1. Lesson 2.2.3 Concept: Relationship of Area and Perimeter
You now have learned a lot about area (the number of square units that are needed to cover a shape completely without gaps or overlaps) and perimeter (the sum of the lengths of the sides of a shape). 
If a shape has a particular area, will its perimeter be the same as any other shape with the same area? 
If you change the area of a shape, does the perimeter change?
Today you will use Base Ten Blocks to investigate the relationship between area and perimeter.

2. 2-39. (page 71) Have a manager get a set of Base Ten Blocks.  (Or explore using virtual tiles: Base Ten Blocks (CPM). 
For this lesson, only the top face of the Base Ten Blocks will be considered as part of the shape.  Be sure to use the blocks in a way that all team members can see and touch them.
There are three kinds of blocks.  Find one of each kind of block and trace its sides on your paper. 
The side length of the smallest block is 1 centimeter.  On your paper, mark the lengths of the sides of all three blocks. 
Find the area and perimeter of each of the three blocks.  Indicate the correct units of measurement.  
What is the combined area of the blocks drawn
below?

3. The blocks are named by their area. 
The block that has an area of 100 cm2 is called a hundred block. 
The block that is 1 cm2 in area is called a one block.   Base Ten Blocks 
Which blocks could be used to represent an area of 127 cm2?  With your team, record at least two ways to build 127 cm2.
f. Find all of the ways that you can represent an area of 34 cm2 with Base Ten Blocks. 
Organize and record your list of ways so that it makes sense.  Be ready to explain to the class how you know your list is complete. 

4. 40. CHANGING THE AREA
Jay arranged a hundred block and a one block as shown at right. Explore using: Base Ten Blocks (CPM).
What is the area of Jay’s shape?  What is the perimeter?  Explain how you know.  
Jay added another one block to his shape as shown at right.  Did the area of his shape change?  Did the perimeter change? 
What if Jay added his new one block to a different part of the hundred block?  Would it change the perimeter?  Discuss this with your team and be ready to explain your ideas to the class.  
Summarize what you discovered in parts (a) through (c) above.  That is, what can happen to the perimeter when the area of a shape is changed? 

5. 41. CHANGING THE PERIMETER
Instead of changing the area, as Jay did in the previous problem, what if you keep the area the same?  Will the perimeter still change sometimes?  Consider this as you complete parts (a) and (b) below. Explore using: Base Ten Blocks (CPM).
What different combinations of Base Ten Blocks could you use to make a figure with an area of 101 cm2?  Carefully list the ways
Create a shape with Base Ten Blocks that has an area of 101 cm2 with the largest possible perimeter.  How can you tell there is no larger perimeter possible? 

6. 42. 
Use Base Ten Blocks to make shapes that have the smallest and the largest possible perimeters with the areas given below. 
Build and sketch each shape and record each perimeter. 
Which areas can you make into rectangles with both dimensions (length and width) greater than 1? 
Which can you make into a square? 
Explain your thinking. Explore using: Base Ten Blocks (CPM).
110 cm2
107 cm2
144 cm2

7. 43. Find the area of each figure below in at least two ways. 
(Note that in each figure, all of the angles are right angles.) 
Explain how you get your answers. Explore using the 2-43a Student eTool (CPM)  2-43b Student eTool (CPM). 
Use different colors to show finding the area in more than one way!
a b.
44. LEARNING LOG
Is there a relationship between area and perimeter?  Does changing one mean the other one always changes?  Use examples to support your ideas.  Label the entry “Area and Perimeter” and include today’s date. 

8. Tonight’s homework is…
2.2.3 Review & Preview, problems #46-#50. (text page 74)
Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper.
(Lesson 2.2.3)
Show all work and justify your answers for full credit.