pre-algebra&mathline pre-algebra. pre-algebra is intimidating! equality principle equality...

PRE-ALGEBRAPRE-ALGEBRA&&

MathLineMathLine

Pre-Algebra

Pre-algebra is intimidating!Pre-algebra is intimidating!

• Equality PrincipleEquality Principle• Balancing an EquationBalancing an Equation• Definition of a Variable, etc.Definition of a Variable, etc.

Pre-Algebra

MathLine makes Algebraic conceptsMathLine makes Algebraic concepts

EASY TO UNDERSTAND!EASY TO UNDERSTAND!

Pre-Algebra

MathLine makes Algebraic conceptsMathLine makes Algebraic concepts

EASY TO UNDERSTAND!EASY TO UNDERSTAND!

Pre-Algebra

By introducing abstract ideas By introducing abstract ideas

with with

simple languagesimple language

X + 4 = 9X + 4 = 9

Take for exampleTake for example

Pre-Algebra

Students can solve by theStudents can solve by the

““add up” approachadd up” approach

Pre-Algebra

For X + 4 = 9, we know we are For X + 4 = 9, we know we are adding 4, so put 4 on MathLineadding 4, so put 4 on MathLine

Pre-Algebra

Then add up till we get to sumThen add up till we get to sum

Pre-Algebra

11

Pre-Algebra

22

Pre-Algebra

33

Pre-Algebra

44

Pre-Algebra

55

Pre-Algebra

So we add 5 to the 4 and get…So we add 5 to the 4 and get…

99

Pre-Algebra

Pre-Algebra

If X + 4 = 9If X + 4 = 9

Then X = 5Then X = 5

4 5

The “add up” approach is correct, The “add up” approach is correct,

Pre-Algebra

but ideally we want students but ideally we want students solving for X.solving for X.

So ask the student, what do we know in So ask the student, what do we know in this sentence: X + 4 = ? this sentence: X + 4 = ?

Pre-Algebra

We know our sum isWe know our sum is 99 99

So put 9 on MathLineSo put 9 on MathLine

Next ask, “If we added 4 to get 9, Next ask, “If we added 4 to get 9,

Pre-Algebra

can we subtract 4 from 9?”can we subtract 4 from 9?”

So if we added 4 to get 9So if we added 4 to get 9

Can we subtract 4?Can we subtract 4?

Pre-Algebra

So subtract 4 from 9 …So subtract 4 from 9 …

Pre-Algebra

To get X by itselfTo get X by itself

Pre-Algebra

X = 5X = 5

On paper On paper the Algebra looks like the Algebra looks like

this…this…

Pre-Algebra

To get X by itself To get X by itself subtract 4 from both sidessubtract 4 from both sides

of the equation.of the equation.

X + 4 = 9 X + 4 = 9

Pre-Algebra

– – 4 –4 – 44

This is exercising the Equality PrincipleThis is exercising the Equality Principle

What is done to one side What is done to one side of the equation…of the equation…

Pre-Algebra

must be done to the other side must be done to the other side to keep it equal.to keep it equal.

X + 4 = 9 X + 4 = 9

Pre-Algebra

– – 4 –4 – 44

4’s cancel out 4’s cancel out

X = 9 X = 9 – – 44

Pre-Algebra

4’s cancel out 4’s cancel out

and 9 – 4 equals 5and 9 – 4 equals 5

Pre-Algebra

and 9 – 4 equals 5and 9 – 4 equals 5

X = 5X = 5

4’s cancel out 4’s cancel out

2X + 5 = 17X + 5 = 17

Another exampleAnother example

Pre-Algebra

So ask the student, what do we know in So ask the student, what do we know in this sentence: 2X + 5 = ?this sentence: 2X + 5 = ?

Pre-Algebra

We know our sum isWe know our sum is 1717

1717

So put 17 on MathLineSo put 17 on MathLine

Next ask, “If we added 5 to get 17, Next ask, “If we added 5 to get 17,

Pre-Algebra

can we subtract 5 from 17?”can we subtract 5 from 17?”

So if we added 5 to get 17So if we added 5 to get 17

Can we subtract 5?Can we subtract 5?

Pre-Algebra

So subtract 5 from 17…So subtract 5 from 17…

Pre-Algebra

To get 2X by itselfTo get 2X by itself

Pre-Algebra

2X = 17 - 52X = 17 - 5

We now know…We now know…

Pre-Algebra

2X = 122X = 12

Pre-Algebra

For 2 X = 12For 2 X = 12 Ask – What number times 2 Ask – What number times 2

equals 12?equals 12?

Pre-Algebra

There are two ways There are two ways

of finding X forof finding X for 2X = 122X = 12

On MathLineOn MathLine

Pre-Algebra

Divide by 12 by two’s..Divide by 12 by two’s..

112233445566

Pre-Algebra

Or divide 12 into two Or divide 12 into two GROUPS…GROUPS…

6666

Pre-Algebra

Either way Either way X = 6X = 6

6666

On paper On paper the Algebra looks like the Algebra looks like

this…this…

Pre-Algebra

To get X by itself To get X by itself subtract 5 from both sidessubtract 5 from both sides

of the equation.of the equation.

2X + 5 = 17 2X + 5 = 17

Pre-Algebra

– – 5 –5 – 55

This is exercising the Equality PrincipleThis is exercising the Equality Principle

What is done to one side What is done to one side of the equation…of the equation…

Pre-Algebra

must be done to the other side must be done to the other side to keep it equal.to keep it equal.

2X + 5 = 17 2X + 5 = 17

Pre-Algebra

– – 5 –5 – 55

5’s cancel out 5’s cancel out

2X = 17 2X = 17 – – 55

Pre-Algebra

5’s cancel out 5’s cancel out

and 17 – 5 equals 12and 17 – 5 equals 12

Pre-Algebra

and 17 – 5 equals 12and 17 – 5 equals 12

2X = 122X = 12

5’s cancel out 5’s cancel out

Pre-Algebra

2 X 2 X ÷÷ 2 2 = = 1212 ÷ 2÷ 2

2 X2 X 1212 2 2 2 2 =

2X = 122X = 12

So divide by 2 on each sideSo divide by 2 on each side

OrOr

Pre-Algebra

So, XSo, X = = 1212 ÷ 2÷ 2

OrOr

XX = = 66