Columbine Elementary: math

The shaded band is this district'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	100,374	2443.8	− 2436	7.8	× 24 / 127	1.5
4	100,375	2472.9	− 2485	−12.1	× 23 / 127	−2.2
5	100,378	2517.4	− 2528	−10.6	× 25 / 127	−2.1
6	100,379	2566.4	− 2552	14.4	× 18 / 127	2
7	100,382	2594.5	− 2567	27.5	× 19 / 127	4.1
8	100,383	2591.7	− 2586	5.7	× 18 / 127	0.8
Sum, rounded to a whole point						4

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,075	2451.2	− 2436	15.2	× 21 / 128	2.5
4	93,076	2491.4	− 2485	6.4	× 26 / 128	1.3
5	93,078	2509.7	− 2528	−18.3	× 21 / 128	−3
6	93,080	2568.1	− 2552	16.1	× 24 / 128	3
7	93,083	2623.5	− 2567	56.5	× 17 / 128	7.5
8	93,084	2613.6	− 2586	27.6	× 19 / 128	4.1
Sum, rounded to a whole point						15

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	95,836	2438.5	− 2436	2.5	× 22 / 132	0.4
4	95,839	2483.7	− 2485	−1.3	× 22 / 132	−0.2
5	95,841	2513.0	− 2528	−15	× 26 / 132	−3
6	95,842	2571.3	− 2552	19.3	× 20 / 132	2.9
7	95,844	2583.8	− 2567	16.8	× 23 / 132	2.9
8	95,846	2625.9	− 2586	39.9	× 19 / 132	5.7
Sum, rounded to a whole point						9

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,027	2477.4	− 2436	41.4	× 18 / 120	6.2
4	96,029	2519.5	− 2485	34.5	× 20 / 120	5.8
5	96,030	2498.9	− 2528	−29.1	× 20 / 120	−4.9
6	96,033	2547.2	− 2552	−4.8	× 26 / 120	−1
7	96,034	2606.4	− 2567	39.4	× 18 / 120	5.9
8	96,037	2595.3	− 2586	9.3	× 18 / 120	1.4
Sum, rounded to a whole point						13

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,698	2433.4	− 2436	−2.6	× 20 / 118	−0.4
4	96,699	2504.4	− 2485	19.4	× 21 / 118	3.5
5	96,700	2508.0	− 2528	−20	× 21 / 118	−3.6
6	96,701	2553.2	− 2552	1.2	× 19 / 118	0.2
7	96,702	2592.1	− 2567	25.1	× 22 / 118	4.7
8	96,703	2606.9	− 2586	20.9	× 15 / 118	2.7
Sum, rounded to a whole point						7

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	94,623	2421.6	− 2436	−14.4	× 19 / 113	−2.4
4	94,624	2470.3	− 2485	−14.7	× 21 / 113	−2.7
5	94,625	2496.6	− 2528	−31.4	× 19 / 113	−5.3
6	94,626	2577.8	− 2552	25.8	× 18 / 113	4.1
7	94,627	2565.5	− 2567	−1.5	× 19 / 113	−0.3
8	94,628	2543.6	− 2586	−42.4	× 17 / 113	−6.4
Sum, rounded to a whole point						−13

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,888	2394.7	− 2436	−41.3	× 23 / 117	−8.1
4	96,889	2463.0	− 2485	−22	× 20 / 117	−3.8
5	96,890	2535.0	− 2528	7	× 21 / 117	1.3
6	96,891	2570.2	− 2552	18.2	× 18 / 117	2.8
7	96,892	2608.3	− 2567	41.3	× 18 / 117	6.4
8	96,893	2588.4	− 2586	2.4	× 17 / 117	0.3
Sum, rounded to a whole point						−1

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,741	2444.3	− 2436	8.3	× 24 / 127	1.6
4	96,742	2466.9	− 2485	−18.1	× 23 / 127	−3.3
5	96,743	2489.3	− 2528	−38.7	× 21 / 127	−6.4
6	96,744	2599.7	− 2552	47.7	× 22 / 127	8.3
7	96,745	2583.7	− 2567	16.7	× 18 / 127	2.4
8	96,746	2621.0	− 2586	35	× 19 / 127	5.2
Sum, rounded to a whole point						8

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,633	2455.7	− 2436	19.7	× 13 / 114	2.2
4	96,634	2493.4	− 2485	8.4	× 23 / 114	1.7
5	96,635	2513.2	− 2528	−14.8	× 22 / 114	−2.9
6	96,636	2596.9	− 2552	44.9	× 18 / 114	7.1
7	96,637	2601.7	− 2567	34.7	× 22 / 114	6.7
8	96,638	2601.6	− 2586	15.6	× 16 / 114	2.2
Sum, rounded to a whole point						17

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	96,361	2432.7	− 2436	−3.3	× 14 / 112	−0.4
4	96,362	2493.0	− 2485	8	× 13 / 112	0.9
5	96,363	2547.6	− 2528	19.6	× 23 / 112	4
6	96,364	2585.0	− 2552	33	× 22 / 112	6.5
7	96,365	2602.2	− 2567	35.2	× 18 / 112	5.7
8	96,366	2639.1	− 2586	53.1	× 22 / 112	10.4
Sum, rounded to a whole point						27

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 4, 15, 9, 13, 7, −13, −1, 8, 17, 27 → 8.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 11 · 2016→2017: 6 · 2017→2018: 4 · 2018→2019: 6 · 2019→2021: 20 · 2021→2022: 12 · 2022→2023: 9 · 2023→2024: 9 · 2024→2025: 10 → average 9.7
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 9.7 × 2.66 = 25.8. Upper limit 34.4, lower limit −17.2.

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 — for a district, the total across its schools. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.

Schools in Columbine Elementary

Columbine Elementary