around the block by andrew derer and gail warren

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Around the Block By Andrew Derer and Gail Warren

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Page 1: Around the Block By Andrew Derer and Gail Warren

Around the Block

By Andrew Derer

and

Gail Warren

Page 2: Around the Block By Andrew Derer and Gail Warren

Math “Talk”

Some terms we need to know:

EQUATION:

A math sentence containing an equal sign.

=2+2 4

Page 3: Around the Block By Andrew Derer and Gail Warren

Math “Talk”

VARIABLE:

A letter or symbol used to represent a number.

2 + = 42x

Page 4: Around the Block By Andrew Derer and Gail Warren

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.

Page 5: Around the Block By Andrew Derer and Gail Warren

at your 3 different Algeblocks®.

What do you see?

Write down some of your observations.

Discovery Activity

Page 6: Around the Block By Andrew Derer and Gail Warren

Discovery Activity

Trace your tiles onto your paper.

You have 2 minutes to complete this part

Page 7: Around the Block By Andrew Derer and Gail Warren

Which is which?

x

1

x2

Page 8: Around the Block By Andrew Derer and Gail Warren

Show and Tell

Using your Algeblocks® , show:

x2 + 3x + 2It would look like this:

Page 9: Around the Block By Andrew Derer and Gail Warren

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

Page 10: Around the Block By Andrew Derer and Gail Warren

Let’s try another

Using your Algeblocks® , can you show:

x2 + x + 4Excellent!

Page 11: Around the Block By Andrew Derer and Gail Warren

Just One More Together

Using your Algeblocks® , can you show:

Great!Draw x + 1 on your sheet where it belongs.

x + 1

Page 12: Around the Block By Andrew Derer and Gail Warren

Now it’s your turn!

Finish the front of the sheet.

Lay out the tiles for each problem.

Trace the tiles.

Page 13: Around the Block By Andrew Derer and Gail Warren

x + xPull down one x. Pull down another x.

Place the tiles under x + x.

Trace both tiles.

Page 14: Around the Block By Andrew Derer and Gail Warren

2x + 1Pull down two x. Pull down a 1.

Place the tiles under 2x + 1.

Trace the tiles.

Page 15: Around the Block By Andrew Derer and Gail Warren

x2

Pull down one x2.

Place the tiles under x2.

Trace both tiles.

Page 16: Around the Block By Andrew Derer and Gail Warren

2x2 + 3x + 5

Pull down two x2.

Pull down 3x.

Pull down 5.

Page 17: Around the Block By Andrew Derer and Gail Warren

These two expressions would combine to make:

Putting it all together

• If I have “like tiles” I can combine them.

x2

4x+ 2x

6x

+

Page 18: Around the Block By Andrew Derer and Gail Warren

Oh, I see

x2 + 2x and 4x

Combine to make

x2 + 6x

Page 19: Around the Block By Andrew Derer and Gail Warren

Now it’s your turn2x2 + 3x2

5x2

Page 20: Around the Block By Andrew Derer and Gail Warren

Now it’s your turn2x2 + 3x + x2 + 5x

3x2 + 8x

Page 21: Around the Block By Andrew Derer and Gail Warren

What About…4x2 + 2x

4x2 + 2x

Page 22: Around the Block By Andrew Derer and Gail Warren

Finally2x2 + 4x + 4 + x2 + 2x + 2

3x2 + 6x + 6

Page 23: Around the Block By Andrew Derer and Gail Warren

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…

Page 24: Around the Block By Andrew Derer and Gail Warren

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 +

Page 25: Around the Block By Andrew Derer and Gail Warren

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!

Page 26: Around the Block By Andrew Derer and Gail Warren

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.

Page 27: Around the Block By Andrew Derer and Gail Warren

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…

Page 28: Around the Block By Andrew Derer and Gail Warren

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...

Page 29: Around the Block By Andrew Derer and Gail Warren

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!

Page 30: Around the Block By Andrew Derer and Gail Warren

The area of our rectangles Stems Leaves

0

1

2

3

4

5

Page 31: Around the Block By Andrew Derer and Gail Warren

Please place all your tiles in groups like this:

x2

x

1

Page 32: Around the Block By Andrew Derer and Gail Warren

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

Page 33: Around the Block By Andrew Derer and Gail Warren

Questions?Thank you