Hamilton 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.

Many students here are still learning English. The math test is written in English, with some translation help, and many of its questions are word problems. In 2026, 108 of the 272 students who took the math test were English learners.

All students

3rd The average 3rd grader scores 19 points under the grade 3 bar. 2417 vs. 2436.
4th The average 4th grader scores 35 points under the grade 3 bar. 2401 vs. 2436. The 4th-grade bar is 2485.
5th The average 5th grader scores 11 points under the grade 3 bar. 2425 vs. 2436. The 5th-grade bar is 2528.
6th The average 6th grader scores 22 points under the grade 4 bar. 2464 vs. 2485. The 6th-grade bar is 2552.
7th The average 7th grader scores 40 points under the grade 4 bar. 2446 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores 21 points under the grade 4 bar. 2464 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 3rd 14 students 25 points under the grade 3 bar. 4th 26 students 25 points under the grade 3 bar. 5th 25 students Just under the grade 3 bar. 6th 34 students 40 points under the grade 5 bar. 7th 32 students 13 points under the grade 4 bar.

English learners

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

Grade bars 3rd 20 students 15 points under the grade 3 bar. 4th 22 students 47 points under the grade 3 bar. 5th 25 students 16 points under the grade 3 bar. 6th 15 students 29 points under the grade 3 bar. 7th 16 students 43 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	13,301	2349.4	− 2436	−86.6	× 51 / 274	−16.1
4	13,302	2374.6	− 2485	−110.4	× 36 / 274	−14.5
5	13,304	2446.3	− 2528	−81.7	× 46 / 274	−13.7
6	13,307	2418.3	− 2552	−133.7	× 42 / 274	−20.5
7	13,308	2495.0	− 2567	−72	× 35 / 274	−9.2
8	13,311	2497.1	− 2586	−88.9	× 64 / 274	−20.8
Sum, rounded to a whole point						−95

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,321	2374.4	− 2436	−61.6	× 36 / 255	−8.7
4	12,322	2387.7	− 2485	−97.3	× 55 / 255	−21
5	12,324	2426.6	− 2528	−101.4	× 38 / 255	−15.1
6	12,327	2451.9	− 2552	−100.1	× 48 / 255	−18.8
7	12,329	2464.6	− 2567	−102.4	× 44 / 255	−17.7
8	12,331	2511.9	− 2586	−74.1	× 34 / 255	−9.9
Sum, rounded to a whole point						−91

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,651	2385.5	− 2436	−50.5	× 57 / 272	−10.6
4	12,654	2404.6	− 2485	−80.4	× 34 / 272	−10.1
5	12,656	2443.4	− 2528	−84.6	× 49 / 272	−15.2
6	12,657	2453.1	− 2552	−98.9	× 37 / 272	−13.5
7	12,660	2494.6	− 2567	−72.4	× 46 / 272	−12.2
8	12,661	2475.5	− 2586	−110.5	× 49 / 272	−19.9
Sum, rounded to a whole point						−81

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,673	2400.8	− 2436	−35.2	× 42 / 269	−5.5
4	12,676	2408.3	− 2485	−76.7	× 60 / 269	−17.1
5	12,677	2451.0	− 2528	−77	× 36 / 269	−10.3
6	12,680	2457.9	− 2552	−94.1	× 49 / 269	−17.1
7	12,681	2475.5	− 2567	−91.5	× 35 / 269	−11.9
8	12,684	2515.3	− 2586	−70.7	× 47 / 269	−12.4
Sum, rounded to a whole point						−74

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,775	2370.9	− 2436	−65.1	× 46 / 264	−11.3
4	12,776	2422.5	− 2485	−62.5	× 41 / 264	−9.7
5	12,777	2453.2	− 2528	−74.8	× 57 / 264	−16.2
6	12,778	2450.0	− 2552	−102	× 42 / 264	−16.2
7	12,779	2477.9	− 2567	−89.1	× 46 / 264	−15.5
8	12,780	2516.0	− 2586	−70	× 32 / 264	−8.5
Sum, rounded to a whole point						−77

