Columbia 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 6.

All students

3rd The average 3rd grader scores 75 points under the grade 3 bar. 2361 vs. 2436.
4th The average 4th grader scores 25 points under the grade 3 bar. 2411 vs. 2436. The 4th-grade bar is 2485.
5th The average 5th grader scores 35 points under the grade 3 bar. 2401 vs. 2436. The 5th-grade bar is 2528.
6th The average 6th grader scores 45 points under the grade 4 bar. 2440 vs. 2485. The 6th-grade bar is 2552.

Students fluent in English

Math with English out of the way. Includes students who have only ever spoken English.

Grade bars 3rd 63 students 77 points under the grade 3 bar. 4th 62 students 23 points under the grade 3 bar. 5th 84 students 36 points under the grade 3 bar.

English learners

Students leave this group as they become fluent, so its average stays low even where they learn well.

Grade bars 3rd 15 students 69 points under the grade 3 bar. 4th 15 students 36 points under the grade 3 bar. 5th 14 students 33 points under the grade 3 bar.

the group's average that grade's own bar the distance between

2026 results. "Meets standard" is the state's mark for being on track for that grade. The state leaves out any group of ten students or fewer, so a grade may be missing from the charts.

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	22,985	2377.2	− 2436	−58.8	× 118 / 418	−16.6
4	22,987	2400.8	− 2485	−84.2	× 116 / 418	−23.4
5	22,989	2415.7	− 2528	−112.3	× 94 / 418	−25.3
6	22,991	2446.9	− 2552	−105.1	× 90 / 418	−22.6
Sum, rounded to a whole point						−88

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,584	2391.5	− 2436	−44.5	× 120 / 443	−12.1
4	21,585	2395.2	− 2485	−89.8	× 121 / 443	−24.5
5	21,587	2418.8	− 2528	−109.2	× 106 / 443	−26.1
6	21,590	2440.9	− 2552	−111.1	× 96 / 443	−24.1
Sum, rounded to a whole point						−87

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,006	2364.3	− 2436	−71.7	× 93 / 451	−14.8
4	22,009	2418.9	− 2485	−66.1	× 122 / 451	−17.9
5	22,010	2420.7	− 2528	−107.3	× 120 / 451	−28.5
6	22,013	2435.1	− 2552	−116.9	× 116 / 451	−30.1
Sum, rounded to a whole point						−91

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,991	2374.9	− 2436	−61.1	× 95 / 410	−14.2
4	21,994	2410.2	− 2485	−74.8	× 88 / 410	−16.1
5	21,995	2414.5	− 2528	−113.5	× 115 / 410	−31.8
6	21,998	2446.4	− 2552	−105.6	× 112 / 410	−28.8
Sum, rounded to a whole point						−91

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,170	2355.3	− 2436	−80.7	× 108 / 420	−20.8
4	22,171	2420.9	− 2485	−64.1	× 97 / 420	−14.8
5	22,172	2435.0	− 2528	−93	× 94 / 420	−20.8
6	22,173	2436.9	− 2552	−115.1	× 121 / 420	−33.2
Sum, rounded to a whole point						−90

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,143	2349.7	− 2436	−86.3	× 97 / 378	−22.1
4	22,144	2387.2	− 2485	−97.8	× 89 / 378	−23
5	22,145	2424.2	− 2528	−103.8	× 80 / 378	−22
6	22,146	2442.5	− 2552	−109.5	× 112 / 378	−32.4
Sum, rounded to a whole point						−100

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,114	2352.1	− 2436	−83.9	× 93 / 378	−20.6
4	22,115	2391.5	− 2485	−93.5	× 93 / 378	−23
5	22,116	2413.8	− 2528	−114.2	× 106 / 378	−32
6	22,117	2431.9	− 2552	−120.1	× 86 / 378	−27.3
Sum, rounded to a whole point						−103

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,968	2369.1	− 2436	−66.9	× 97 / 393	−16.5
4	21,969	2394.4	− 2485	−90.6	× 96 / 393	−22.1
5	21,970	2398.5	− 2528	−129.5	× 92 / 393	−30.3
6	21,971	2431.0	− 2552	−121	× 108 / 393	−33.3
Sum, rounded to a whole point						−102

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,875	2381.6	− 2436	−54.4	× 76 / 364	−11.4
4	21,876	2400.7	− 2485	−84.3	× 96 / 364	−22.2
5	21,877	2418.3	− 2528	−109.7	× 91 / 364	−27.4
6	21,878	2414.3	− 2552	−137.7	× 101 / 364	−38.2
Sum, rounded to a whole point						−99

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,933	2360.7	− 2436	−75.3	× 78 / 342	−17.2
4	21,934	2410.7	− 2485	−74.3	× 77 / 342	−16.7
5	21,935	2400.6	− 2528	−127.4	× 98 / 342	−36.5
6	21,936	2440.2	− 2552	−111.8	× 89 / 342	−29.1
Sum, rounded to a whole point						−100

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −88, −87, −91, −91, −90, −100, −103, −102, −99, −100 → −95.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 1 · 2016→2017: 4 · 2017→2018: 0 · 2018→2019: 1 · 2019→2022: 10 · 2022→2023: 3 · 2023→2024: 1 · 2024→2025: 3 · 2025→2026: 1 → average 2.7
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 2.7 × 2.66 = 7.2. Upper limit −87.9, lower limit −102.3.

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.