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PRE-ALGEBRAPRE-ALGEBRA&&
MathLineMathLine
Pre-Algebra
Pre-algebra is difficult because Pre-algebra is difficult because of the confusing language.of the confusing language.
• 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
2x + 5 = 17 + 5 = 17
Let’s solveLet’s solve
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
We know we added 5 to 2xWe know we added 5 to 2x
With 2x + 5 = 17With 2x + 5 = 17
Pre-Algebra
to get 17to get 17
Pre-Algebra
So ask, “If we added 5 to get 17, So ask, “If we added 5 to get 17,
can we subtract 5 from 17?”can we subtract 5 from 17?”
If we added 5 to get 17If we added 5 to get 17
Can we subtract 5?Can we subtract 5?
Pre-Algebra
Pre-Algebra
So subtract 5 from 17…So subtract 5 from 17…
1122334455
Pre-Algebra
So subtract 5 from 17…So subtract 5 from 17…
Pre-Algebra
2x = 122x = 12
So ask, “What number times 2 So ask, “What number times 2 equals 12?”equals 12?”
Pre-Algebra
There are two ways There are two ways of finding X for of finding X for
2x = 122x = 12
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
Pre-Algebra
Divide 12 by two’s..Divide 12 by two’s..
1 2 3 4 5 6
Pre-Algebra
Or divide 12 into two GROUPS…Or divide 12 into two GROUPS…
6 6
Pre-Algebra
Either way Either way x = 6x = 6
6 6
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 the Equality PrincipleThis is 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 - 5 2x = 17 - 5
Pre-Algebra
and 17 – 5 equals 12and 17 – 5 equals 12
Pre-Algebra
and 17 – 5 equals 12and 17 – 5 equals 12
2x = 122x = 12
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
x = x = 66
Pre-Algebra
Using MathLine Using MathLine
to introduce Pre-Algebra to introduce Pre-Algebra
is is
effective and simple.effective and simple.
Pre-Algebra
MathLine makes Pre-Algebra MathLine makes Pre-Algebra
Easy to visualize Easy to visualize
And keeps the confusing language And keeps the confusing language simple.simple.