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,621	2362.0	− 2436	−74	× 39 / 262	−11
4	12,622	2411.3	− 2485	−73.7	× 40 / 262	−11.3
5	12,623	2403.5	− 2528	−124.5	× 45 / 262	−21.4
6	12,624	2457.2	− 2552	−94.8	× 40 / 262	−14.5
7	12,625	2445.3	− 2567	−121.7	× 56 / 262	−26
8	12,626	2462.9	− 2586	−123.1	× 42 / 262	−19.7
Sum, rounded to a whole point						−104

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,804	2364.6	− 2436	−71.4	× 45 / 269	−11.9
4	12,805	2408.8	− 2485	−76.2	× 38 / 269	−10.8
5	12,806	2423.4	− 2528	−104.6	× 39 / 269	−15.2
6	12,807	2388.1	− 2552	−163.9	× 47 / 269	−28.6
7	12,808	2431.2	− 2567	−135.8	× 45 / 269	−22.7
8	12,809	2410.2	− 2586	−175.8	× 55 / 269	−35.9
Sum, rounded to a whole point						−125

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,785	2387.7	− 2436	−48.3	× 43 / 261	−8
4	12,786	2434.8	− 2485	−50.2	× 48 / 261	−9.2
5	12,787	2400.0	− 2528	−128	× 41 / 261	−20.1
6	12,788	2450.8	− 2552	−101.2	× 38 / 261	−14.7
7	12,789	2423.5	− 2567	−143.5	× 49 / 261	−26.9
8	12,790	2409.7	− 2586	−176.3	× 42 / 261	−28.4
Sum, rounded to a whole point						−107

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,746	2394.6	− 2436	−41.4	× 52 / 283	−7.6
4	12,747	2403.6	− 2485	−81.4	× 45 / 283	−12.9
5	12,748	2414.4	− 2528	−113.6	× 46 / 283	−18.5
6	12,749	2440.2	− 2552	−111.8	× 43 / 283	−17
7	12,750	2441.1	− 2567	−125.9	× 42 / 283	−18.7
8	12,751	2427.3	− 2586	−158.7	× 55 / 283	−30.8
Sum, rounded to a whole point						−106

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,721	2386.2	− 2436	−49.8	× 49 / 281	−8.7
4	12,722	2408.1	− 2485	−76.9	× 51 / 281	−14
5	12,723	2430.4	− 2528	−97.6	× 46 / 281	−16
6	12,724	2477.8	− 2552	−74.2	× 46 / 281	−12.1
7	12,725	2447.4	− 2567	−119.6	× 43 / 281	−18.3
8	12,726	2439.1	− 2586	−146.9	× 46 / 281	−24
Sum, rounded to a whole point						−93

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	12,737	2416.9	− 2436	−19.1	× 34 / 272	−2.4
4	12,738	2400.8	− 2485	−84.2	× 48 / 272	−14.9
5	12,739	2425.4	− 2528	−102.6	× 50 / 272	−18.9
6	12,740	2463.5	− 2552	−88.5	× 49 / 272	−15.9
7	12,741	2445.5	− 2567	−121.5	× 48 / 272	−21.4
8	12,742	2464.0	− 2586	−122	× 43 / 272	−19.3
Sum, rounded to a whole point						−93

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −95, −91, −81, −74, −77, −104, −125, −107, −106, −93, −93 → −95.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 4 · 2016→2017: 10 · 2017→2018: 7 · 2018→2019: 3 · 2019→2021: 27 · 2021→2022: 21 · 2022→2023: 18 · 2023→2024: 1 · 2024→2025: 13 · 2025→2026: 0 → average 10.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 10.4 × 2.66 = 27.7. Upper limit −67.4, lower limit −122.8.

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.