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Teacher: Mr. Richard Riobaldez Date: 06/03/ Module 3
Lesson 1 – Sharing your Research (Presenting and Revising a
Written Research Report)
WARMING UP
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PRACTICE TASK 1
Line Binomial Multiplier
PRACTICE TASK 2
Scope and Delimitation of the Study This study will be conducted at Marcial O. Rañola Memorial School Guinobatan, Albay. This study mainly focuses on multiplying binomials and the device’s effectiveness as educational tool for students and teachers in Marcial O. Ranola Memorial School. The device is delimited only that user must only apply the concept of binomials.
Ice
INQUIRIES,
INVESTIGATION AND
IMMERSION
Teacher: Mr. Richard Riobaldez Date: 06/03/
PRACTICE TASK 3
Significance of the study The common methods for multiplying numbers/binomial, polynomials using foil method or simply distributing terms. Instead of doing calculations by pencil and paper, let the student work actively with math using teacher/student manipulative materials. Math is boring if we don’t know how to make it better. Line Binomial Multiplier (LBM) gives a new phase on how we simply multiply binomial factors. It guides the student to gain the skills in multiplying binomials. LBM help teach math positively affects student learning. Incorporating this device in multiplying binomials into meaningful ways help students grasp the concept with greater ease, making teaching most effective. School. This device would be of help to provide direction to the administrators, teachers, and students’ goal for quality education. Mathematics Teachers. This device would encourage the teachers to use new teaching strategies that are in line with their subject areas. This would create learning situations that are more effective and consequently lead to more interesting and more meaningful classroom activities for the students. In addition, teaching such topic would not be difficult to teachers for it will also serve as their motivation in learning. Students. This device asserts that their learning would be retained in their minds for acquiring the knowledge was done using manipulative device or through hands-on and minds-on process. Parents. This device will make parents to realize the important roles of manipulative and mathematics to their children.
Teacher: Mr. Richard Riobaldez Date: 06/03/ B. Related Studies The trick of multiplying using lines is either called Japanese Way, Chinese or Line Multiplication. Whatever it’s called it would remain as a trick if you just memorize it with learning. In order to understand how Japanese multiplication works, we must start back at the good old, reliable method of organizing equal groups in rows and columns, or array. When we say “3 times 2”, that is the same as saying “3 groups of 2” and we can show these three groups as 3 rows and 2 columns or 3 columns and two rows. This basic idea of multiplication is what the proponents incorporated in the device. The proponents gathered this information necessary for showing how the multiplication process works for the benefit of the future students will use it.
Teacher: Mr. Richard Riobaldez Date: 06/03/ Task 3 CHAPTER I INTRODUCTION Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since the beginning of recorded history, mathematic discovery has been at the forefront of every civilized society, and in use in even the most primitive of cultures. The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count, but also relied on math to calculate the position of the sun and the physics of hunting. Early humans counted and performed simple calculations using tools such as their fingers, notches in sticks, knotted strings, and pebbles. Most early cultures evolved some form of a counting board or abacus to perform calculations. Pencil and paper eventually replaced these early counting boards, but a modern form of the abacus may still be seen in use in parts of Russia and Asia in the twenty-first century. Often, such devices have simple rules and match procedures such as our own invented mathematical device entitled Line Binomial Multiplier or LBM. Teaching and learning Mathematics related lessons are often puzzling and difficult especially for students. Having a device as an educational tool to serve an alternative to learn mathematics can help students to conveniently comprehend the lesson presented to them. The device is inspired by the Japanese way of multiplication using lines. The proponents came up with this idea to aid teachers in conveniently give lessons to multiplying binomials. This device would act as a teaching material and categorized under manipulative since the students need to manipulate the device to answer a particular problem. Most students cannot easily multiply binomials since they could not
