The Translator
Algebraic Equations
Warm - up
Translating English into Algebraic Expressions
Power point
The Translator
Guided Practice
Lost in Translation
Independent Practice
So You Think You Can Translate?
Translating English into Algebraic Expressions
warm up
Directions: Find Someone Who Can Translate English into Algebraic Expressions . Ask him
or her to solve the problem and write the solution in the space provided. You may not use
same person for more than one box.
1.
Which phrase below best represents the following
expression:
4n + 7
A
B
C
D
7 more than a number divided 4
4 times the sum of a number and 7
7 more than 4 times a number
4 times a number
***Signature
2.
Write a verbal phrase for x + 13 = 28
3. Write the expression for the product of 3 and a number.
*** Signature
4. Which of the following below represents the following
expression?
3+m
5
A The quotient of a number and 5
B
3 more than the product of 5 and a number
C
The product of 5 and 3 more than number
D
3 more than a number divided by 5
***Signature
*** Signature
Translating English into Algebraic Expressions
warm up
Directions: Find Someone Who Can Translate English into Algebraic Expressions . Ask him
or her to solve the problem and write the solution in the space provided. You may not use
same person for more than one box.
1. Which phrase below best represents the following
3. Write the expression for the product of 3 and a number.
expression:
4n + 7
A
B
C
D
7 more than a number divided 4
4 times the sum of a number and 7
7 more than 4 times a number
4 times a number
***Signature
2. Write a verbal phrase for x + 13 = 28
Answer will vary.
***Signature
3n
*** Signature
4. Which of the following below represents the following
expression?
3+m
5
A The quotient of a number and 5
B
3 more than the product of 5 and a number
C
The product of 5 and 3 more than number
D
3 more than a number divided by 5
*** Signature
The Translator
• Taking information
(words) from a
sentence and turning it
into an algebraic
equation is called
translating.
• An algebraic equation
is a number sentence
that contains variables
and the = symbol.
We will be taking sentences and turning
them into algebraic equations.
is
es
The Translator
equal
igualar
Just like verbal languages, math is a language
that uses verbs and sentences to
communicate information.
• An algebraic equation is a number sentence in
mathematics that contains numbers and
variables and an “equal” symbol.
Equations use math verbs like is, of in
representing the = symbol.
From words
The Translator
• Just like English, Spanish and
other languages, math is a
language that uses verbs in
sentences to communicate
information. In French and
Spanish languages, adjectives
mostly appear after nouns, which
is the opposite order from
English. In French, “brown cat”
becomes chat brun! In Spanish,
“brown cat” becomes “gato café”.
To numbers, symbols
and variables
• The same often
happens in math: The
order of terms might
have to change in order
to translate the correct
meaning.
Now, what makes this a sentence is; it has the verb is which
what’s separates an equation from an expression.
Six less than a number is ten.
In this sentence, “is” says that
one quantity is equal to one another.
=
When you see the verb is that breaks the sentence
where the “=“ will be. Let look at the words on the left
of the “=“ sign
Six less than a number = ten.
• In translating sentences to algebraic equations the order
of terms might have to change in order to translate the
correct meaning.
Lets translate a Verbal Sentence into an Equation.
• Sentence
Six less than a number is ten.
Let n = a number
• Variable
• Constants
Translation
Equation
6
-
(than)
reverse
In subtraction, the amount you subtract
"from" is written first.
n- 6 = 10
=
10
Lets translate verbal sentences into equations.
Three times Jack’s age equals 12.
Can you translate this problem
another way?
Show Your work
the unknown
Three times Jack’s age equals 12
variable
Let a represent Jack’s age.
a
3a = 12
let a
represents
Jack’s age
3
=
a
Equation
3a = 12
12
• Which problem situation matches the equation x – 5.83 = 3.17?
A Tyler ran 3.17 kilometers. His friend ran the same distance 5.83
seconds faster than Tyler. What is x, the time in seconds that Tyler ran?
x
–
5.83
=
3.17?
Time in seconds subtraction
Tyler ran
Friend ran
same distance
equal
Tyler ran
B Lynn and Heather measured the length of worms in science class.
