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
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
32  4 = 8 tables
Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
Mr. and Mrs. Comfort rented
32 chairs and 8 tables!
Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
Oh, no! We’re
missing a chair!
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
1 Unit
1 Unit
1 Unit
Perimeter:
1+1+1+1= 4 units
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
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
No, because the total
perimeter is now 8 units.
So, 4 people do not have a
chair.
2
2
2
2Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
2+2+2+2 = 8
Are there enough seats for the 12 people
now?
Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
2
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
2
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
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
2
2
2
2
2
2
2
2
2+2+2+2 = 8
82 = 16
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
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
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
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
4 more people arrived…
Now we have 24
people!
Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
So, what is our total
perimeter?
Does everyone
have a chair?
Created/Edited by Eddy, McCasland,
Owen at NCTM Conference 2006
2
1
2
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
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