Teacher: Mr. Richard Riobaldez Date: 06/03/ SCOPE AND DELIMITATION This study will be conducted at Marcial O. Rañola Memorial School Guinobatan, Albay. This study mainly focuses on multiplying binomials and the device’s effectiveness as educational tool for students and teachers in Marcial O. Ranola Memorial School. The device is delimited only that user must only apply the concept of binomials. SIGNIFICANCE OF THE STUDY The common methods for multiplying numbers/binomial, polynomials using foil method or simply distributing terms. Instead of doing calculations by pencil and paper, let the student work actively with math using teacher/student manipulative materials. Math is boring if we don’t know how to make it better. Line Binomial Multiplier (LBM) gives a new phase on how we simply multiply binomial factors. It guides the student to gain the skills in multiplying binomials. LBM help teach math positively affects student learning. Incorporating this device in multiplying binomials into meaningful ways help students grasp the concept with greater ease, making teaching most effective. School. This device would be of help to provide direction to the administrators, teachers, and students’ goal for quality education. Mathematics Teachers. This device would encourage the teachers to use new teaching strategies that are in line with their subject areas. This would create learning situations that are more effective and consequently lead to more interesting and more meaningful classroom activities for the students. In addition, teaching such topic would not be difficult to teachers for it will also serve as their motivation in learning. Students. This device asserts that their learning would be retained in their minds for acquiring the knowledge was done using manipulative device or through hands-on and minds-on process. Parents. This device will make parents to realize the important roles of manipulative and mathematics to their children.
- Teacher: Mr. Richard Riobaldez Date: 06/03/
Teacher: Mr. Richard Riobaldez Date: 06/03/
REPUBLIC OF THE PHILIPPINES
Department of Education Region V (Bicol) Division of Albay Marcial O. Rañola Memorial School Guinobatan, Albay LINE BINOMIAL MULTIPLIER (A Mathematical Device) Jedrick O. Colico Jannah Mae N. Dalaay Jeanette Louise L. Guerrero Christine M. Frial Researchers MAY 2021
Teacher: Mr. Richard Riobaldez Date: 06/03/ CHAPTER I INTRODUCTION Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since the beginning of recorded history, mathematic discovery has been at the forefront of every civilized society, and in use in even the most primitive of cultures. The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count, but also relied on math to calculate the position of the sun and the physics of hunting. Early humans counted and performed simple calculations using tools such as their fingers, notches in sticks, knotted strings, and pebbles. Most early cultures evolved some form of a counting board or abacus to perform calculations. Pencil and paper eventually replaced these early counting boards, but a modern form of the abacus may still be seen in use in parts of Russia and Asia in the twenty-first century. Often, such devices have simple rules and match procedures such as our own invented mathematical device entitled Line Binomial Multiplier or LBM. Teaching and learning Mathematics related lessons are often puzzling and difficult especially for students. Having a device as an educational tool to serve an alternative to learn mathematics can help students to conveniently comprehend the lesson presented to them. The device is inspired by the Japanese way of multiplication using lines. The proponents came up with this idea to aid teachers in conveniently give lessons to multiplying binomials. This device would act as a teaching material and categorized under manipulative since the students need to manipulate the device to answer a particular problem. Most students cannot easily multiply binomials since they could not imagine or
Teacher: Mr. Richard Riobaldez Date: 06/03/ SCOPE AND DELIMITATION This study will be conducted at Marcial O. Rañola Memorial School Guinobatan, Albay. This study mainly focuses on multiplying binomials and the device’s effectiveness as educational tool for students and teachers in Marcial O. Ranola Memorial School. The device is delimited only that user must only apply the concept of binomials. SIGNIFICANCE OF THE STUDY The common methods for multiplying numbers/binomial, polynomials using foil method or simply distributing terms. Instead of doing calculations by pencil and paper, let the student work actively with math using teacher/student manipulative materials. Math is boring if we don’t know how to make it better. Line Binomial Multiplier (LBM) gives a new phase on how we simply multiply binomial factors. It guides the student to gain the skills in multiplying binomials. LBM help teach math positively affects student learning. Incorporating this device in multiplying binomials into meaningful ways help students grasp the concept with greater ease, making teaching most effective. School. This device would be of help to provide direction to the administrators, teachers, and students’ goal for quality education. Mathematics Teachers. This device would encourage the teachers to use new teaching strategies that are in line with their subject areas. This would create learning situations that are more effective and consequently lead to more interesting and more meaningful classroom activities for the students. In addition, teaching such topic would not be difficult to teachers for it will also serve as their motivation in learning. Students. This device asserts that their learning would be retained in their minds for acquiring the knowledge was done using manipulative device or through hands-on and minds-on process.
