1. 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

2. 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

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

4. 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

5. 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

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

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

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

9. 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.
= 6 2 1 1 2
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

10. 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

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

12. 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
= 8 2
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

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

14. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 20063 3 2
= 10
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

15. 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

16. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 20064 4 2
= 12
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

17. 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

18. 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

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

20. 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

21. 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

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

23. 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

24. 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

25. Created/Edited by Eddy, McCasland, Owen at NCTM Conference 20064 1 1 4 4 1 1 4
= 10
10  2 = 20
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

26. 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

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

28. 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2
= 6
6  4 = 24
The total perimeter is 24. Everyone has a chair!
Created/Edited by Eddy, McCasland, Owen at NCTM Conference 2006

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

30. 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

31. 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