Transcript Equations and Algebra Tiles

Using Algebra Tiles to Solve
Equations, Combine Like Terms, and
use the Distributive Property
OBJECTIVE: TO UNDERSTAND THE DIFFERENT PARTS OF AN
EQUATION, AND USE ALGEBRA TILES TO HELP US SOLVE
PROBLEMS.
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.
Parts of an Equations!
Like
Terms
5x + 4x + 5 = 50
constant
coefficient
variable
Your Turn…
6y + 5x + 2y = 42
• Coefficients?
• Variables?
• Like Terms?
• Constant?
Discovery
• What do you think the different tiles stand for? Why?
Algebra Tiles
What do
these stand
for? Why?
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 = 9
Build this equation
5+x=2
On your own:
• x–2=3
• x+3=7
• 7–x=9
• x–5=1
• 2 = -x – 4
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
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?
Build this equation
•
This can stand for x/5
(5)
(5)
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
Activity…
Use your algebra tile mat and algebra tiles, to solve
the following equations.
2x – 3 = 9
5 – 5x = -1
Zero
pairs
3x – 1 = 8
7 = 5x + 2
2x + 3 = 3x
4x – 2 = 3x + 6
Make even
groups with
each x
x=6
Summary!
• How will algebra tiles be useful to you in solving
equations and combining like terms?
Combining Like Terms
What does this tile represent?
x2
-x2
What does this tile represent?
What do these tiles represent?
What do these tiles represent?
x
-x
1
-1
Combining Like Terms
4x + 5
These are
NOT the
same shape
Can these be combined? Explain your reasoning.
4x + 5x
Can these be added together? Explain your reasoning.
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 – 2x
3x + 5
2x2 – 6x +2
x2 – 2x – 3
3x2 + 3x – 5x
Combining Like Terms: Build It!
2x2
+ 3x + 5
+x2
– 5x – 1
x2
x2
x x x
1
1
1
1
1
Try these:
2x2+4x+2x2 – x
3x2
– 2x – 1 –
3x2
-1
– 2x – 2
x2
x2+2x+1 – 3x2 – x
3x2
– 3x +
x2
– 1 + 2x – 3
3x2 – 2x + 4
What’s left??
-x -x -x -x -x
Summary
• Write 2 – 3 sentences explaining how you use
algebra tiles to combine like terms. Pretend you are
teaching this concept to a 4th grader.
Distributive Property
• Using 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.
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 + 6
Let’s Practice!
Simplify the following expressions:
2(x – 4)
2 groups of x – 4
On your own:
(2x + 1)4
6(-x – 2) + 3
= 2x – 8
(3 – 2x)3 + x
After grouping like tiles, what do we have?
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
x=2
After making zero pairs, we are left with 2 x’s
And 4 unit tiles. What does x equal?
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.