SOLVING EQUATIONS Manuel Navarro and Dirk Hodges

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #10

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “Baseball is ninety percent mental and the other half is physical.” (percentage) #10

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #9

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “Half the lies they tell about me aren't true.” (fractions) #9

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #8

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

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #7

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

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #6

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “I take a two hour nap, from one o'clock to four.” (subtraction) #6

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #5

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “90% of the putts that are short don't go in.” (percentage) #5

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #4

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

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #3

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “The towels were so thick there I could hardly close my suitcase.” (Volume) #3

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #2

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “A nickel ain't worth a dime anymore.” (value of money) #2

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA #1

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA “He hits from both sides of the plate. He's amphibious.” #1

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)

ONE POSSIBLE REASON WHY ADULT LEARNERS STRUGGLE WITH SOLVING EQUATIONS

A Tale of Two Minds

A common learning theory proposes that the minds of our adult learners are like swiss cheese.

As instructors we find out where the holes in their learning are, then simply plug the holes.

Exponents

Square Roots

The problem with this theory is that if we do not evaluate the holes correctly we can create cognitive overload.

….And, the concepts are detached from each other.

A second theory proposes that our adult learners have minds that are similar to Legos.

Our minds learn best when they are building concept upon concept…

….and they are attached to each other.

The Brownie Story

6 Simple Rules to solve equations

1 st Simple Rule The Value of Unknown

The goal of algebra is to find the value of an unknown. 1 st Simple Rule The Value of Unknown

X must be…

Isolated – like the Queen of England

X must be… Positive – not like Country and Western music Isolated – like the Queen of England

The answer needs to look like this:

X

Not like this: The answer needs to look like this: X

2x Not like this: The answer needs to look like this: X

or2x Not like this: The answer needs to look like this: X

- xor2x Not like this: The answer needs to look like this: X

2 nd Simple Rule Balance

A prerequisite for learning algebra is understanding balance. 2 nd Simple Rule Balance

You can do pretty much anything that you want to do to an equation, as long as you do it to both sides..

3 = 3

Balanced

3 = 3+1

3 = 4 Unbalanced

3 = 3+1

3 = 3+11+

4 = 4

Balanced

4x

=

8 =

4

4 =

4 = 8

4 = 8

4 = 8

4 = 8 4

4 = 8 4

x = 8 4

x =2

3 rd Simple Rule Distributive Property

If there are parentheses in an equation, then multiply across the parentheses distributing evenly. 3 rd Simple Rule Distributive Property

Kind of like one bowl of fruit with many people in which to distribute.

A banana to Tom

An apple to George A banana to Tom

An apple to George A banana to Tom An orange to Lebron

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)

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

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

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

4 th Simple Rule Addition Property of Equality

4 th Simple Rule Addition 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).

Much like corralling cattle and sheep.

3x= 6

x +2=-4

3x x +2=-4

3x -x+2 = -4

3x -x+2 = -4

3x-x-2=-4

5 th Simple Rule Like terms

5 th Simple Rule Like terms Collect Like terms (same variables raised to the same power) by adding the numerical coefficients.

We cannot combine a chicken and a goat and create a Chickengoat Combining like terms

Or a Zonkey? Combining like terms

6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y

Combining like terms 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2

Combining like terms 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 – 11xy

Combining like terms 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 – 11xy Can’t be combined (since the terms are not like terms)

6 th Simple Rule Multiplication Property of Equality

6 th Simple Rule Multiplication Property of Equality Divide (or multiply) both sides of an equation to get the variable isolated and positive.

3x-x-2 = -4 2x = -6

2x = x=-3

In Conclusion…

In Conclusion we have… 1. Quoted a great mathematician.

In Conclusion we have… 2. Discussed why some adult learners may struggle with solving equations.

In Conclusion we have… 3. Provided 6 simple rules for solving equations.

In Conclusion we have… 4. Illustrated a hands on method of teaching algebra.