With space utilization such a hot topic at CPS right now, of course it makes sense that some of you would be curious about how I arrived at my conclusion that the **CPS Space Utilization formula from 2011-2012 was incorrect and misleading** as to the number of under-utilized elementary schools in the Apples to Apples Elementary Data set.

So let me, as my 4^{th} grade math teacher required me to do, show my work. (*Big shout out to my 4 ^{th} grade math teacher, Toni Sulkowski, and all of the fantastic math teachers working in public education. You are so very appreciated*.

*I hated Algebra at the time, but wow, so helpful in creating Excel formulas.)*

**Question: Where did you get the numbers for each school in 2011-2012?**

Each elementary school page on the CPS website has that school’s Space Utilization Report for 2011-2012 listed as a downloadable PDF.

This CPS provided report tells you the following:

- The total number of usable classrooms in the school in 2011-2012. (Thanks to a Tweet from CPS, we now know that a full-sized classroom has to be 600 sq ft. at minimum)
- The total of homerooms vs. “extra” (ancillary) rooms at the school in 2011-2012. Ancillary rooms are rooms used for special education, art, computer lab, etc. (They don’t count gyms, auditoriums, etc. in this number.)
- The “ideal enrollment” for this school in 2011-2012.
- The lowest enrollment and the highest enrollment that the school could have and still be considered “efficient” by CPS in 2011-2012.
- The percentage of under or over-enrollment based on the ideal enrollment in 2011-2012.
- The label that CPS applied to the school in 2011-2012: Under-Utilized, Efficient, or Overcrowded.

**Bottom line? I got the numbers from CPS.** They are **not** the most current numbers because those numbers have not been released as of December 4, 2012 at 12:38 p.m.

**Question: Where did these numbers—classroom vs. ancillary—come from?**

I’m not sure who was responsible for gathering or giving the information on each school to CPS.

I have walked through two schools and compared the classrooms to the numbers on their 2011-2012 reports, they were pretty close (and I’m not sure if the use of some of these classrooms have changed since last year.)

I also used recent school floor plans from the Asbestos Inspection Reports that CPS also posts for each school. If you open up the PDF “Asbestos Inspection Report 2010” and scroll through it, all of them that I have reviewed have a floor plan of the school with classrooms identified.~~ (Here is an example from Beaubien Elementary and it begins on Page 28) ~~*These reports are no longer publicly accessible via CPS.edu as of January 2018.*

The formula for calculating the number of ancillary classrooms for each school is reported in the CPS Space Utilization guidelines as follows:

**Total # of Classrooms x .769 = Total # of Homerooms**

**Total # of Classrooms – Total # of Homerooms = Total # of Ancillary Classrooms**

Not all of the elementary schools in Apples to Apples have exactly .769 of total classrooms as homerooms. Some have less than that. The least amount of homerooms was 66.7% of total classrooms. The most was 76.8%

**This is significant because the fewer homerooms you have, the fewer students you are required to have enrolled in the school and still be considered “efficient” by CPS**. So under-reporting potential homerooms can make an underutilized school appear more efficient according to CPS’ formula.

To give CPS the FULL benefit of the doubt, I corrected for under-reporting of homerooms in my “adjusted formula”. This increased the potential number of schools that were considered as under-utilized under the old formula.

**Question: What WAS the formula that CPS uses to calculate IDEAL enrollment in 2011-12?**

The formula was relatively straightforward:

**Total # of Homerooms x 30 students per homeroom = Ideal Enrollment of Students at School**

**Question: Where did this 30 students number come from? I thought CPS Guidelines on Class Limits were 28 students in K-3 ^{rd} grades and 31 students in 4th-8^{th} grades?**

I can’t say for sure why they used 30 as the number in the formula because I haven’t confirmed this with CPS. My best guess is that they arrived at it this way:

K = 28

1st grade = 28

2^{nd} grade = 28

3^{rd} grade = 28

4^{th} grade = 31

5^{th} grade = 31

6^{th} grade = 31

7^{th} grade = 31

8^{th} grade = 31

**28 + 28 + 28 + 28 + 31+ 31+ 31 + 31 +31 = 267**

**267/9 grades = 29.667**

Round 29.667 to the nearest whole number = **30**

**Question: So, what is the problem with this formula?**

This is a bit more complicated, so bear with me here.

If we take an average of 30 students per homeroom as the MAXIMUM limit of students in a homeroom, then **any enrollment OVER an average of 30 students** **per classroom should be considered overcrowding.**

**But that is not what the 2011-2012 CPS formula is showing.**

The 2011-2012 CPS formula used an average of 30 students per homeroom as their IDEAL enrollment for the school. (If that is true and they keep to their own limits, but that is another story for another day. See Apples to Apples Class Sizes Dataset here.)

CPS used a RANGE of efficiency in 2011-2012 to determine school enrollment. Which means:

**30 students per homeroom was the ideal**or “midpoint” of the range**30 students per homeroom + 20% MORE**was the “top” of the efficiency range**30 students per homeroom – 20%**was the “bottom” of the efficiency range.

After the top of the range was reached? CPS considered a school officially overcrowded.

After enrollment went under the bottom of the range? CPS considered the school officially underutilized.

**The problem with this formula was that it set a NEW maximum for the average number of students in the classroom BEFORE CPS considered that classroom (and school) to be overcrowded.**

How?

Because **30 + (20% of 30) = 36 **

(This can also be written as **30 x 120% = 36)**

So CPS did not officially consider a school overcrowded in 2011-2012 until it had an average of 36 students in each homeroom.

**36 student maximum in each homeroom ≠ 30 student maximum in each homeroom **

**Now, let’s explore the effects on under-utlization and determine a formula more in line with the CPS classroom limits in PART 2…**

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