1. Parallelogram - quadrilateral with two pairs of parallel sides
Vocabulary:
Parallelogram - quadrilateral with two pairs of parallel sides
In Lesson 5.3.1, you worked with your study team to rearrange two irregular shapes into rectangles to find their areas more easily.  Today, you will use a technology tool to investigate this question: Can all shapes be rearranged to make rectangles?  As you work, visualize what each shape will look like if it is cut into pieces.  Also picture how those pieces could fit back together to make a rectangle. 
Ask yourself these questions while you investigate:
How can I break this shape apart?
How can I rearrange the pieces of the shape to make a new shape?

2. 76. CHANGE IT UP
What kinds of shapes can be rearranged to make rectangles?  If one complete rectangle is not possible, can any shape be divided into a few different  rectangles?
Use the Area Decomposer eTools:
Shape 1 (Desmos)
Shape 2 (Desmos)
Shape 3 (Desmos)
Shape 4 (Desmos)
Shape 5 (Desmos)
Shape 6 (Desmos)
Shape 7 (Desmos)
Shape 8 (Desmos)
Figure out which shapes can be rearranged into rectangles. 
If you find a way to rearrange the shape on the computer, record your work on the resource page by:
Drawing lines on the original shape to show the cuts you made.
Drawing the rectangle made out of the cut pieces.
Finding the area of the shape.

3. 77. REARRANGING CHALLENGE — PARALLELOGRAMS
The shapes at right are examples of parallelograms. 
A parallelogram is a quadrilateral with two pairs of opposite, parallel sides. 
With your team, decide if there is a strategy for cutting and rearranging any parallelogram that will always change it into a rectangle. 
To start, set Area Decomposer: Shape 8 (Desmos) to show a parallelogram like one of those shown at right
While one person controls the computer, the other(s) should show on the Lesson 5.3.2C Resource Page how the parallelogram was cut and rearranged.  Remember that everyone should share ideas about how to try to cut and rearrange the shape.  Make sure that each person has an opportunity to control the computer during the investigation.
How can you cut and rearrange the parallelogram so that you end up with a rectangle?  Draw your cuts on the original figure, and then draw what the final rectangle looks like.  Use arrows to show where the pieces move. 
Will this cutting strategy work for any parallelogram?  On a new sketch of a different parallelogram, show the cuts that you would make, and use arrows to show where the pieces would move.  Use your picture to explain a general strategy.

4. 78. AREA OF A PARALLELOGRAM
On her homework assignment, Lydia encountered the parallelogram shown at right.  The homework problem
asked her to find the area of the shape.
Lydia decided to cut and rearrange the shape to make a rectangle, as she did in problem 5-77.  However, she was not sure what the measurements of that rectangle would be
With your team, figure out what the base and height of Lydia’s new rectangle will be.  Which side did you use for the height?  How do you know which side is the height?  Draw a diagram to show how you know.
What is the area of the parallelogram?  Show your work.
Now consider other parallelograms.  For example, the parallelogram at right has lengths marked b, c, and h.   What will be the base of the new rectangle?  What will be its height?  Talk with your team about the difference between the parts labeled h  and  c.
How would you find the area of the rectangle?  Which lengths would you use?  Why?
What is the area of the parallelogram?  That is, if  A  represents the area of the parallelogram, use the variables in the picture to write a formula for calculating the area of any parallelogram

5. Tonight’s homework is… 5.3.2 Review & Preview, problems # 80-84
Show all work and justify your answers for full credit.
Vocabulary Review…
Distributive Property
 a(b + c) = ab + ac . 
For example, 10( 7 + 2) = 10 · · 2.