VARIABLES & PROPERTIES Identities, Inverses, Commutative, Associative, Distributive

Shared Learning Target I will be able to… ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall… ~ properties & order of operations I will demonstrate my knowledge by… ~ showing correct work and answers on my classwork, clicker questions, and homework.

WHAT IS A MATH PROPERTY?  A shortcut  They teach about the character of numbers  They may be used to rearrange an expression or an equation to make the problem a little easier to work with limits to the properties  There are limits to the properties…  Some of them can only be used in certain cases.

ADDITIVE IDENTITY  What number can you add to anything and still get the same number as the answer? Zero (0) ADDITIVE IDENTITY PROPERTY  So the ADDITIVE IDENTITY PROPERTY tells us… n + 0 = n

MULTIPLICATIVE IDENTITY  What number can you multiply by anything and still get the same number as the answer? ONE (1) multiplicative IDENTITY PROPERTY  So the multiplicative IDENTITY PROPERTY tells us… n 1 = n

ADDITIVE INVERSE  What number can you add to a number and get zero for the answer? The number’s opposite! ADDITIVE Inverse PROPERTY  So the ADDITIVE Inverse PROPERTY tells us… n + -n = 0  The additive inverse “undoes” what you have.

MULTIPLICATIVE INVERSE

WHICH PROPERTY IS THIS AN EXAMPLE? 15 + (-15) = ? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

WHICH PROPERTY IS THIS AN EXAMPLE? = ? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

WHICH PROPERTY IS THIS AN EXAMPLE? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

WHICH PROPERTY IS THIS AN EXAMPLE? 1. Additive Identity 2. Multiplicative Identity 3. Additive Inverse 4. Multiplicative Inverse

COMMUTATIVE PROPERTY Only for … ADDITION & MULTIPLICATION n + s = s + nns = sn  What does this tell us?  It’s okay to switch the order of the numbers when adding or multiplying…  NO COMBINING THE OPERATIONS!

IS THIS THE COMMUTATIVE PROPERTY? = Yes 2. No

IS THIS THE COMMUTATIVE PROPERTY? A B C = B C A 1. Yes 2. No

IS THIS THE COMMUTATIVE PROPERTY? = Yes 2. No

ASSOCIATIVE PROPERTY Only for … ADDITION & MULTIPLICATION a + (b + c) = (a + b) +ca(bc) = (ab)c  What does this tell us?  It’s okay to change how the numbers are grouped in the parenthesis…  NO COMBINING THE OPERATIONS !

IS THIS THE ASSOCIATIVE PROPERTY? ( ) = ( ) 1. Yes 2. No 0 of 20 Countdown 20

IS THIS THE ASSOCIATIVE PROPERTY? 56 + ( ) + 12 = ( ) + ( ) 1. Yes 2. No 0 of 20 Countdown 20

IS THIS THE ASSOCIATIVE PROPERTY? (AB)C= A(BC) 1. Yes 2. No 0 of 20 Countdown 20

IS THIS THE ASSOCIATIVE PROPERTY? = ( ) 2 1. Yes 2. No 0 of 20 Countdown 20

DISTRIBUTIVE PROPERTY May use… ADDITION & Subtraction a(b + c) = ab + aca(b - c) = ab - ac  What does this tell us?  We can take the number outside the parenthesis and multiply it by each term (number or variable) inside the parenthesis.

DISTRIBUTIVE PROPERTY Example…ADDITION 4( ) = 4(25) + 4(10) 4(35) = = 140

DISTRIBUTIVE PROPERTY Example… Subtraction 5( ) = 5(52) – 5(22) 5(30) = = 150

DISTRIBUTIVE PROPERTY Example…Algebraic ADDITION & Subtraction 5(b + 2) = 5b + 5(2)8(x - 6) = 8x – 8(6) 5(b + 2) = 5b + 108(x - 6) = 8x – 48  How are these expressions equal?  We don’t know what “b” or “x” are…  That’s okay…it’s supposed to be like that!

SUMMARY  Additive Identity  Multiplicative Identity  Additive Inverse  Multiplicative Inverse  Commutative Property  Associative Property  Distributive Property

Shared Learning Target I will be able to… ~ use the properties that we discuss to simplify and solve numerical and algebraic expressions. I will need to learn/recall… ~ properties & order of operations I will demonstrate my knowledge by… ~ showing correct work and answers on my classwork, clicker questions, and homework.

DO YOU FEEL THAT YOU HAVE MET THE TARGET OF: USE THE PROPERTIES THAT WE DISCUSS TO SIMPLIFY AND SOLVE NUMERICAL AND ALGEBRAIC EXPRESSIONS 1. Yes, I can see where the properties can/should be used. 2. I understand what they say but need to see more examples. 3. I remember their names.