Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 Finding Perimeter Suggested Book to Use: Burns, M. (1997). Spaghetti and Meatballs for All! New York, NY: Scholastic Press. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 Mr. and Mrs. Comfort invited 30 people to the reunion. So, there will be 32 people eating dinner. If there are 4 people at each table, how many tables and chairs should they rent? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 32  4 = 8 tables Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Mr. and Mrs. Comfort rented 32 chairs and 8 tables! Oh, no! We’re missing a chair! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

8 tables with 4 chairs at each table Mrs. Comfort’s Seating Arrangement is… 8 tables with 4 chairs at each table Each table’s length is 1 unit, and each table’s width is 1 unit. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 1 Unit Perimeter: 1+1+1+1= 4 units 1 Unit 1 Unit 1 Unit 48 = 32 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

And their company began to arrive… Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

How many chairs did we lose? Why? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

We lost 2 chairs because our total perimeter went from 8 units to 6 units. The perimeter of 2 separate tables = 8 units. 4+4 = 8 So, the perimeter of 2 tables pushed together = 6 units. 1+2+1+2 = 6 2 1 1 2 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Now we have 12 total people. 6 more people arrived… Now we have 12 total people. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

But… is this enough seats for 12 people? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 No, because the total perimeter is now 8 units. So, 4 people do not have a chair. 2 2 2 2+2+2+2 = 8 2 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Are there enough seats for the 12 people now? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 3 3 2 3+2+3+2 = 10 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

No, we need to push together 2 more tables… Now, all 12 people have a seat. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 4 4 2 4+2+4+2 = 12 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

The Comfort’s neighbors arrived with their 2 children… Now we have 16 people! But wait… We don’t have enough seats! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 The total perimeter of the 2 BIG tables is now 16 units. All 16 people have a seat. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 82 = 16 2+2+2+2 = 8 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 Mr. Comfort’s mother and father arrive… We now have 18 people! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 What is our new perimeter? Are there enough seats for all 18 people? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

The new perimeter is 18 units. All 18 people have a chair! 8 1 1 8 1+8+1+8= 18 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 Mrs. Comfort’s mother and father arrive… Now we have 20 people! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Can you figure out the total perimeter of our 2 tables? The total perimeter is 20 units. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 4 1 1 4 4 1 1 4 1+4+1+4 = 10 10  2 = 20 Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 4 more people arrived… Now we have 24 people! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Does everyone have a chair? So, what is our total perimeter? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 1+2+1+2 = 6 6  4 = 24 The total perimeter is 24. Everyone has a chair! Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

The final 8 guests arrive… Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006 What must we do with the tables in order for all 32 people to have a seat? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

Move the tables back to Mrs. Comfort’s original plan! What is the total perimeter? Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006