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A Learner-Centered Learning Environment (LCLE) Module in Elementary Algebra Prepared by Mr. Roy S. Daz Name: _______________________ Section: _____ School-Year:_____ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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? _________________________________ _________________________________ _________________________________ _________________________________ _________________________________. _________________________________ _________________________________. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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.” 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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? _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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? __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14