OK, now is the time... we are going to whip our ALGEBRA TOOLKIT into shape!
Don't do any updating of your toolkit book just yet... I would like each of you to review the text book thru chapters 1 and 2 up to where we are now. Then I want you to list on a separate sheet of paper the definitions, properties and examples that should be a part of our toolkit. ACTUALLY, I WOULD LIKE YOU TO POST THE LIST TO THIS BLOG. I expect that this toolkit will be useful to you when you take geometry next year AND when you take algebra2 in high school.
SO, post your suggestions here on the blog!!
Make sure you understand the homework from last class (literal equations) or you better be asking some questions!
you gotsk it Mr. Camberlin!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ReplyDeleteHopefully no one should need help with that
Here are some terms I think should go in the toolkit, but I'm a little confused. Aren't everyone else's lists supposed to be here too or did I read that wrong? Oh well..
ReplyDelete1)Simplify- replacing a phrase with its single, numerical value or simplest name.
2)Evaluate- replacing each varialble with a given value. Then, simplify with the Order of Operations.
3)Algabraic Expression- mathematical phrase with one or more variables.
4)Numerical Expression- mathematical phrase with operations and numbers, but without a varialble.
5)Perfect Square- the square of an integer.
ie. 49=7^2
6)Rational Numbers- Numbers that can be expressed a/b when b is not equal to zero and equal a terminaing decimal (5.25) or a repeating decimal (3.3333).
7)Natural Number- 1,2,3,...
8)Whole Numbers- 0,1,2,3,...
9)Integers- ...-3,-2,-1,0,1,2,3...
10)Irrational Numbers- non-rational numbers
11)Absolute Value- the distance of a number from zero.
12)Reciprocal- the inverse of a fraction.
ie a/b, b/a. Note: A fraction and its reciprol always equal 1.a/b*b/a=1
13)Inverse Operation- the opposite operation.
(+)and(-) or(*) and (/).
14)isolte- to get the variable alone on one side with the coefficient of 1.
15)Literal Equation- equation involving two or more variables.
Thank you for posting your homework assignment, Julia. One suggestion if I may... if you find it frustrating/confusing that a group of students (in this case, the "best and the brightest" sometimes choose to lag in completing assignments, then NEVER become a teacher!!
ReplyDeleteP.S. I'm sure that several of your classmates are allocating time for this beautiful sunny Sunday afternoon to do their assignment.
P.P.S. I'd like to hear a bit more about the various algebraic properties granted by the math gods. Which are worthy of posting in our TOOLKIT?
Alright so I agree with all the things Julia said but some I might add are:
ReplyDeleteVariable:A symbol, usually a letter, that represents a value.
Real Number: Any number that is within the rational and irrational sets.
Equivalent Expressions: Two algebraic expressions that have the same value for all the variables.
Term: A number, a variable, or the product of a number and a variable.
Constant: A term with no variable.
Coefficient: A numerical factor of a term.
Like Terms: Terms with the same variable factor.
Solution of an Equation: A value of a variable that makes an equation true.
Identity: An equation that is true for every possible solution.
Formula: An equation that states a relationship among quantities.
Important Properties are:
Distributive Property: a(b+c)= ab+ac
All Equality Properties: Adding/subtracting the same value from both sides or multiplying/dividing by the same nonzero number on both sides produces an equivalent equation.
Gosh... you don't have to be so enthusiastic about it...
ReplyDeleteI'd like someone else to explicitly state each of the properties of equality... apparently we pushed Ryan to the edge of a sunny day!
Also, I think some of the definitions offered up by Julia and Ryan could use some additional clarification... anyone up to the task?
Our finished product (at the end of the year) will be an online Algebra Toolkit that we can all be proud of... and learn something from as well!
Sounds exciting, eh?!
This is Lotta! (I have no idea how to get your name on)
ReplyDeleteAddition Property of Equality: If the same number is added to both sides, both sides remain equal; In order to maintain balance, whatever number you add to one side of an equation must be added to the other side also
Subtraction Property of Equality: If the same number is subtracted from both sides, both sides remain equal; In order to maintain balance, whatever number you subtract from one side of an equation must be subtracted from the other side also
Multiplication Property of Equality: If the same number is multiplied on both sides, both sides remain equal; To maintain the balance of the equation, you must always remember to multiply BOTH sides of the equation by the same number
Division Property of Equality: If the same number is divided by on both sides, both sides remain equal; To maintain the balance of the equation, you must always remember to divide BOTH sides of the equation by the same number
I already posted a comment but its not up so I will re type it. I agree with Ryan and Julia but some properties I would like to add are:
ReplyDeletecommutative property of addition and multiplication- changing the order of numbers in an equation does not change the product or sum
associative property of addition and multiplication- changing the grouping of numbers in an equation does not change the product or sum
identity property of addition- if zero is added to a term the value of the term remains the same
identity property of multiplication- if one is multiplied by a term the value of the term remains the same
multiplication property of negative one- if negative one is multiplied by a term the product is the terms opposite
zero product property- any real number multiplied by zero is equal to zero
Order of operations- grouping symbols, exponents, multiplication/division, addition/subtraction
ReplyDeleteInverse properties- opposites, Multiplication=division, addition=subtraction and vice versa
Real numbers- rational, irrational, whole, natural, integers
2 negatives do not always equal a positive -3-7=10
rewriting division as multiplication 30/2=30*1/2
Distributive property in reverse bx+ax=x(a+b)
heyy, i wrote mine down, instead of putting it hear, was that ok?
ReplyDeletei have a question but there is no place to put it so im putting it here.....for number 18, how many kg is one poun????????????????
ReplyDeleteI believe one kilo gram is worth 2.20462262 pounds :)
ReplyDeletefor 21, 1 cm equals .393700787 inches.
ReplyDelete