Hamilton TK-8: 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, 122 of the 324 students who took the math test were English learners.

All students

3rd The average 3rd grader scores 48 points under the grade 3 bar. 2389 vs. 2436.
4th The average 4th grader scores 36 points under the grade 4 bar. 2449 vs. 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 just under the grade 3 bar. 2431 vs. 2436. The 6th-grade bar is 2552.
7th The average 7th grader scores 13 points under the grade 4 bar. 2472 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores 26 points under the grade 5 bar. 2502 vs. 2528. 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 28 students Meets the grade 3 bar. 4th 26 students Meets the grade 4 bar. 5th 32 students 41 points under the grade 4 bar. 6th 33 students 30 points under the grade 4 bar. 7th 38 students 21 points under the grade 5 bar. 8th 45 students 23 points under the grade 6 bar.

English learners

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

Grade bars 3rd 30 students 98 points under the grade 3 bar. 4th 27 students 28 points under the grade 3 bar. 5th 18 students 45 points under the grade 3 bar. 6th 22 students 42 points under the grade 3 bar. 7th 14 students 59 points under the grade 3 bar. 8th 11 students 42 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	42,297	2443.9	− 2436	7.9	× 95 / 450	1.7
4	42,300	2514.2	− 2485	29.2	× 85 / 450	5.5
5	42,302	2483.4	− 2528	−44.6	× 88 / 450	−8.7
6	42,304	2480.3	− 2552	−71.7	× 59 / 450	−9.4
7	42,305	2544.9	− 2567	−22.1	× 61 / 450	−3
8	42,308	2551.1	− 2586	−34.9	× 62 / 450	−4.8
Sum, rounded to a whole point						−19

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,108	2439.7	− 2436	3.7	× 79 / 417	0.7
4	39,110	2476.1	− 2485	−8.9	× 81 / 417	−1.7
5	39,111	2521.7	− 2528	−6.3	× 85 / 417	−1.3
6	39,113	2487.7	− 2552	−64.3	× 59 / 417	−9.1
7	39,116	2519.7	− 2567	−47.3	× 55 / 417	−6.2
8	39,117	2560.3	− 2586	−25.7	× 58 / 417	−3.6
Sum, rounded to a whole point						−21

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,090	2404.7	− 2436	−31.3	× 95 / 425	−7
4	40,093	2440.3	− 2485	−44.7	× 75 / 425	−7.9
5	40,094	2459.7	− 2528	−68.3	× 83 / 425	−13.3
6	40,096	2504.6	− 2552	−47.4	× 58 / 425	−6.5
7	40,098	2533.8	− 2567	−33.2	× 59 / 425	−4.6
8	40,100	2503.7	− 2586	−82.3	× 55 / 425	−10.7
Sum, rounded to a whole point						−50

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,115	2422.6	− 2436	−13.4	× 53 / 388	−1.8
4	40,118	2455.2	− 2485	−29.8	× 86 / 388	−6.6
5	40,119	2480.7	− 2528	−47.3	× 76 / 388	−9.3
6	40,122	2490.6	− 2552	−61.4	× 62 / 388	−9.8
7	40,123	2527.5	− 2567	−39.5	× 56 / 388	−5.7
8	40,126	2499.1	− 2586	−86.9	× 55 / 388	−12.3
Sum, rounded to a whole point						−46

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,270	2400.6	− 2436	−35.4	× 66 / 382	−6.1
4	40,271	2493.8	− 2485	8.8	× 50 / 382	1.2
5	40,272	2463.7	− 2528	−64.3	× 85 / 382	−14.3
6	40,273	2498.4	− 2552	−53.6	× 60 / 382	−8.4
7	40,274	2502.4	− 2567	−64.6	× 62 / 382	−10.5
8	40,275	2518.7	− 2586	−67.3	× 59 / 382	−10.4
Sum, rounded to a whole point						−49

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,237	2389.7	− 2436	−46.3	× 70 / 350	−9.3
4	39,238	2409.1	− 2485	−75.9	× 54 / 350	−11.7
5	39,239	2440.3	− 2528	−87.7	× 63 / 350	−15.8
6	39,240	2471.8	− 2552	−80.2	× 54 / 350	−12.4
7	39,241	2459.0	− 2567	−108	× 52 / 350	−16
8	39,242	2496.5	− 2586	−89.5	× 57 / 350	−14.6
Sum, rounded to a whole point						−80

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,047	2373.0	− 2436	−63	× 49 / 336	−9.2
4	40,048	2428.7	− 2485	−56.3	× 58 / 336	−9.7
5	40,049	2442.5	− 2528	−85.5	× 58 / 336	−14.8
6	40,050	2454.3	− 2552	−97.7	× 59 / 336	−17.2
7	40,051	2502.4	− 2567	−64.6	× 56 / 336	−10.8
8	40,052	2455.0	− 2586	−131	× 56 / 336	−21.8
Sum, rounded to a whole point						−83

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,096	2420.1	− 2436	−15.9	× 60 / 337	−2.8
4	40,097	2424.5	− 2485	−60.5	× 48 / 337	−8.6
5	40,098	2442.2	− 2528	−85.8	× 60 / 337	−15.3
6	40,099	2473.9	− 2552	−78.1	× 60 / 337	−13.9
7	40,100	2471.0	− 2567	−96	× 51 / 337	−14.5
8	40,101	2513.7	− 2586	−72.3	× 58 / 337	−12.4
Sum, rounded to a whole point						−68

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,911	2386.7	− 2436	−49.3	× 55 / 324	−8.4
4	39,912	2454.9	− 2485	−30.1	× 60 / 324	−5.6
5	39,913	2414.5	− 2528	−113.5	× 52 / 324	−18.2
6	39,914	2473.3	− 2552	−78.7	× 59 / 324	−14.3
7	39,915	2508.1	− 2567	−58.9	× 53 / 324	−9.6
8	39,916	2510.5	− 2586	−75.5	× 45 / 324	−10.5
Sum, rounded to a whole point						−67

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,684	2403.4	− 2436	−32.6	× 56 / 329	−5.5
4	39,685	2421.4	− 2485	−63.6	× 53 / 329	−10.2
5	39,686	2441.7	− 2528	−86.3	× 59 / 329	−15.5
6	39,687	2469.4	− 2552	−82.6	× 48 / 329	−12.1
7	39,688	2494.6	− 2567	−72.4	× 59 / 329	−13
8	39,689	2514.8	− 2586	−71.2	× 54 / 329	−11.7
Sum, rounded to a whole point						−68

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,592	2388.5	− 2436	−47.5	× 58 / 324	−8.5
4	39,593	2449.4	− 2485	−35.6	× 53 / 324	−5.8
5	39,594	2424.8	− 2528	−103.2	× 50 / 324	−15.9
6	39,595	2430.5	− 2552	−121.5	× 55 / 324	−20.6
7	39,596	2472.3	− 2567	−94.7	× 52 / 324	−15.2
8	39,597	2502.2	− 2586	−83.8	× 56 / 324	−14.5
Sum, rounded to a whole point						−81

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −19, −21, −50, −46, −49, −80, −83, −68, −67, −68, −81 → −57.5
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 2 · 2016→2017: 29 · 2017→2018: 4 · 2018→2019: 3 · 2019→2021: 31 · 2021→2022: 3 · 2022→2023: 15 · 2023→2024: 1 · 2024→2025: 1 · 2025→2026: 13 → average 10.2
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 10.2 × 2.66 = 27.1. Upper limit −30.4, lower limit −84.6.

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.