UNDERSTANDING ALGEBRA MATH WORKOUTS THROUGH ONLINE VIDEOS
MINDY TAY PEI LIN
First Published 2017 Copyright © Mindy Tay Pei Lin Copyright © Taylor’s University Lakeside Campus Malaysia All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means - except in the case of brief quotations embodied in artciles or reviews - without written permission from its publisher. Published in Malaysia by e-LEARNING ACADEMY TAYLOR’S UNIVERSITY LAKESIDE CAMPUS Jalan Taylors, Subang Jaya, 47500 Subang Jaya, Selangor, Malaysia https://university.taylors.edu.my email: mindy.tay@taylors.edu.my
Understanding Algebra – Math Workouts Through Online Videos Mindy Tay Pei Lin ISBN
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TABLE OF CONTENT
1 Learning inverse operations through function machines 1.1
Post-Video Activity
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2 Multiplying binomials via the F.O.I.L method 2.1
Post-Video Activity
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3 Simplifying expressions made easy 3.1
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Post-Video Activity
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Title: Learning inverse operations through function machines
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Inverse operations are opposite operations that undo each other. Before undoing an operation, it is important that students are able to describe in words a mathematical expression with at least two operations such as ‘2a + 1’. This is to ensure that they know what happens to ‘a’ first. In this case, we can say that the variable ‘a’ is multiplied by two first, and then one is added to it. If we show what happens to ‘a’ in ‘2a + 1’ in a function machine, it will look like this:
And the idea of inverse operations is that whatever you do last must get ‘undone’ first. Hence the diagram below:
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When students are comfortable with using the function machine to explain and work with inverses, they may then proceed to solving algebraic problems which largely incorporates the idea of undoing a series of operations to solve for the unknown. Check out this BBC link for explanation on what a function machine is and how it can be used in algebra. http://www.bbc.co.uk/education/guides/zscmtfr/revision/2 The following video on Inverse Operations shows how this concept of undoing operations are used to solve equations. COMPONENT: Algebra TOPIC: Inverse Operations
Video: Algebra: Inverse Operations THIS VIDEO WILL COVER THE FOLLOWING AREAS: -
definition of inverse operations inverse operations in Algebra
[Correction: In the video (at 1:05) the number 1 is positive. Hence the elimination involves subtracting 1 from both sides. The mistake is that the narrator circled the positive sign for x instead when explaining that the operation to be undone is addition.] 2
1.1 Post-Video Activity Try using the function machine to solve Po’s problem in the video. Please follow these steps below: -
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PARTNER UP! Draw a function machine for an expression with at least two operations (such as 2a + 1).
Exchange your diagrams. Now create a story with that expression and explain the inverse operations involved. OPTION 5
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ALGEBRA
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Title: Multiplying binomials via the F.O.I.L method MULTIPLYING BINOMIALS CAN BE DONE IN TWO WAYS The distributive law method The F.O.I.L method
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THE DISTRIBUTIVE LAW METHOD
The distributive law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. This is done to remove the brackets for an expression. In doing so, we multiply the term on the outside of the bracket with the term inside each bracket. In the expression ‘a(b + c)’, the monomial factor ‘a’ is distributed, or separately applied, to each term of the binomial factor ‘b + c’, resulting in the product ‘ab + ac’.
You distribute the
a to the b and, then you distribute the a to the c.
Let’s apply this to an expression that consists of two binomials: ‘(y + 3)(y + 2)’. Using the distributive law method by letting ‘A = y + 3’, the equivalent form becomes: (y + 3)(y + 2) [let A = y + 3] = A (y + 2) [expand the brackets] = Ay + 2A [substituting A] = (y + 3)y + 2(y + 3) [expand the brackets] 2 = y + 3y + 2y + 6 [collect like terms/simplify] 2 = y + 5y + 6
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THE F.O.I.L METHOD
The F.O.I.L method can be a great alternative strategy for expanding brackets. Watch the following video that explains how this method can be used to multiply binomials in algebra. COMPONENT: Algebra TOPIC: The F.O.I.L Method
Video: Algebra: The F.O.I.L method THIS VIDEO WILL COVER THE FOLLOWING AREAS: -
Recap on addition and multiplication of variables Using the F.O.I.L method to expand binomials in algebra 5
Multiplying out the brackets in binomials is an essential skill that supports other algebraic activities such as finding a solution for the variable (unknown) or rewriting the expression in its equivalent form. Hence, it is important to practise expanding binomials using either the good old distributive law method or the infallible F.O.I.L method. Click on the link in the following section to put those skills to practice.
