

Distributive: breaking down multiplication sentences could help students with memorization issues (e.g. 3x7872=21000+2400+210+6=23616)

Algorithms: Standard, Place Value, Expanded Notation, Lattice

STANDARD IS ALWAYS THE LAST STEP

Youtube Video: https://www.youtube.com/watch?v=jG9E2pev3bQ

34-12=22 (34=minuend, 12=subtrahend, 22=difference)

Algorithms: American Standard, European-Mexican, Reverse Indian, Left to Right, Expanded Notation, Integer Subtraction

No Emphasis on PV: American Standard, Euro-Mexican, Reverse Indian

STANDARD IS ALWAYS THE LAST STEP

Identity=When you add 0, # stays the same

Commutative= the order does not matter

Associative= the way the #'s are grouped does not matter

Algorithms: Standard, Partial Sums, PS w/emphasis on PV, Left to Right, Expanded Notation, Lattice Method

STANDARD IS ALWAYS THE LAST STEP

Youtube Video: https://www.youtube.com/watch?v=GtyUzH7FWN0

All students have different methods of problem solving

Could be done through trial and error, visualizing, using physical items, etc.

Sharing strategies often helps everyone who is trying to solve the problem

1) Understand the Problem

2) Devise a Plan

3) Carry Out the Plan

4) Look Back (reflect)

Youtube Link: https://www.youtube.com/watch?v=aMlVcGEn7EE