Rooftop 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.

Measured against the grade bars

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 8.

3rd The average 3rd grader meets the grade 3 bar. 2455 vs. 2436.
4th The average 4th grader scores 20 points under the grade 4 bar. 2465 vs. 2485.
5th The average 5th grader scores 18 points under the grade 5 bar. 2510 vs. 2528.
6th The average 6th grader scores 14 points under the grade 6 bar. 2539 vs. 2552.
7th The average 7th grader meets the grade 7 bar. 2602 vs. 2567.
8th The average 8th grader scores 11 points under the grade 8 bar. 2575 vs. 2586.

2026 results. "Meets standard" is the state's mark for being on track for that grade.

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	78,472	2440.8	− 2436	4.8	× 62 / 382	0.8
4	78,474	2488.1	− 2485	3.1	× 66 / 382	0.5
5	78,477	2509.0	− 2528	−19	× 63 / 382	−3.1
6	78,478	2561.4	− 2552	9.4	× 65 / 382	1.6
7	78,480	2598.6	− 2567	31.6	× 63 / 382	5.2
8	78,482	2621.7	− 2586	35.7	× 63 / 382	5.9
Sum, rounded to a whole point						11

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,668	2454.1	− 2436	18.1	× 64 / 386	3
4	72,670	2464.9	− 2485	−20.1	× 63 / 386	−3.3
5	72,673	2500.7	− 2528	−27.3	× 65 / 386	−4.6
6	72,674	2549.9	− 2552	−2.1	× 64 / 386	−0.3
7	72,676	2590.8	− 2567	23.8	× 65 / 386	4
8	72,678	2625.1	− 2586	39.1	× 65 / 386	6.6
Sum, rounded to a whole point						5

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,640	2442.0	− 2436	6	× 64 / 380	1
4	74,642	2489.1	− 2485	4.1	× 67 / 380	0.7
5	74,645	2487.4	− 2528	−40.6	× 64 / 380	−6.8
6	74,646	2574.8	− 2552	22.8	× 65 / 380	3.9
7	74,649	2593.0	− 2567	26	× 62 / 380	4.2
8	74,650	2608.6	− 2586	22.6	× 58 / 380	3.4
Sum, rounded to a whole point						6

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,814	2441.9	− 2436	5.9	× 61 / 374	1
4	74,817	2469.0	− 2485	−16	× 63 / 374	−2.7
5	74,818	2529.7	− 2528	1.7	× 66 / 374	0.3
6	74,821	2543.7	− 2552	−8.3	× 61 / 374	−1.4
7	74,822	2621.9	− 2567	54.9	× 66 / 374	9.7
8	74,825	2610.0	− 2586	24	× 57 / 374	3.7
Sum, rounded to a whole point						11

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,343	2434.4	− 2436	−1.6	× 64 / 376	−0.3
4	75,344	2474.1	− 2485	−10.9	× 62 / 376	−1.8
5	75,345	2509.2	− 2528	−18.8	× 61 / 376	−3.1
6	75,346	2569.0	− 2552	17	× 65 / 376	2.9
7	75,347	2575.0	− 2567	8	× 62 / 376	1.3
8	75,348	2620.2	− 2586	34.2	× 62 / 376	5.6
Sum, rounded to a whole point						5

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,525	2417.4	− 2436	−18.6	× 52 / 337	−2.9
4	75,526	2462.2	− 2485	−22.8	× 61 / 337	−4.1
5	75,527	2511.9	− 2528	−16.1	× 64 / 337	−3.1
6	75,528	2555.4	− 2552	3.4	× 56 / 337	0.6
7	75,529	2551.1	− 2567	−15.9	× 50 / 337	−2.4
8	75,530	2571.9	− 2586	−14.1	× 54 / 337	−2.3
Sum, rounded to a whole point						−14

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,495	2424.3	− 2436	−11.7	× 64 / 372	−2
4	75,496	2482.0	− 2485	−3	× 65 / 372	−0.5
5	75,497	2502.6	− 2528	−25.4	× 61 / 372	−4.2
6	75,498	2524.6	− 2552	−27.4	× 63 / 372	−4.6
7	75,499	2574.2	− 2567	7.2	× 60 / 372	1.2
8	75,500	2551.8	− 2586	−34.2	× 59 / 372	−5.4
Sum, rounded to a whole point						−16

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,507	2461.9	− 2436	25.9	× 60 / 379	4.1
4	75,508	2478.8	− 2485	−6.2	× 66 / 379	−1.1
5	75,509	2521.6	− 2528	−6.4	× 64 / 379	−1.1
6	75,510	2539.1	− 2552	−12.9	× 62 / 379	−2.1
7	75,511	2540.7	− 2567	−26.3	× 64 / 379	−4.4
8	75,512	2557.5	− 2586	−28.5	× 63 / 379	−4.7
Sum, rounded to a whole point						−9

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,167	2417.0	− 2436	−19	× 66 / 388	−3.2
4	75,168	2486.5	− 2485	1.5	× 66 / 388	0.3
5	75,169	2494.6	− 2528	−33.4	× 66 / 388	−5.7
6	75,170	2564.5	− 2552	12.5	× 65 / 388	2.1
7	75,171	2554.5	− 2567	−12.5	× 62 / 388	−2
8	75,172	2579.7	− 2586	−6.3	× 63 / 388	−1
Sum, rounded to a whole point						−10

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,063	2454.7	− 2436	18.7	× 64 / 382	3.1
4	75,064	2464.9	− 2485	−20.1	× 60 / 382	−3.2
5	75,065	2510.0	− 2528	−18	× 66 / 382	−3.1
6	75,066	2538.5	− 2552	−13.5	× 64 / 382	−2.3
7	75,067	2601.7	− 2567	34.7	× 65 / 382	5.9
8	75,068	2575.4	− 2586	−10.6	× 63 / 382	−1.7
Sum, rounded to a whole point						−1

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 11, 5, 6, 11, 5, −14, −16, −9, −10, −1 → −1.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 6 · 2016→2017: 1 · 2017→2018: 5 · 2018→2019: 6 · 2019→2022: 19 · 2022→2023: 2 · 2023→2024: 7 · 2024→2025: 1 · 2025→2026: 9 → average 6.2
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.2 × 2.66 = 16.5. Upper limit 15.3, lower limit −17.7.

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.