Leonardo Da Vinci: 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. 2486 vs. 2436.
4th The average 4th grader meets the grade 4 bar. 2494 vs. 2485.
5th The average 5th grader scores 11 points under the grade 5 bar. 2517 vs. 2528.
6th The average 6th grader meets the grade 6 bar. 2571 vs. 2552.
7th The average 7th grader scores 10 points under the grade 6 bar. 2542 vs. 2552. The 7th-grade bar is 2567.
8th The average 8th grader meets the grade 8 bar. 2590 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	61,864	2416.7	− 2436	−19.3	× 101 / 517	−3.8
4	61,867	2435.5	− 2485	−49.5	× 98 / 517	−9.4
5	61,868	2496.8	− 2528	−31.2	× 101 / 517	−6.1
6	61,871	2528.9	− 2552	−23.1	× 101 / 517	−4.5
7	61,872	2545.2	− 2567	−21.8	× 62 / 517	−2.6
8	61,875	2563.1	− 2586	−22.9	× 54 / 517	−2.4
Sum, rounded to a whole point						−29

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	57,426	2454.9	− 2436	18.9	× 94 / 524	3.4
4	57,428	2449.4	− 2485	−35.6	× 97 / 524	−6.6
5	57,430	2498.8	− 2528	−29.2	× 98 / 524	−5.5
6	57,432	2520.4	− 2552	−31.6	× 98 / 524	−5.9
7	57,433	2533.8	− 2567	−33.2	× 77 / 524	−4.9
8	57,436	2545.6	− 2586	−40.4	× 60 / 524	−4.6
Sum, rounded to a whole point						−24

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,100	2451.0	− 2436	15	× 97 / 531	2.7
4	59,103	2488.8	− 2485	3.8	× 97 / 531	0.7
5	59,105	2502.0	− 2528	−26	× 99 / 531	−4.8
6	59,106	2539.5	− 2552	−12.5	× 100 / 531	−2.4
7	59,109	2519.5	− 2567	−47.5	× 73 / 531	−6.5
8	59,111	2537.7	− 2586	−48.3	× 65 / 531	−5.9
Sum, rounded to a whole point						−16

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,216	2456.8	− 2436	20.8	× 104 / 548	3.9
4	59,218	2479.8	− 2485	−5.2	× 99 / 548	−0.9
5	59,220	2522.4	− 2528	−5.6	× 97 / 548	−1
6	59,222	2536.7	− 2552	−15.3	× 96 / 548	−2.7
7	59,224	2543.5	− 2567	−23.5	× 83 / 548	−3.6
8	59,226	2548.2	− 2586	−37.8	× 69 / 548	−4.8
Sum, rounded to a whole point						−9

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,473	2458.8	− 2436	22.8	× 98 / 544	4.1
4	59,474	2483.8	− 2485	−1.2	× 103 / 544	−0.2
5	59,475	2514.2	− 2528	−13.8	× 97 / 544	−2.5
6	59,476	2564.9	− 2552	12.9	× 93 / 544	2.2
7	59,477	2542.4	− 2567	−24.6	× 75 / 544	−3.4
8	59,478	2552.5	− 2586	−33.5	× 78 / 544	−4.8
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	59,556	2443.4	− 2436	7.4	× 97 / 494	1.5
4	59,557	2494.7	− 2485	9.7	× 94 / 494	1.8
5	59,558	2511.5	− 2528	−16.5	× 98 / 494	−3.3
6	59,559	2531.5	− 2552	−20.5	× 83 / 494	−3.4
7	59,560	2531.0	− 2567	−36	× 62 / 494	−4.5
8	59,561	2536.9	− 2586	−49.1	× 60 / 494	−6
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	59,514	2449.9	− 2436	13.9	× 91 / 479	2.6
4	59,515	2498.0	− 2485	13	× 91 / 479	2.5
5	59,516	2507.2	− 2528	−20.8	× 98 / 479	−4.3
6	59,517	2574.8	− 2552	22.8	× 95 / 479	4.5
7	59,518	2502.1	− 2567	−64.9	× 47 / 479	−6.4
8	59,519	2556.1	− 2586	−29.9	× 57 / 479	−3.6
Sum, rounded to a whole point						−5

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,445	2465.8	− 2436	29.8	× 97 / 503	5.7
4	59,446	2493.0	− 2485	8	× 96 / 503	1.5
5	59,447	2519.7	− 2528	−8.3	× 98 / 503	−1.6
6	59,448	2554.7	− 2552	2.7	× 103 / 503	0.6
7	59,449	2544.1	− 2567	−22.9	× 64 / 503	−2.9
8	59,450	2514.6	− 2586	−71.4	× 45 / 503	−6.4
Sum, rounded to a whole point						−3

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,202	2457.0	− 2436	21	× 92 / 505	3.8
4	59,203	2517.0	− 2485	32	× 95 / 505	6
5	59,204	2505.5	− 2528	−22.5	× 96 / 505	−4.3
6	59,205	2563.3	− 2552	11.3	× 95 / 505	2.1
7	59,206	2552.3	− 2567	−14.7	× 68 / 505	−2
8	59,207	2556.8	− 2586	−29.2	× 59 / 505	−3.4
Sum, rounded to a whole point						2

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,123	2485.8	− 2436	49.8	× 90 / 481	9.3
4	59,124	2493.5	− 2485	8.5	× 92 / 481	1.6
5	59,125	2516.7	− 2528	−11.3	× 95 / 481	−2.2
6	59,126	2570.8	− 2552	18.8	× 87 / 481	3.4
7	59,127	2542.2	− 2567	−24.8	× 49 / 481	−2.5
8	59,128	2589.8	− 2586	3.8	× 68 / 481	0.5
Sum, rounded to a whole point						10

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −29, −24, −16, −9, −5, −14, −5, −3, 2, 10 → −9.3
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: 7 · 2018→2019: 4 · 2019→2022: 9 · 2022→2023: 9 · 2023→2024: 2 · 2024→2025: 5 · 2025→2026: 8 → average 6.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.3 × 2.66 = 16.8. Upper limit 7.5, lower limit −26.1.

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.