A Learner-Centered Learning

Environment (LCLE) Module in

Elementary AlgebraPrepared by Mr. Roy S. Daz

Name: _______________________

Section: _____ School-Year:_____1 2 3 4 5 6 7 8 9 10 11 12

13 14

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?

The Age Problem

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Worksheet #1: Mind Map

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.

I have another

idea: ____________________________________

_______ .

Think of two numbers

and check whether

they fit the given

condition.

Translate the verbal phrases and sentences

into math expressions and equations and then solve for the unknown.

Their ages cannot be

determined. I am sure Mark is older than Dave

though.

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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.

Why do you think their ages cannot be determined? ___________________________________________________________________________________________________.

I have another idea.What is your idea? How do you think this will work? ______________________________________________________________________________________________________________________________________________________________________________________________________.

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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.

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.

Certain key words/phrases indicate certain mathematical operations.

List down some of these.

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

Algebraic expression/equa

tion

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.”

Using the equation you answered on the left, solve now for the ages of Dave

and Mark.

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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

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?____________________________________________________________________________________________________________________________________________________________________________________

Use complete sentences in answering the following questions:

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Final Output It is now time to create your own WORD PROBLEM.

WHAT TO DO?

Find a partner. Ask the age of your partner, and together, make

accurate translations of your ages to algebraic expressions using only

one variable.

We will grade your output using the

RUBRIC on the next page.

YOU NEED…..

Scratch papers

Ballpen

Bond Paper

…and a Partner 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

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RubricWe will grade your output using the rubric below. The perfect score is ten (10) points.

Criteria for Scoring

Excellent Developing Beginning

The Word Problem

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/equatio

n. (0)

The Solution

The solution is step-by-step 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)

GrammarThe 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)

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