MATH Unit 2 Chapter 03 - Operations & Algebraic Reasoning

breaking apart

A mental math strategy used to add and subtract. EXAMPLE: If your asked what is 28 plus 35 (28+35=) you would first break apart the 28; 28 equals 20 plus 8; (28 = 20 + 8) breaking apart the 28 then break apart 35 35 equals 30 plus 5; (35 = 30 + 5) breaking apart the 35 Add the TENS, 20 plus 30 equal 50 (20 + 30 = 50) Add the ONES, 8 plus 5 equals 13 (8 + 5 = 13) Add the sums of the TENS and ONES, 50 plus 13 equals 63 (50 + 13 = 63) so, 28 plus 35 equals 63 (28 + 35 = 63)

front-end estimation

A method of estimating sums, differences, products, and quotients using front digits. EXAMPLE: To answer 473 + 128 this way, you would round 473 to 500 and round 128 to 100. The 5 and 1 are the FRONT-END DIGITS. Adding the FRONT-END DIGITS, the 5 (from the 500) and 1 (100) which, in this case, are in the hundreds place you can conclude/estimate the answer to be about 600.

addend

A number which is involved in addition. Numbers being added are considered to be the addends.

inverse operations

Opposite operations. EXAMPLE: Addition is the inverse operation of subtraction. Multiplication is the inverse operation of division.

Associative Property of Addition

The property which states that the way in which addends are grouped does not change the sum. It is also called the Grouping Property of Addition. EXAMPLE: (3 + 4) + 5, is equal to, 3 + (4 + 5) Add the numbers in the parenthesis, 3 plus 4 which equals 7 then add 5 which equals 12. This is EQUAL to 3 plus 12. The 12 being the sum of the numbers in the parenthesis, 4 plus 5 which equals 12 They both equal 12. How they are grouped by the parenthesis does not change the sum.

difference

the number that is obtained by subtracting one number from another

number sentence

an equation expressed using numbers and common symbols EXAMPLE: A number sentence: 3 + 7 = 10. A number sentence using a 'less than' symbol: 3 + 6 < 10.

estimating

the approximate value, size, or cost based on experience or observation rather than actual measurement

sum

the whole amount

regrouping

to form into a new group EXAMPLE: In order to subtract 129 from 531, you need to regroup 531: 5 hundreds, 2 tens, and 11 ones.

compensation

Adding one amount to an addend and subtracting an equal amount from another addend to add mentally. EXAMPLE: 47 minus 28 ( 47-28= ) can be easier to work out in your mind by compensating the 28 to become 30. By rounding the 28 up to 30, you have COMPENSATED it by adding 2. To work it out in your head more quickly, your new math sentence would be 47 minus 30 plus 2 equals 19. (47- 30 + 2 = 19) now adding the 2 you COMPENSATED the 28 when rounding it up to 30.

clustering

An estimation strategy for finding sums. EXAMPLE: If your asked what is 117 plus 105 plus 91 ? [117+ 105 + 91 = ??] The addends are all close in value. You can skip count by hundreds (rounding the numbers) 100 plus 100 plus 100 and estimate the answer is about 300.

Commutative Property of Addition

The property which states that the order of addends (numbers) does not change the sum. It is also called the Order Property of Addition. EXAMPLE: 2 plus 4 is equal to/or the same as 4 plus 2 [2 + 4 = 4 + 2]

Zero Property of Addition

The property which states that the sum of any number and 0 is that number. EXAMPLE: 9 plus 0 equals 9 or 5 plus 0 equals 5 [9 + 9 = 0] [0 + 5 = 5]