The Age Problem
description
Transcript of The Age Problem
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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