solving equations manuel navarro and dirk hodges

SOLVING EQUATIONS

Manuel Navarro and Dirk Hodges

TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN,

YOGI BERRA

“Baseball is ninety percent mental and the other half is physical.” (percentage)

YOGI BERRA

“Half the lies they tell about me aren't true.” (fractions)

YOGI BERRA

“I knew I was going to take the wrong train, so I left early.” (distance formula)

YOGI BERRA

“You better cut the pizza in four pieces because I'm not hungry enough to eat six.” (fractions)

YOGI BERRA

“I take a two hour nap, from one o'clock to four.” (subtraction)

YOGI BERRA

“90% of the putts that are

short don't go in.”

(percentage)

YOGI BERRA#4

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)

YOGI BERRA#3

YOGI BERRA

“The towels were so thick there I could hardly close my suitcase.” (Volume)

YOGI BERRA#2

YOGI BERRA

“A nickel ain't worth a dime anymore.” (value of money)

YOGI BERRA#1

YOGI BERRA

“He hits from both sides of the plate. He's amphibious.”

YOGI BERRA

“He hits from both sides of the plate. He's amphibious.”

(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

1st Simple Rule

1st Simple RuleThe Value of Unknown

The goal of algebra is to find the value of an

unknown.

1st Simple RuleThe Value of Unknown

X must be…

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:

Not like this:

- xor2x

Not like this:

2nd Simple RuleBalance

A prerequisite for learning algebra is

understanding balance.

2nd Simple RuleBalance

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

sides..

3 = 3Balanced

3 = 3 +1

3 = 4Unbalanced

3 = 3 +1

3 = 3 +11+

4 = 4Balanced

3rd Simple RuleDistributive Property

If there are parentheses in an equation, then multiply across the parentheses distributing

evenly.

3rd Simple RuleDistributive 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)

a.) 2(x + y) = 2x + 2y

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

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

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).

Much like corralling cattle and sheep.

3x = 6

3x x+2 = -4

3x -x +2 = -4

3x -x -2= -4

5th Simple RuleLike 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

Zonkey?

6x2 + 7x2

19xy – 30xy

13xy2 – 7x2y

6x2 + 7x2

19xy – 30xy

13xy2 – 7x2y

6x2 + 7x2

19xy – 30xy

13xy2 – 7x2y

– 11xy

6x2 + 7x2

19xy – 30xy

13xy2 – 7x2y

– 11xy

Can’t be combined (since the terms are not like terms)

6th Simple RuleMultiplication Property of Equality

Divide (or multiply) both sides of an equation to get the

variable isolated and positive.

3x -x -2= -42x = -6

2x = -62 2

x = -3

In Conclusion…

In Conclusion we have…

1. Quoted a great mathematician.

2. Discussed why some adult learners may

struggle with solving equations.

3. Provided 6 simple rules for solving equations.

4. Illustrated a hands on method of teaching

algebra.

solving equations manuel navarro and dirk hodges

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