ELL Math
NOTES
Name _______________________
Topic: Translate Algebra
Period _______ Date_________
Vocabulary
Changing words from
one language to
another is called
________________
CLOs: translate verbal phrases into expressions. Look for words that indicate mathematical
operations.
Let’s explore some important vocabulary:

Variable - a letter that represents a number. A variable can represent one
specific number, or it can stand for many different numbers.

Constant - a number that never changes, is added or subtracted

Expression - is a phrase that contains one or more symbols and numbers and
it does not contain an equal sign
verbal model:
rate: a fraction that
compares two
quantities measured
in different units.
unit rate: if the
denominator of the
fraction is 1 unit, the
rate is called unit
rate.
the quantity:
You are going to "translate" word, or verbal, expressions into algebraic expressions.
Let's start with some easy expressions with only one variable and one
constant. Although you can use any symbol for your variable, we will keep it
simple by.....
Letting n = "the number" in all expressions, but the constants will be different in
each expression
addition:
subtraction:
one-half:
Let's start by showing expressions using addition. Notice, because
addition is commutative, order doesn't matter.
Expressions using the addition sign to connect variable and constant
three-halves:
five-halves:
one-third:
one-fourth:
verbal (word) expressions
algebraic expressions
a number plus 5
10 more than a number
20 added to a number
8 greater than a number
a number increased by 4
the sum of a number plus ½
n + 5 or 5 + n
10 + n or n + 10
20 + n or n + 20
n + 8 or 8 + n
n + 4 or 4 + n
n + ½ or ½ + n
one-fifth:
two-thirds:
The following expressions all use subtraction. Notice because
subtraction is NOT commutative, order is important.
Expressions using the subtraction sign to connect variable and constant
two-fourths:
two-fifths:
three-fourths:
three-fifths:
three-sixths:
verbal (word) expressions
algebraic expressions
a number minus 10
20 minus a number
5 less than a number *
the difference of a number and 9
a number decreased by 6
a number diminished by 7
n - 10
20 - n
n - 5*
n-9
n-6
n-7
*Notice this algebraic expression is not in the same order as
the verbal expression; so be careful with "less than". You have
to really think about that one.
twice:
Expressions using the multiplication sign to connect variable and constant
double:
verbal (word) expressions
algebraic expressions
3xn
triple:
three times a number
or
3n
3n is more correct, because the times
sign looks like an "x" which is sometimes
the chosen variable
sum:
difference:
Expressions using the division sign to connect variable and constant
product:
verbal (word) expressions
quotient:
algebraic expressions
a number divided by 6
n÷6
a number ‘n’:
the quotient of a number ‘n’ and six
Write the sign for each math terminology.
label:
plus _____
minus _______
times _______ divided by _________
each:
Label the components of each equation.
the sum of:
4 + 3 = 7
15 ÷ 3 = 5
the difference of:
the product of:
7 - 4 = 3
2 x 8 = 16
the quotient of:
variable:
IMPORTANT NOTE:
When problem says “a number”, it means you need to put in a variable.
one term:
Example: Twice a number minus three
______________________
two terms:
MORE EXAMPLES :
three terms:
twice:
1)
The quantity 7 minus t raised to a number ______________________
2)
Three plus the quantity 2a minus 6 ____________________________
3)
Three times the sum of a and c
4)
Four plus the difference between 2 and 9
5)
Twice the quotient of 18 and 3 ______________________
6)
Three times the difference between a and 18 ______________________
7)
One third the sum of 9 and 6
______________________
raised to a number:
difference between:
______________________
______________________
CHANGING THE ORDER
When the problem uses the words “than” or “from,” like for example,” less than”
”more than” or “subtracted from,” you have to change the order.
For example: Five less than twice a number ‘b’ ______________________
8)
4 less than a number
______________________
9)
12 subtracted from the product of the number ‘m’ and 3. ________________
10)
Twice a number subtracted from 8
11)
Twelve more than 3 equals B ______________________
______________________
INEQUALITIES
< or >
( they all
include the
word “is” )
Words for <
is less than
Words for >
is greater than
is at most
is at least
Examples: A number ‘a’ is at least ten. ______________________
Twenty is greater than the sum of a number and three _____________________
The quotient of a number and five is less than two. ______________________
The sum of a number “m” and five is at most eight. ______________________
SUMMARY: What did you learn today? Write three things you learned today.
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