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