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A Learner-Centered
Learning Environment
(LCLE) Module in
Elementary Algebra
Prepared by Mr. Roy S. Daz
Name: _______________________
Section: _____ School-Year:_____
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The Age Problem
Dave and Mark are cousins
enrolled in La Salle Green
Hills - Adult Night High
School. One of their fellow
students is asking the two
how old they are. Dave,
wanting to challenge the
student, answered “Mark is
twice as old as I am. The sum
of our ages is 5 times my age,
less 48.”
Can you determine how old
Dave and Mark are? How?
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Worksheet #1: Mind Map
Translate the
verbal phrases and
sentences into
math expressions
and equations and
then solve for the
unknown.
Think of two
numbers and
check
whether they
fit the given
condition.
Their ages cannot
be determined. I
am sure Mark is
older than Dave
though.
I have
another idea:
___________
___________
___________
__________ .
How will you determine the ages of
Dave and Mark? Put a check mark on
your choice/s. Be ready to explain
your choice/s.
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Worksheet #2: Thinking About Your Choice
Think of two numbers and check
whether they fit the given condition.
Why do you think this will work?
_________________________________
_________________________________.
What is/are the disadvantage/s of
using this?
_________________________________
_________________________________.
Translate the verbal phrases and
sentences into math expressions and
equations and then solve for the
unknown.
How do you think this will work?
_________________________________
_________________________________
_________________________________
_________________________________.
Their ages cannot be determined. I
am sure Mark is older than Dave
though.
I have another idea.
What is your idea? How do you think
this will work?
Why do you think their ages cannot be _________________________________
_________________________________
determined?
_________________________________ _________________________________
_________________________________ _________________________________
_________________________________. _________________________________
_________________________________.
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The Lesson
The hardest thing about doing word
problems is taking the English words
and translating them into
mathematics. Usually, once you get
the math equation, you're fine; the
actual math involved is often fairly
simple. But figuring out the actual
equation can seem nearly impossible.
Be advised, however: To really learn
"how to do" word problems, you will
need to practice, practice, practice.
-purplemath.com
Before we clarify our ideas, we need
to learn first how to translate word
phrases to algebraic expressions and
vice-versa. To do that, visit any of the
websites on the right of this slide.
Algebra Lab
Purple Math
Ideal Math
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Worksheet #3: Translating Words into Math
Now that you have learned how to
translate word phrases into algebraic
expressions, you are now ready to fill
the following tables. Feel free to go
back to the websites if you need to.
Certain key words/phrases indicate
certain mathematical operations. List
down some of these.
When solving real-world problems, you
may need to determine the action to
know which operation to use.
Action
Operation
Put parts together.
Put equal parts together.
Find how much more.
Separate into equal parts.
Addition
Subtraction
Multiplication
Division
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Worksheet #4: Guided Practice
DIRECTION. Write an algebraic expression for each word phrase.
Compare your answers with your seatmates.
Word Phrase
Algebraic Expression
9 less than a number w
9 less w
the sum of 12 and m
the product of 8 and y
the quotient of f and 17
3 increased by the difference of p and 5
88 times the difference of f and 2
88 times the sum of f and 2
h multiplied to the ratio of k and 19
the sum of j and the product of 7 and f
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Worksheet #5: Independent Practice
DIRECTION. Write a word phrase/sentence for each algebraic
expression/equation.
Algebraic Expression
Word Phrase
6+c
g-1
5v
b/2
6 + 2f
m – 3n
6/(2 + e)
u+h
k – 2r
2c + 3d
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Worksheet #6: Enrichment Activity
DIRECTION. Write an algebraic expression/equation for each word
phrase/sentence. You can use any variable.
Word Phrase
Algebraic Expression
8 less than a number
8 less a number
15 increased by a number
the product of 8 and a number
the difference of y and a number
the sum of two consecutive integers
a number is equal to 5
10 is equal to the product of 2 and a number
twice a number
thrice a number
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Worksheet #7: The Age Problem
Going Back to the Age Problem at the
beginning of this module, can you now
express the following phrases/sentences
into algebraic expressions/equations? You
can use any variable.
Word
phrase/sentence
Using the equation you
answered on the left, solve
now for the ages of Dave and
Mark.
Algebraic
expression/equation
Dave’s age
Mark’s age (twice
Dave’s age)
the sum of Dave’s
age and Mark’s age
The sum of Dave’s
age and Mark’s age is
5 times Dave’s age,
less 48.”
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Worksheet #8: Quiz
Now that we have done some guided and
independent practices, it’s time for us to have a
short quiz.
Ready?! Take the QUIZ now!
1. How many items were you able to answer correctly? _____
2. Which item/s did you find difficult? Why?
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
3. What should you remember in order to answer this/these correctly next
time?
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
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Worksheet #9: Reflective Log
Use complete sentences in answering the following questions:
Which of the word
phrase/s used in the
class is/are hard to
understand? Why?
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
Which of the word
phrase/s used in the
class is/are easy to
understand? Why?
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
What is the benefit
of knowing how to
translate word
phrases to algebraic
expressions and
vice-versa?
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
__________________
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Final Output
It is now time to create your own WORD PROBLEM.
WHAT TO DO?
YOU NEED…..
Scratch papers
Ballpen
Bond Paper
…and a Partner
We will grade your
output using the
RUBRIC on the
next page.
Find a partner. Ask the age
of your partner, and
together, make accurate
translations of your ages
to algebraic expressions
using only one variable.
In a bond paper, create a
word sentence that will
help your classmates solve
for your ages (similar to
The Age Problem). Also,
show a step-by-step
solution on how to
determine your ages.
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Rubric
Criteria for
Scoring
We will grade your output using the rubric below. The perfect score is
ten (10) points.
Excellent
Developing
Beginning
The problem can be
solved using skills
related to translating
word phrase/sentence
into algebraic
expression/equation
and the problem is
solvable.
(3 - 4)
The problem can be
solved using skills
related to translating
word
phrase/sentence into
algebraic
expression/equation
but the problem is
not solvable. (1 - 2)
The problem cannot
be solved using skills
related to translating
word
phrase/sentence into
algebraic
expression/equation.
(0)
The Solution
The solution is step-bystep and the final
answer is correct.
(3 - 4)
The solution is not
step-by-step but the
final answer is
correct. (1 - 2)
The solution is not
step-by-step and the
final answer is wrong.
(0)
Grammar
The sentences are easily
understood and there
are no grammatical
errors. (2)
The sentences can be
understood but with
some grammatical
errors. (1)
The sentences cannot
be understood at all.
(0)
The Word
Problem
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