Teacher: Mr. Richard Riobaldez Date: 06/03/ Parents. This device will make parents to realize the important roles of manipulative and mathematics to their children.
Teacher: Mr. Richard Riobaldez Date: 06/03/ are well-aligned to their learning styles tend to be more committed to their field. Experiential learning can be good for helping people explore their own strengths when learning new things. "The nature of mathematics is independent of us personally and of the world outside." (Jourdain) Mathematics in its purest sense is an abstraction. Whether it was discovered by or has been created by mankind is perhaps a philosophical point and need not concern us here; but the fact is that it exists, and it is extremely useful in describing and predicting events in the world around us. How then is it so useful if it exists "independent of us personally and of the world outside?" The answer lies in the ability of mathematics to model effectively numerous aspects of the real world. It does this by creating abstract structures that have properties or attributes similar to its real-world counterpart. If the model behaves in a manner that truly parallels the original, then it becomes possible to manipulate and use the model to make conclusions and/or predictions about its counterpart in the real world. Lesh (1979) has suggested that manipulative materials can be effectively used as an intermediary between the real world and the mathematical world. He contends that such use would tend to promote problem-solving ability by providing a vehicle through which children can model real-world situations. The use of manipulative materials (concrete models) in this manner is thought to be more abstract than the actual situation yet less abstract than the formal symbols. Early humans counted and performed simple calculations using tools such as their fingers, notches in sticks, knotted strings, and pebbles. Most early cultures evolved some form of a counting board or abacus to perform calculations. Pencil and paper eventually replaced these early counting boards, but a modern form of the abacus may still be seen in use in parts of Russia and Asia in the twenty-first century.
Teacher: Mr. Richard Riobaldez Date: 06/03/ REVIEW OF RELATED STUDIES The trick of multiplying using lines is either called Japanese Way, Chinese or Line Multiplication. Whatever it’s called it would remain as a trick if you just memorize it with learning. In order to understand how Japanese multiplication works, we must start back at the good old, reliable method of organizing equal groups in rows and columns, or array. When we say “3 times 2”, that is the same as saying “3 groups of 2” and we can show these three groups as 3 rows and 2 columns or 3 columns and two rows. We can also use arrays to practice skip counting, visualizing “doubles”, “triples” and all kinds of other useful skills that many “back to basics” advocates would love to see improved in our students. They can also help us understand why Japanese multiplication actually works. As numbers get bigger, like 6 groups of 7, it can often be helpful for students to show the number of groups and number of items in each group (also known as factors). But multiplying big numbers would be difficult to visualize so the base 10 is introduced. Examples below.
Teacher: Mr. Richard Riobaldez Date: 06/03/ Discuss Concepts BINOMIAL THEOREM A binomial is a polynomial with two terms
FACTOR
INTERSECTION
is a number you multiply with others to get to a desired number. Whatever numbers you use to multiply together to get to a number of your choice are factors is a single point where two lines meet or cross each other
Teacher: Mr. Richard Riobaldez Date: 06/03/ PEMDAS PEMDAS is a mnemonic device that can help us remember the order of operations which we already know stands for “Please Excuse My Dear Aunt Sally”. P – Parentheses E – Exponents M – Multiplication D – Division A – Addition S – Subtraction Below illustrates an example where there are two possible answers. The first solution yields the wrong answer because it calculates the numerical expression from left to right. While the second solution is the correct one because it follows the rules of the Order of Operations. Simplify the numerical expression. Wrong Solution:
