John J. Montgomery Elementary: math

The shaded band is this school's normal range. If nothing about how it works changes, nearly every future year should land inside it. Zero means the typical student just meets the state standard. The small numbers under the years are how many students were tested.

Step 1 · Each year's result

For each grade tested, take the average (mean) scale score from the California Department of Education's results file, and subtract the lowest score that counts as "Standard Met" for that grade. That is the grade's distance from standard. Weight each grade by its share of the students tested, then add the grades up. Grades where the state hides the average because ten or fewer students tested are left out entirely.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	87,041	2406.2	− 2436	−29.8	× 85 / 390	−6.5
4	87,044	2440.6	− 2485	−44.4	× 96 / 390	−10.9
5	87,045	2453.0	− 2528	−75	× 99 / 390	−19
6	87,048	2512.1	− 2552	−39.9	× 110 / 390	−11.3
Sum, rounded to a whole point						−48

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	80,782	2393.3	− 2436	−42.7	× 78 / 354	−9.4
4	80,784	2438.1	− 2485	−46.9	× 91 / 354	−12.1
5	80,787	2470.5	− 2528	−57.5	× 93 / 354	−15.1
6	80,788	2489.5	− 2552	−62.5	× 92 / 354	−16.2
Sum, rounded to a whole point						−53

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,012	2407.5	− 2436	−28.5	× 55 / 311	−5
4	83,014	2431.0	− 2485	−54	× 78 / 311	−13.5
5	83,016	2457.1	− 2528	−70.9	× 92 / 311	−21
6	83,018	2474.5	− 2552	−77.5	× 86 / 311	−21.4
Sum, rounded to a whole point						−61

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,228	2410.7	− 2436	−25.3	× 71 / 291	−6.2
4	83,230	2465.5	− 2485	−19.5	× 61 / 291	−4.1
5	83,232	2451.0	− 2528	−77	× 73 / 291	−19.3
6	83,234	2489.1	− 2552	−62.9	× 86 / 291	−18.6
Sum, rounded to a whole point						−48

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,842	2410.6	− 2436	−25.4	× 71 / 280	−6.4
4	83,843	2458.2	− 2485	−26.8	× 67 / 280	−6.4
5	83,844	2459.9	− 2528	−68.1	× 62 / 280	−15.1
6	83,845	2495.8	− 2552	−56.2	× 80 / 280	−16.1
Sum, rounded to a whole point						−44

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	84,027	2415.1	− 2436	−20.9	× 71 / 311	−4.8
4	84,028	2450.3	− 2485	−34.7	× 77 / 311	−8.6
5	84,029	2440.0	− 2528	−88	× 75 / 311	−21.2
6	84,030	2490.9	− 2552	−61.1	× 88 / 311	−17.3
Sum, rounded to a whole point						−52

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,968	2395.7	− 2436	−40.3	× 71 / 306	−9.4
4	83,969	2444.6	− 2485	−40.4	× 77 / 306	−10.2
5	83,970	2453.5	− 2528	−74.5	× 81 / 306	−19.7
6	83,971	2487.2	− 2552	−64.8	× 77 / 306	−16.3
Sum, rounded to a whole point						−56

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,969	2413.0	− 2436	−23	× 74 / 312	−5.5
4	83,970	2436.7	− 2485	−48.3	× 75 / 312	−11.6
5	83,971	2460.6	− 2528	−67.4	× 83 / 312	−17.9
6	83,972	2503.4	− 2552	−48.6	× 80 / 312	−12.5
Sum, rounded to a whole point						−47

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,651	2412.7	− 2436	−23.3	× 58 / 288	−4.7
4	83,652	2446.2	− 2485	−38.8	× 73 / 288	−9.8
5	83,653	2449.4	− 2528	−78.6	× 74 / 288	−20.2
6	83,654	2498.7	− 2552	−53.3	× 83 / 288	−15.4
Sum, rounded to a whole point						−50

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −48, −53, −61, −48, −44, −52, −56, −47, −50 → −51
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 8 · 2017→2018: 13 · 2018→2019: 4 · 2019→2022: 8 · 2022→2023: 4 · 2023→2024: 9 · 2024→2025: 3 → average 6.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.8 × 2.66 = 18.1. Upper limit −32.9, lower limit −69.1.

Why 2.66? It is the standard factor from quality control, the work of Walter Shewhart and W. Edwards Deming. It turns "how much the result typically changes in a year" into "how far it can wander by chance alone".

Years with no result (no state tests were given in spring 2020) are skipped: the year-to-year change runs from the last year with a result to the next one.

Step 3 · Free or reduced-price meals

The share of enrolled students eligible for free or reduced-price meals. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.