PRE-ALGEBRA&MathLine Pre-Algebra. Pre-algebra is intimidating! Equality Principle Equality Principle...
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Transcript of PRE-ALGEBRA&MathLine Pre-Algebra. Pre-algebra is intimidating! Equality Principle Equality Principle...
![Page 1: PRE-ALGEBRA&MathLine Pre-Algebra. Pre-algebra is intimidating! Equality Principle Equality Principle Balancing an Equation Balancing an Equation Definition.](https://reader035.fdocuments.net/reader035/viewer/2022062305/56649d845503460f94a6b201/html5/thumbnails/1.jpg)
PRE-ALGEBRAPRE-ALGEBRA&&
MathLineMathLine
Pre-Algebra
![Page 2: PRE-ALGEBRA&MathLine Pre-Algebra. Pre-algebra is intimidating! Equality Principle Equality Principle Balancing an Equation Balancing an Equation Definition.](https://reader035.fdocuments.net/reader035/viewer/2022062305/56649d845503460f94a6b201/html5/thumbnails/2.jpg)
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
![Page 3: PRE-ALGEBRA&MathLine Pre-Algebra. Pre-algebra is intimidating! Equality Principle Equality Principle Balancing an Equation Balancing an Equation Definition.](https://reader035.fdocuments.net/reader035/viewer/2022062305/56649d845503460f94a6b201/html5/thumbnails/3.jpg)
MathLine makes Algebraic conceptsMathLine makes Algebraic concepts
EASY TO UNDERSTAND!EASY TO UNDERSTAND!
Pre-Algebra
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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
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X + 4 = 9X + 4 = 9
Take for exampleTake for example
Pre-Algebra
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Students can solve by theStudents can solve by the
““add up” approachadd up” approach
Pre-Algebra
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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
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Then add up till we get to sumThen add up till we get to sum
Pre-Algebra
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Pre-Algebra
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Pre-Algebra
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Pre-Algebra
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44
Pre-Algebra
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55
Pre-Algebra
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So we add 5 to the 4 and get…So we add 5 to the 4 and get…
99
Pre-Algebra
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Pre-Algebra
If X + 4 = 9If X + 4 = 9
Then X = 5Then X = 5
4 5
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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.
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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
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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?”
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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
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So subtract 4 from 9 …So subtract 4 from 9 …
Pre-Algebra
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To get X by itselfTo get X by itself
Pre-Algebra
X = 5X = 5
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On paper On paper the Algebra looks like the Algebra looks like
this…this…
Pre-Algebra
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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
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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.
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X + 4 = 9 X + 4 = 9
Pre-Algebra
– – 4 –4 – 44
4’s cancel out 4’s cancel out
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X = 9 X = 9 – – 44
Pre-Algebra
4’s cancel out 4’s cancel out
and 9 – 4 equals 5and 9 – 4 equals 5
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Pre-Algebra
and 9 – 4 equals 5and 9 – 4 equals 5
X = 5X = 5
4’s cancel out 4’s cancel out
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2X + 5 = 17X + 5 = 17
Another exampleAnother example
Pre-Algebra
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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
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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?”
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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
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So subtract 5 from 17…So subtract 5 from 17…
Pre-Algebra
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To get 2X by itselfTo get 2X by itself
Pre-Algebra
2X = 17 - 52X = 17 - 5
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We now know…We now know…
Pre-Algebra
2X = 122X = 12
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Pre-Algebra
For 2 X = 12For 2 X = 12 Ask – What number times 2 Ask – What number times 2
equals 12?equals 12?
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Pre-Algebra
There are two ways There are two ways
of finding X forof finding X for 2X = 122X = 12
On MathLineOn MathLine
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Pre-Algebra
Divide by 12 by two’s..Divide by 12 by two’s..
112233445566
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Pre-Algebra
Or divide 12 into two Or divide 12 into two GROUPS…GROUPS…
6666
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Pre-Algebra
Either way Either way X = 6X = 6
6666
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On paper On paper the Algebra looks like the Algebra looks like
this…this…
Pre-Algebra
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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
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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.
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2X + 5 = 17 2X + 5 = 17
Pre-Algebra
– – 5 –5 – 55
5’s cancel out 5’s cancel out
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2X = 17 2X = 17 – – 55
Pre-Algebra
5’s cancel out 5’s cancel out
and 17 – 5 equals 12and 17 – 5 equals 12
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Pre-Algebra
and 17 – 5 equals 12and 17 – 5 equals 12
2X = 122X = 12
5’s cancel out 5’s cancel out
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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
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Pre-Algebra
So, XSo, X = = 1212 ÷ 2÷ 2
OrOr
XX = = 66