Transcript around_block_print

Around the Block
By Andrew Derer
and
Gail Warren
Some terms we need to know
• Algebra
• a generalization of math in which
letters representing numbers are
combined according to certain rules.
• Equation • A math sentence containing an equal
sign.
• Variable • A letter or symbol used to represent a
number.
Discovery Activity
• Describe the characteristics of each tile for part 1.
• Trace your tiles onto your paper
Discovery Activity
• Describe the characteristics of each tile for part 1.
• Trace your tiles onto your paper
• You have 2 minutes to complete this part 
Which is which?
x
2
x
1
Which is which?
x
2
x
1
Example
1x2 + 3x + 2
This is
called an
algebraic
expression!
Example
1x2 + 3x + 2
This is
called an
algebraic
expression!
It would look like this:
Example
1x2 + 3x + 2
If there isn’t a
number in front of
the variable, the
coefficient is
automatically 1.
The number in
front of a
variable is called
a coefficient.
Putting it all together
• If I have “like tiles” I can combine them.
x2 + 2x
4x
These two
expressions
would combine
to make:
Putting it all together
• If I have “like tiles” I can combine them.
These two
expressions
would combine
to make:
4x + 2x
x2
Putting it all together
• If I have “like tiles” I can combine them.
These two
expressions
would combine
to make: x2 + 6x
Oh, I see
2
x
+ 2x
and
4x
Combine to make
2
x
+ 6x
2
x
+ 2x
2
x
and
+ 6x
4x
Now it’s your turn
Let’s see if we can all be finished
in 5 minutes
Creating Rectangles
• You can create rectangles with your
Algeblocks® .
• You must use at least one of each kind of
tile.
• Using variables, you can describe the
length and width.
• Let’s try one together…
Creating a rectangle
Here is one example…
Remember,
a square
is also a
rectangle!
Creating a rectangle
Here is one example…
x
1
x+1
• Notice the line
segments go from
one side to the other.
• Each x is exactly 1
unit wide.
• Each x2 is exactly x
wide
• So this rectangle is
x + 1 wide
Creating a rectangle
Here is one example…
x
x+1
1
• Each x is exactly 1
unit wide.
• Each x2 is exactly x
tall
• So this rectangle is
x + 1 tall
Creating Rectangles
• Your turn!
• Trace your rectangle onto the sheet
provided.
• Using x, give the length and width of your
creation.
• Like this…
Creating Rectangles
Trace your rectangle here. Write the length and width in the spaces below.
x+1
x+1
Width:
x+1
Length:
x+1
If area is length times width, what is the area of your rectangle? (______________) x (_____________)
If I told you each x had a value of 2, could you find the area? (
_________ ) x ( _________)
Creating Rectangles
Trace your rectangle here. Write the length and width in the spaces below.
x+1
Width:
x+1
Length:
x+1
x+1
If area is length times width, what is the area of your rectangle? (______________
) x (_____________
)
If I told you each x had a value of 2, could you find the area? (
_________ ) x ( _________)
Creating Rectangles
Trace your rectangle here. Write the length and width in the spaces below.
x+1
Width:
x+1
Length:
x+1
x+1
If area is length times width, what is the area of your rectangle? (______________
) x (_____________
)
If I told you each x had a value of 2, could you find the area? (
2+1
2+1
_________
) x ( _________
)
Creating Rectangles
Trace your rectangle here. Write the length and width in the spaces below.
x+1
Width:
x+1
Length:
x+1
x+1
If area is length times width, what is the area of your rectangle? (______________
) x (_____________
)
If I told you each x had a value of 2, could you find the area? (
3
3
_________
) x ( _________
)= 9
Creating Rectangles
Trace your rectangle here. Write the length and width in the spaces below.
x+1
Width:
x+1
Length:
Place the value of
the ones place on a
sticky note and put it
with its appropriate
stem on the board
9
x+1
x+1
If area is length times width, what is the area of your rectangle? (______________
) x (_____________
)
If I told you each x had a value of 2, could you find the area? (
3
3
_________
) x ( _________
)= 9
The area of our rectangles
Stems
0
1
2
3
4
5
Leaves
9
The area of our rectangles
Stems
0
Leaves
9
1
2
3
2
Another Example:
If the area of my
rectangle is 32, I
would put a 2 on
my sticky note.
4
5
Your turn!
Please place all your tiles in groups like this:
1
x2
x
Let’s see what you remember
• Coefficient • A number that is in front of a variable.
• Equation
• A math sentence containing an equal
sign.
• Variable
• A letter or symbol used to represent a
number.
• Like Terms • Two or more pieces that are the
same size.
2
x
1
x
Questions?
Thank you