around the block by andrew derer and gail warren

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

Math “Talk”

VARIABLE:

A letter or symbol used to represent a number.

2 + = 42x

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.

at your 3 different Algeblocks®.

What do you see?

Write down some of your observations.

Discovery Activity

Discovery Activity

Trace your tiles onto your paper.

You have 2 minutes to complete this part

Which is which?

x

1

x2

Show and Tell

Using your Algeblocks® , show:

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

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

Let’s try another

Using your Algeblocks® , can you show:

x2 + x + 4Excellent!

Just One More Together

Using your Algeblocks® , can you show:

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

x + 1

Now it’s your turn!

Finish the front of the sheet.

Lay out the tiles for each problem.

Trace the tiles.

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

Place the tiles under x + x.

Trace both tiles.

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

Place the tiles under 2x + 1.

Trace the tiles.

x2

Pull down one x2.

Place the tiles under x2.

Trace both tiles.

2x2 + 3x + 5

Pull down two x2.

Pull down 3x.

Pull down 5.

These two expressions would combine to make:

Putting it all together

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

x2

4x+ 2x

6x

+

Oh, I see

x2 + 2x and 4x

Combine to make

x2 + 6x

Now it’s your turn2x2 + 3x2

5x2

Now it’s your turn2x2 + 3x + x2 + 5x

3x2 + 8x

What About…4x2 + 2x

4x2 + 2x

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

3x2 + 6x + 6

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…

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 +

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!

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.

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…

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...

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!

The area of our rectangles Stems Leaves

0

1

2

3

4

5

Please place all your tiles in groups like this:

x2

x

1

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

Questions?Thank you