Lynn’s worm was 5.83 centimeters long, and Heather’s worm was 3.17
centimeters long. What is x, the average length of the worms?
x
–
5.83
=
3.17?
Average length of
worms
subtraction
Lynn’s worm
length
equals
Heather’s
worm length
C Keisha’s lunch cost $5.83. She received $3.17 in change when she paid
the bill. What is x, the amount of money she gave the cashier?
X
-
5.83
Amount money to
subtraction
cashier
Lunch
cost
=
3.17
equals
Change rec from
bill payment
D Mr. Carlos paid $3.17 for a notebook that originally cost $5.83.
What is x, the amount of money that Carlos saved?
X
5.83
=
3.17
Amount money subtraction
Carlos saved
Origin cost
notebook
equals
Amount paid
for notebook
Round Robin: Match Makers
1. Read the problem, your group solve for first answer choice.
2. Upon completion, pass the paper to the right again and solve the second answer choice.
3. Continue the process until all answer choices have been solve.
4. Upon completion, return the paper to the original owner or group, who select the correct answer choice
with justification.
Which problem situation matches the equation: 4x + 8 = 128
• Which problem situation matches the equation 4x +8 =128
A Bill drove 8 more miles than David. Together they drove 128 miles. What
is x, the number of miles driven by David?
4x
+
8
=
128?
Pairs
compare
B Maria jogs 4 miles and bikes 8 miles daily to train for a marathon. If she
covers a total distance of 128 miles, what is x, the number of days she
trained?
4x
+
8
=
128?
C Joshua bought 8 concert tickets for himself and his friends to see their favorite
rock band. He also had to pay a service charge of $4. If he spent a total of $128,
what is x, the cost of 1 concert ticket?
4
x
+
8
=
128
D Eight chaperons will accompany 4 classes to the museum. If each class has the same
number of students and a total of 128 people go the museum, what is x, the number of
students in one class?
4x
+
8
=
128
• Which problem situation matches the equation 4x +8 =128
A Bill drove 8 more miles than David. Together they drove 128 miles. What
is x, the number of miles driven by David?
4x
+
8
=
128?
Number of
driven by David
add
Bill drove
addition 8 than David
equals
Pairs
compare
Total Miles
B Maria jogs 4 miles and bikes 8 miles daily to train for a marathon. If she
covers a total distance of 128 miles, what is x, the number of days she
trained?
4x
+
4 times number
of days Maria train
add
8
=
bikes
equals
128?
total distance
covered
C Joshua bought 8 concert tickets for himself and his friends to see their favorite
rock band. He also had to pay a service charge of $4. If he spent a total of $128,
what is x, the cost of 1 concert ticket?
4
x
4 times cost
one concert ticket
+
8
=
128
add
number
people
equal
total amount
spent for 8 tickets
D Eight chaperons will accompany 4 classes to the museum. If each class has the same
number of students and a total of 128 people go the museum, what is x, the number of
students in one class?
4x
4 times numb
students in each class
+
add
8
chaperons
=
equal
128
total number people
went to museum
Lost in Translation
(Guided Practice)
• Write an algebraic equation
The sum of a number and four is equal to -8.
Ten times the number of students is 280.
The Mavericks scored 122 points in their last game. This was 5 points
less than they scored in the previous game.
The sum of the measures of the angles of a triangle is 180º. Write
xº
an equation that represent the model.
35º
45º
Lost in Translation
(Guided Practice Key)
Sentence
Write an Algebraic Equation
The sum of a number and four is equal to -8
X + 4 = -8
Ten times the number of students is 280
10x = 280
The Mavericks scored 122 points in their last
game. This was 5 points less than they scored
in the previous game.
122 = p - 5
35 + 45 + x = 180
The sum of the measures of the angles of a
triangle is 180◦.
x
35◦
45◦
Writing in Math
Part 1
• Write a problem about a real-world situation that
can be represented by the equation
p – 25 =50
Part 2
Translate the mathematical sentence to a
verbal sentence.
Write look for clues to help someone in tutoring how to understand and
translate sentences to algebraic equations. Clues could include; what is the
unknown, what is constant what representation does the verbs play in the verbal
description of the problem.