2.1 Post-Video Activity Please [CLICK HERE] to try the free FOIL Cruncher game.
HAVE FUN!
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Title: Simplifying expressions made easy
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The first step towards solving any algebraic problem is knowing how to simplify an expression. However, this can be intimidating if students are not familiar with the common terminologies used in its context. This video captures a great way to introduce many algebraic nomenclatures before explaining what are like and unlike terms. The difference between them is explained through comparisons between terms with different variables and exponents, which are commonly confused by many algebra novices. When simplifying an algebraic expression, one common misconception stems from conjoining algebraic terms as such: ‘a + b = ab’ and ‘x + y + z = xyz’. This is due to the expectation that the sum of two or more quantities must result in one value - from conjoining terms through arithmetic addition and subtraction, such as ‘5 + 8 = 13’ and ‘7 - 3 - 1 = 3’.
One effective way to address this is to make clear to students the difference between a like term and an unlike term. Students must also have a clear understanding on the concept of equality to comprehend that conjoining algebraic terms may result in one or more terms. That is, it is valid and justifiable if the collection of sums and/or differences in algebra result in expressions such as ‘a + b’, or even ‘a2 - a + b’.
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Check out the video below on combining like terms in algebra COMPONENT: Algebra TOPIC: Combining Like Terms
Video: Algebra: Combining Like Terms THIS VIDEO WILL COVER THE FOLLOWING AREAS: -
Definitions of: Term, Expression, Variable, Exponent, Coefficient What are like terms? How to combine like terms? It is important that students are able to grasp the idea of combining like terms in order to proceed to solving equations or any other transformational activities in algebra. A comprehension check is provided below for this purpose. After watching the video, students can attempt the Post-Video Activity on their own. Teachers and parents can also administer them for a quick (10-minute) comprehension check. The answer keys are available from page 10 onwards.
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3.1 Post-Video Activity
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Complete the table below. The first row has been done for you.
OPTION 5
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Are x and x2 like terms? Why?
Why do we collect like terms in an equation?
Simplify: Simplify: OPTION 1. 5 2a + 3a 2. 3a - 2a + 5a2 - a2 3. 4y + y2 - 2y + 6 + 3y2 4. 5 + 2x - 3 + 6x - x2 Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
The sample answers are available in page 11.
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ANSWER KEYS
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LEARNING INVERSE OPERATIONS THROUGH MAPPING DIAGRAMS
1.1 Ans: Post-Video Activity: A:
Try using the function machine to solve Po’s problem in the video.
The equation to calculate the number of bowls of noodles that Po ate was 5n - 6 = 44. This equation has two operations. First, the variable n was multiplied by 5 and then 6 is subtracted from that product. This can be represented as such:
Applying the concept of inverse, the diagram below shows how the value of n is found by undoing the two operations:
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SIMPLIFYING EXPRESSIONS MADE EASY
3.1 Ans: Post-Video Activity: A:
Complete the table below. The first row has been done for you.
The equation to calculate the number of bowls of noodles that Po ate was 5n - 6 = 44. This equation has two operations. First, the variable n was multiplied by 5 and then 6 is subtracted from that product. This can be represented as such:
1 1 2 1 2 3 2 3 4 3 4 5 4 5 5
Are x and x2 like terms? Why?
Ans: They are not like terms. Although both terms have the same variable but the degree of both terms are different. Why do we collect like terms in an equation?
Ans: To simplify or solve an equation OPTION 5
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Simplify: OPTION 5
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
Simplify: OPTION 1. 5 2a + 3a = 5a 2. 3a - 2a + 5a2 - a2 = 4a2 + a 3. 4y + y2 - 2y + 6 + 3y2 = 4y2 + 2y + 6 4. 5 + 2x - 3 + 6x - x2 = -x2 + 8x + 2 Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
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