Sections 3.1, 3.2, and 3.3

addends

"a & b"

minuend

"a"

subtrahend

"b"

difference

"c"

sum

"c"

Algorithm

A systematic procedure used to accomplish an operation.

Identity Property

A unique whole number 0 such that for any number "a", a + 0 = a = 0 + a.

rounding and compensating

A variation on the make-a-round method is to round and compensate. One addend gets rounded up and then that amount gets subtracted from the answer.

strip diagram

A way of visualizing the relationship between "a" , "b" and "c" in both addition and subtraction problems. b + c = a and a - b = c (or a - c = b)

Place value/Expanded notation

By writing the numbers in their expanded notation or place value form we can see how like terms are add and regrouping takes place.

Base 10 blocks

Can be used to illustrate the place values as well as the beginnings of "carrying" or "regrouping".

comparison

Ex: Doug solved 19 problems and Ted solved 17 problems. How many more problems has Doug solved than Ted?

take away

Ex: George has a book of 8 pizza coupons. If he used 5 coupons to buy pizza for Friday's party, how many coupons does he have left?

Measurement

Ex: On Maggie's 13 - mile hike to a lake, she came to a sign that said she had 3 miles left to reach the lake. How far has Maggie walked so far?

Subtraction of whole numbers

For any whole numbers "a" and "b" such that a __>__ b, then a - b is a unique number "c" (a - b = c) such that b + c = a.

Associative Property

If "a" , "b", and "c" are any numbers, then (a + b) + c = a + (b + c). It doesn't matter if the first two numbers are added first or if the last two numbers are added first.

Commutative Property

If "a" and "b" are any numbers, then a + b = b + a. Order does not matter which will allow us to rearrange and regroup as needed.

Addition of Whole Numbers

Let A and B two disjoint, finite sets. if n(A) = a and n(B) = b then a + b = n(A U B) = c.

Missing addend

The definition of subtract shows that an equation can be turned into an addition problem, that concept can be used to solve problems. Ex: Michael has saved $45 toward the $60 CD player he wants to buy. How much money does he have t0 add to his savings to purchase the player?

Make-a-round-number (make-a-ten)

Uses the associative property to shift one piece of an addend and join the piece with the other addend to make a "rounded" number.

Set Model

in scale representation of finished set

Number line (measurement) model

useful when you don't have "sets".