Willows Intermediate: 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 4 bar

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.

All students

5th The average 5th grader scores 36 points under the grade 4 bar. 2449 vs. 2485. The 5th-grade bar is 2528.
6th The average 6th grader scores 22 points under the grade 4 bar. 2463 vs. 2485. The 6th-grade bar is 2552.
7th The average 7th grader scores 18 points under the grade 4 bar. 2467 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores just under the grade 4 bar. 2481 vs. 2485. The 8th-grade bar is 2586.

Students fluent in English

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

Grade bars 5th 67 students 24 points under the grade 4 bar. 6th 115 students Just under the grade 4 bar. 7th 90 students Just under the grade 4 bar. 8th 92 students 33 points under the grade 5 bar.

English learners

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

Grade bars 5th 17 students 37 points under the grade 3 bar. 6th 19 students 86 points under the grade 3 bar. 7th 12 students 80 points under the grade 3 bar. 8th 16 students 38 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
6	13,223	2483.2	− 2552	−68.8	× 101 / 319	−21.8
7	13,224	2454.6	− 2567	−112.4	× 117 / 319	−41.2
8	13,227	2441.2	− 2586	−144.8	× 101 / 319	−45.8
Sum, rounded to a whole point						−109

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,236	2476.7	− 2552	−75.3	× 95 / 316	−22.6
7	12,238	2509.0	− 2567	−58	× 102 / 316	−18.7
8	12,240	2483.4	− 2586	−102.6	× 119 / 316	−38.6
Sum, rounded to a whole point						−80

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,573	2477.0	− 2552	−75	× 121 / 323	−28.1
7	12,575	2499.9	− 2567	−67.1	× 94 / 323	−19.5
8	12,578	2503.9	− 2586	−82.1	× 108 / 323	−27.5
Sum, rounded to a whole point						−75

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,595	2458.3	− 2552	−93.7	× 119 / 350	−31.9
7	12,596	2491.3	− 2567	−75.7	× 129 / 350	−27.9
8	12,599	2473.9	− 2586	−112.1	× 102 / 350	−32.7
Sum, rounded to a whole point						−92

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,692	2478.5	− 2552	−73.5	× 101 / 344	−21.6
7	12,693	2472.8	− 2567	−94.2	× 113 / 344	−30.9
8	12,694	2500.1	− 2586	−85.9	× 130 / 344	−32.5
Sum, rounded to a whole point						−85

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,538	2451.3	− 2552	−100.7	× 91 / 279	−32.8
7	12,539	2498.7	− 2567	−68.3	× 99 / 279	−24.2
8	12,540	2495.5	− 2586	−90.5	× 89 / 279	−28.9
Sum, rounded to a whole point						−86

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,721	2468.1	− 2552	−83.9	× 99 / 295	−28.2
7	12,722	2496.9	− 2567	−70.1	× 94 / 295	−22.3
8	12,723	2477.4	− 2586	−108.6	× 102 / 295	−37.5
Sum, rounded to a whole point						−88

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,706	2463.8	− 2552	−88.2	× 100 / 294	−30
7	12,707	2465.6	− 2567	−101.4	× 99 / 294	−34.1
8	12,708	2481.2	− 2586	−104.8	× 95 / 294	−33.9
Sum, rounded to a whole point						−98

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	12,671	2489.3	− 2552	−62.7	× 107 / 314	−21.4
7	12,672	2466.2	− 2567	−100.8	× 106 / 314	−34
8	12,673	2473.6	− 2586	−112.4	× 101 / 314	−36.2
Sum, rounded to a whole point						−92

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	12,645	2439.8	− 2528	−88.2	× 129 / 456	−25
6	12,646	2484.8	− 2552	−67.2	× 101 / 456	−14.9
7	12,647	2496.1	− 2567	−70.9	× 113 / 456	−17.6
8	12,648	2465.0	− 2586	−121	× 113 / 456	−30
Sum, rounded to a whole point						−87

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	12,661	2448.8	− 2528	−79.2	× 84 / 428	−15.5
6	12,662	2462.9	− 2552	−89.1	× 134 / 428	−27.9
7	12,663	2467.1	− 2567	−99.9	× 102 / 428	−23.8
8	12,664	2480.8	− 2586	−105.2	× 108 / 428	−26.5
Sum, rounded to a whole point						−94

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −109, −80, −75, −92, −85, −86, −88, −98, −92, −87, −94 → −89.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 29 · 2016→2017: 5 · 2017→2018: 17 · 2018→2019: 7 · 2019→2021: 1 · 2021→2022: 2 · 2022→2023: 10 · 2023→2024: 6 · 2024→2025: 5 · 2025→2026: 7 → average 8.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.9 × 2.66 = 23.7. Upper limit −65.9, lower limit −113.3.

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.