SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.
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Transcript of SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.
![Page 1: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/1.jpg)
SOLVING EQUATIONS
Manuel Navarro and Dirk Hodges
![Page 2: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/2.jpg)
TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
![Page 3: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/3.jpg)
TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
![Page 4: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/4.jpg)
TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#10
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“Baseball is ninety percent mental and the other half is physical.” (percentage)
#10
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#9
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“Half the lies they tell about me aren't true.” (fractions)
#9
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#8
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“I knew I was going to take the wrong train, so I left early.” (distance formula)
#8
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#7
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“You better cut the pizza in four pieces because I'm not hungry enough to eat six.” (fractions)
#7
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#6
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“I take a two hour nap, from one o'clock to four.” (subtraction)
#6
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
#5
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“90% of the putts that are
short don't go in.”
(percentage)
#5
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA#4
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“You give 100 percent in the first half of the game, and if that isn't enough in the second half you give what's left.” (percentage)
#4
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA#3
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“The towels were so thick there I could hardly close my suitcase.” (Volume)
#3
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA#2
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“A nickel ain't worth a dime anymore.” (value of money)
#2
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA#1
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“He hits from both sides of the plate. He's amphibious.”
#1
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TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,
YOGI BERRA
“He hits from both sides of the plate. He's amphibious.”
#1
(okay it’s a biology question)
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ONE POSSIBLE REASON WHY ADULT LEARNERS
STRUGGLE WITH SOLVING EQUATIONS
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A Tale of Two Minds
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A common learning theory proposes that the minds of our adult learners are like
swiss cheese.
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As instructors we find out where the holes in their learning are, then simply
plug the holes.
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Exponents
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Exponents
Square Roots
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The problem with this theory is that if we do not
evaluate the holes correctly we can create cognitive
overload.
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….And, the concepts are detached from each other.
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A second theory proposes that our adult learners have
minds that are similar to Legos.
![Page 35: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/35.jpg)
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Our minds learn best when they are building concept
upon concept…
![Page 37: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/37.jpg)
Our minds learn best when they are building concept
upon concept…
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Our minds learn best when they are building concept
upon concept…
….and they are attached to each other.
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The Brownie Story
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The Brownie Story
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6 Simple Rules to solve equations
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1st Simple Rule
1st Simple RuleThe Value of Unknown
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The goal of algebra is to find the value of an
unknown.
1st Simple RuleThe Value of Unknown
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X must be…
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X must be…Isolated – like the Queen of England
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X must be…
Positive – not like Country and Western music
Isolated – like the Queen of England
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The answer needs to look like this:
![Page 48: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/48.jpg)
The answer needs to look like this:
X
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Not like this:
The answer needs to look like this:
X
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2x
Not like this:
The answer needs to look like this:
X
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or2x
Not like this:
The answer needs to look like this:
X
![Page 52: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/52.jpg)
- xor2x
Not like this:
The answer needs to look like this:
X
![Page 53: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/53.jpg)
2nd Simple RuleBalance
![Page 54: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/54.jpg)
A prerequisite for learning algebra is
understanding balance.
2nd Simple RuleBalance
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You can do pretty much anything that you want to do to an equation, as long as you do it to both
sides..
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3 = 3
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3 = 3Balanced
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3 = 3 +1
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3 = 4Unbalanced
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3 = 3 +1
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3 = 3 +11+
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4 = 4
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4 = 4Balanced
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4x
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=4x
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8=4x
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4x
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4x
![Page 70: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/70.jpg)
44x
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44x
=
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44x
= 8
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44x
= 8
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44x
=8
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44x
=84
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44x
=84
![Page 77: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/77.jpg)
x =84
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x = 2
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3rd Simple RuleDistributive Property
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If there are parentheses in an equation, then multiply across the parentheses distributing
evenly.
3rd Simple RuleDistributive Property
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Kind of like one bowl of fruit with many people in
which to distribute.
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A banana to Tom
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An apple to George
A banana to Tom
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An apple to George
A banana to Tom
An orange to Lebron
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Using the Distributive Property
Example: Find each product by using the distributive property to remove the parentheses.
a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)
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Using the Distributive Property
Example: Find each product by using the distributive property to remove the parentheses.
a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)
a.) 2(x + y) = 2x + 2y
![Page 88: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/88.jpg)
Using the Distributive Property
Example: Find each product by using the distributive property to remove the parentheses.
a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)
a.) 2(x + y) = 2x + 2y
b.) 7(x + 2y – 5z) = 7x + 14y – 35z
![Page 89: SOLVING EQUATIONS Manuel Navarro and Dirk Hodges.](https://reader037.fdocuments.in/reader037/viewer/2022110401/56649e0f5503460f94af9bbe/html5/thumbnails/89.jpg)
Using the Distributive Property
Example: Find each product by using the distributive property to remove the parentheses.
a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)
a.) 2(x + y) = 2x + 2y
b.) 7(x + 2y – 5z) = 7x + 14y – 35z
c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c
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4th Simple RuleAddition Property of Equality
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4th Simple RuleAddition Property of Equality
Move variables to one side of the fence (equal sign) and non-
variables to the other side (making sure to change the sign
if they cross over).
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Much like corralling cattle and sheep.
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Much like corralling cattle and sheep.
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Much like corralling cattle and sheep.
3x = 6
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3x x+2 = -4
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3x x+2 = -4
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3x -x +2 = -4
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3x -x +2 = -4
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3x -x -2= -4
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5th Simple RuleLike terms
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5th Simple RuleLike terms
Collect Like terms (same variables raised to the same
power) by adding the numerical coefficients.
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We cannot combine a chicken and a goat and create a
Chickengoat
Combining like terms
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Or a
Zonkey?
Combining like terms
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Combining like terms
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Combining like terms
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
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Combining like terms
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
13x2
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Combining like terms
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
13x2
– 11xy
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Combining like terms
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
13x2
– 11xy
Can’t be combined (since the terms are not like terms)
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6th Simple RuleMultiplication Property of Equality
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6th Simple RuleMultiplication Property of Equality
Divide (or multiply) both sides of an equation to get the
variable isolated and positive.
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3x -x -2= -42x = -6
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2x = -62 2
x = -3
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In Conclusion…
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In Conclusion we have…
1. Quoted a great mathematician.
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In Conclusion we have…
2. Discussed why some adult learners may
struggle with solving equations.
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In Conclusion we have…
3. Provided 6 simple rules for solving equations.
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In Conclusion we have…
4. Illustrated a hands on method of teaching
algebra.
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