Date post: | 04-Jan-2016 |
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Variables in Algebra
Goals
• I can evaluate a variable expression.
• I can write variable expressions for word phrases.
• I can write a variable expression that models a real life situation.
Variables and ExpressionsSpecial Vocabulary: variable, constant, numerical expression, algebraic expression
• Variable- a letter or symbol that can be used for a value that can change.
Numerical expression – a mathematical phrase that contains only constants and/or operations
• Constant – a value that does not change.
Algebraic expression – a mathematical phrase that may contain variables, constants, and/or operations
Variables and Expressions
• We can replace the variables with numbers and evaluate the expression.
• To evaluate an expression is to find it’s value. We evaluate when we simplify to the lowest possible value after substituting the number for the variable.
We have to be able to “translate” words into expressions
What words indicate a particular operation?
Add Subtract SumPlus
More thanIncrease(d) by
PerimeterDeposit
GainGreater than
Up (flights of stairs)Total
MinusTake awayDifference
Reduce(d) byDecrease(d) by
WithdrawalLess than
Fewer (than)Loss of
We have to be able to “translate” words into expressions
What words indicate a particular operation?
Multiply DivideTimes
ProductOf
Twice (×2), double (×2), triple (×3), etc.Half (×½), Third (×⅓), Quarter (×¼)
Area (by)Percent (of)
Square (times itself 2 times)Cube (times itself 3 times)
… to the power of ___(times itself ___ times)
Split into __ partsCost eachQuotient
One-half (÷2), Third (÷3), Quarter (÷4)
IntoPer
Percent (out of 100)
Variables and Expressions
Let’s try an example of “translating” a phrase into an algebraic expression:
Nine more than a number y
Can you identify the operation?
“more than” means add
Answer: y + 9
Variables and Expressions
Let’s try another example of “translating” a phrase into an algebraic expression:
4 less than a number n
Can you identify the operation?
“less than” means Subtract
Answer: n – 4.
Why not 4 – n?????
**Expressions that contain subtracting will be the hardest for us!
Variables and Expressions
Let’s try another example of “translating” a phrase into an algebraic expression:
A number a divided by 12
Can you identify the operation?
Variables and Expressions
This one is harder……
5 times the quantity 4 plus a number c
Can you identify the operation(s)? What does the word quantity mean? Hmm……