Using Algebra Tiles to Solve Equations Combine Like Terms and use the Distributive Property Important Vocabulary Equation An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value ID: 726431
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Slide1
Objective: To understand the different parts of an equation, and use algebra tiles to help us solve problems.
Using Algebra Tiles to Solve Equations, Combine Like Terms, and use the Distributive PropertySlide2
Important Vocabulary!
Equation –
An equation is a mathematical statement that uses an equal sign to show that two expressions have the same value.
To
solve
an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the
solution
of the equation.
Term
– the
parts of an expression that are added or subtracted.
Like
Term
– Two
or more terms that have the same variable raised to the same power.
Coefficient
– The
number that is multiplied by a variable in an algebraic expression.
Constant
– A
value that does not change.
Equivalent
Expression
– Equivalent
expressions have the same value for all values of the
variables.Slide3
Parts of an Equations!
5x + 4x + 5 = 50
coefficient
variable
constant
Like TermsSlide4
Your Turn…
6y + 5x + 2y = 42
Coefficients?
Variables?
Like Terms?
Constant?Slide5
Discovery
What do you think the different tiles stand for? Why?Slide6
Algebra Tiles
What do these stand for? Why?Slide7
Let’s Try It
Represent the following equations on your tile mat.
Compare your answer with a neighbor. Assist each other as needed.
5 + x = 2
5 – 5x = -1
2x – 5 = 9Slide8
Build this equation
5 + x =
2
On your own:
x – 2 = 3
x + 3 = 7
7 – x = 9
x – 5 = 1
2 = -x – 4 Slide9
Build this equation
2x = 6
-3x = 15
-12 = -4x
3x = 12
6x = 3
5 = 5x
To solve for the variable, you must do the
inverse operation
.
With tiles, in order to divide, you must
create even groups
of x tiles and unit tiles.
x = 3 Slide10
When should we NOT use tiles?
Let’s say this
piece of paper represents our whole x
.
How many sections are there on the paper?
How many positive tiles will go in each section?
Using the visual, what is the value of
x
?Slide11
Build this equation
To solve for the variable, you must do the
inverse operation
.
With tiles, you must isolate x first, then you can figure out what x equals.
x = 50
This can stand for x/5
(5)
(5)Slide12
Use your algebra tile mat and algebra tiles, to solve the following equations.
2x – 3 = 9
5 – 5x = -1
3x – 1 = 8
7 = 5x + 2
2x + 3 = 3x
4x – 2 = 3x + 6
Activity…
Make even groups with each x
x = 6
Zero pairsSlide13
Summary!
How will algebra tiles be useful to you in solving equations and combining like terms?Slide14
Combining Like Terms
What does this tile represent?
What does this tile represent?
What do these tiles represent?
What do these tiles represent?
1
x
2
-x
2
x
-x
-1Slide15
Combining Like Terms
4x + 5
Can these be combined? Explain your reasoning.
4x + 5x
Can these be added together? Explain your reasoning.
These are NOT the same shapeSlide16
Let’s Try It!
Represent
the following
expressions
on your tile mat. Compare your answer with a neighbor. Assist each other as needed.
3x + 4 – 2x3x + 5
2x2 – 6x +2
x2 – 2x – 3
3x2 + 3x – 5xSlide17
Combining Like Terms: Build It!
2x
2
+ 3x + 5 +x
2
– 5x – 1
Try these:
2x
2+4x+2x2 – x
3x2
– 2x – 1 – 3x2 – 2x – 2
x
2+2x+1 – 3x2 – x
3x2
– 3x + x2 – 1 + 2x – 3
What’s left??
x
2
x
2
x
x
x
1
1
1
1
1
x
2
-x
-x
-x
-x
-x
-1
3x
2
– 2x + 4Slide18
Summary
Write 2 – 3 sentences explaining how you use algebra tiles to combine like terms. Pretend you are teaching this concept to a 4
th
grader.Slide19
Distributive PropertyUsing algebra tiles, we will use Distributive Property to help us combine like terms and solve equations.
Distributive Property
-
The property that states that if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products.Slide20
How does it work?
Represent the following expression using algebra tiles:
3 (x + 2)
3 groups of x plus 2
When we group our like tiles, what expression
do we have?
3 (x + 2) =
3x + 6Slide21
Let’s Practice!
Simplify the following expressions:
2(x – 4)
On your own
:
(2x + 1)4
6(-x – 2) + 3
(3 – 2x)3 + x
2 groups of x – 4
After grouping like tiles, what do we have?
= 2x – 8Slide22
Distributive Property and Equations
Use distributive property to solve the following equations!
2(x + 3) = 10
You try
:
(-x – 4)3 = 3
2 + 2(2x – 3) = 8
4 = 3x – (-x + 3)2
After making zero pairs, we are left with 2 x’s
And 4 unit tiles. What does x equal?
x = 2Slide23
Summary
Pair up with a partner. Each partner will make up a problem that uses the concepts learned in today’s lesson. Switch problems with your partner and solve.