around the block by andrew derer and gail warren
TRANSCRIPT
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Around the Block
By Andrew Derer
and
Gail Warren
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Math “Talk”
Some terms we need to know:
EQUATION:
A math sentence containing an equal sign.
=2+2 4
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Math “Talk”
VARIABLE:
A letter or symbol used to represent a number.
2 + = 42x
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Math “Talk”
ALGEBRA:
A generalization of math in which letters representing numbers are combined according to certain rules.
Our algebra today will have ONE variable in an equation.
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at your 3 different Algeblocks®.
What do you see?
Write down some of your observations.
Discovery Activity
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Discovery Activity
Trace your tiles onto your paper.
You have 2 minutes to complete this part
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Which is which?
x
1
x2
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Show and Tell
Using your Algeblocks® , show:
x2 + 3x + 2It would look like this:
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Show and Tell
+ +x2 3x 2
This is called an algebraic expression!
The number in front of a variable is called a coefficient.
If there isn’t a number in front of the variable, the coefficient is automatically 1.
1 3
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Let’s try another
Using your Algeblocks® , can you show:
x2 + x + 4Excellent!
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Just One More Together
Using your Algeblocks® , can you show:
Great!Draw x + 1 on your sheet where it belongs.
x + 1
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Now it’s your turn!
Finish the front of the sheet.
Lay out the tiles for each problem.
Trace the tiles.
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x + xPull down one x. Pull down another x.
Place the tiles under x + x.
Trace both tiles.
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2x + 1Pull down two x. Pull down a 1.
Place the tiles under 2x + 1.
Trace the tiles.
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x2
Pull down one x2.
Place the tiles under x2.
Trace both tiles.
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2x2 + 3x + 5
Pull down two x2.
Pull down 3x.
Pull down 5.
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These two expressions would combine to make:
Putting it all together
• If I have “like tiles” I can combine them.
x2
4x+ 2x
6x
+
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Oh, I see
x2 + 2x and 4x
Combine to make
x2 + 6x
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Now it’s your turn2x2 + 3x2
5x2
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Now it’s your turn2x2 + 3x + x2 + 5x
3x2 + 8x
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What About…4x2 + 2x
4x2 + 2x
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Finally2x2 + 4x + 4 + x2 + 2x + 2
3x2 + 6x + 6
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Creating Rectangles
• You can create rectangles with your Algeblocks® .
• You must use at least one of each kind of tile.
• You can find the “value” of your rectangle.
Let’s try one together…
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Creating a rectangle
Notice the line segments go from one side to the other.
Here is one example…
Remember, a square
is also a rectangle!
Label each tile correctly as x2, x, or 1
x2
x
x
1
Write the equation for your rectangle.
x2 + x + x + 1
Remember to combine ‘like terms’.
2x + 1x2 +
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Creating Rectangles
• Use your Algeblocks® to make a rectangle.
• Trace your rectangle onto the sheet provided.
• Mark each tile by writing x2, x or 1 inside.
• Write your equation; remember to combine like
terms.
Your Turn!
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x2
x
x4
2
2
1
Creating a rectangle
Find the value of your rectangle by adding up the value for each tile. + + + = 9
Now give x the value of 2.
Write the value of each tile inside.
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Our Class Results
• Look at the value of your ENTIRE rectangle.
• We are going to show our class results in a “Stem and Leaf” plot.
Like this…
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Our Class Results Stems Leaves
0
1
2
3
4
5
Remember our sample rectangle.
It had a value of 9.
9 •Write the ones place of your value on the sticky note.
•Place the sticky note next to the tens place on the plot, like this...
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The value of our rectangles Stems Leaves
0
1
2
3
4
5
9
2
Another Example: If the area of my rectangle is 32, I would put a 2 on
my sticky note and place it next to the
3 on the plot.
Your turn!
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The area of our rectangles Stems Leaves
0
1
2
3
4
5
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Please place all your tiles in groups like this:
x2
x
1
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Let’s see what you remember• Coefficient• Equation
• Variable
• Like Terms
• A number that is in front of a variable.• A math sentence containing an equal
sign.• A letter or symbol used to represent a
number.• Two or more pieces that are the
same size.
1 xx2
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Questions?Thank you