Transcript MJ2A - Davidsen Middle School

MJ2A
Ch 1.3 Variables & Expressions
Bellwork
•
1.
2.
3.
4.
Write a numerical expression for each
verbal phrase
Six minus three
Nine multiplied by five
Eleven more than fifteen
The cost of three notebooks at $6 each
Before we begin…
• Please take out your notebook and get ready to
work!
• On Friday we looked at words that mean the
mathematical operations of add, subtract, multiply
and divide….
• Today we will increase out understanding of
expressions incorporating variables…
• But first what is a variable and what do they
represent?....raise you hand if you know the
answer
The answer…
• A variable is a letter used in an expression
or equation to represent some unknown
number.
• Most often the variable represents one
number….however, in some instances the
variable can represent a range of numbers
called a solution set….
Objective
• Students will evaluate expressions
containing variables and translate verbal
phrases into algebraic expressions
Evaluating Expressions
•
To evaluate expressions use the following
process:
1. Write the expression
2. Substitute
3. Do the math
Example
Evaluate the expression:
x + y – 9 if x = 15 and y = 26
1. x + y – 9
2. 15 + 26 – 9
3. 41 – 9
32
Note:
1. Write the expression
2. Substitute
3. Do the math
When “doing the math” use the
order of operations
Substitution Property of Equality
• Replacing a variable with a number
demonstrates the Substitution Property of
Equality which states:
• If two quantities are equal then one quantity
can be replaced by the other
• Example:
If a = b, then a may be replaced by b
Multiplication & Algebra
• At this level you are required to be able to
recognize and work with the various forms
of multiplication in Algebra.
• Because the variable x is used often in
algebra the multiplication sign (x) that you
learned in elementary school is not used.
Here are the forms of multiplication:
2x
2∙x
2(x)
mn
Your Turn
•
•
1.
2.
3.
In the notes section of your notebook
write and solve the following:
Evaluate each expression if x = 3, y = 4,
and z = 7
6x – 4y
(z – x)
y
5z + (x + 4y) – 15
Translating Verbal Phrases
• The first step to translating variable phrases
it to identify the variable
• After identifying the variable choose a letter
to represent the variable in the expression.
• Lets see what that looks like…
Example
• Verbal Phrase: Twelve points more than the
Dolphins scored
• In this phrase the variable is the Dolphins…Lets use
p to represent the dolphins
Twelve points more than the Dolphins scored
12
+
p
The algebraic expression for the verbal phrase
becomes:
12 + p
Comments
• When choosing a variable you may use any
letter.
• The key to translating verbal phrases is
identifying the variable
• You can use different strategies to help you
like circling, highlighting, or boxing the
variable in the sentence
• Lets look at another example..
Example
• Four times a number decreased by six.
• Let x represent the variable “a number”
• Four times means multiply 4 times the variable
• Decreased by six means subtract 6
4x - 6
Your Turn
•
In the notes section of your notebook
write the verbal phrase and translate it into
an algebraic expression
1. Eight more than the amount Kira saved
2. Five goals less than the Pirates scored
3. The quotient of a number and four, minus
five
Summary
• In the notes section of your notebook
summarize the key concepts covered in
today's lesson:
• Today we discussed:
• Evaluating variable expressions
• The process for evaluating expressions
• Translating verbal phrases into algebraic
expressions
• Identifying the variable in a verbal phrase
Assignment
• Text p. 20 # 20 – 30 & 33 – 40
• This assignment is due tomorrow
• Check your answers to the odd problems in
the back of the book.
• If you didn’t get the same answer…you need
to figure out why!
• Reminder…I do not accept late assignments!