Portola Valley Elementary: math

The shaded band is this district'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.

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	83,283	2501.4	− 2436	65.4	× 84 / 430	12.8
4	83,284	2568.6	− 2485	83.6	× 68 / 430	13.2
5	83,287	2581.2	− 2528	53.2	× 69 / 430	8.5
6	83,288	2627.4	− 2552	75.4	× 86 / 430	15.1
7	83,291	2638.7	− 2567	71.7	× 63 / 430	10.5
8	83,292	2691.5	− 2586	105.5	× 60 / 430	14.7
Sum, rounded to a whole point						75

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,217	2527.1	− 2436	91.1	× 65 / 419	14.1
4	77,219	2552.7	− 2485	67.7	× 74 / 419	12
5	77,220	2591.2	− 2528	63.2	× 68 / 419	10.3
6	77,223	2616.8	− 2552	64.8	× 72 / 419	11.1
7	77,225	2660.6	− 2567	93.6	× 80 / 419	17.9
8	77,226	2679.2	− 2586	93.2	× 60 / 419	13.3
Sum, rounded to a whole point						79

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,323	2526.7	− 2436	90.7	× 74 / 425	15.8
4	79,326	2561.5	− 2485	76.5	× 68 / 425	12.2
5	79,328	2591.5	− 2528	63.5	× 72 / 425	10.8
6	79,330	2616.8	− 2552	64.8	× 57 / 425	8.7
7	79,331	2636.5	− 2567	69.5	× 71 / 425	11.6
8	79,333	2670.6	− 2586	84.6	× 83 / 425	16.5
Sum, rounded to a whole point						76

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,467	2521.2	− 2436	85.2	× 63 / 395	13.6
4	79,468	2552.1	− 2485	67.1	× 71 / 395	12.1
5	79,471	2610.4	− 2528	82.4	× 63 / 395	13.1
6	79,472	2634.9	− 2552	82.9	× 75 / 395	15.7
7	79,474	2647.2	− 2567	80.2	× 54 / 395	11
8	79,476	2662.9	− 2586	76.9	× 69 / 395	13.4
Sum, rounded to a whole point						79

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,993	2525.4	− 2436	89.4	× 68 / 373	16.3
4	79,994	2566.5	− 2485	81.5	× 64 / 373	14
5	79,995	2604.6	− 2528	76.6	× 68 / 373	14
6	79,996	2627.4	− 2552	75.4	× 55 / 373	11.1
7	79,997	2667.4	− 2567	100.4	× 69 / 373	18.6
8	79,998	2666.4	− 2586	80.4	× 49 / 373	10.6
Sum, rounded to a whole point						84

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	78,454	2496.5	− 2436	60.5	× 57 / 308	11.2
4	78,455	2555.5	− 2485	70.5	× 44 / 308	10.1
5	78,456	2597.9	− 2528	69.9	× 57 / 308	12.9
6	78,457	2617.1	− 2552	65.1	× 54 / 308	11.4
7	78,458	2649.3	− 2567	82.3	× 49 / 308	13.1
8	78,459	2671.9	− 2586	85.9	× 47 / 308	13.1
Sum, rounded to a whole point						72

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	80,263	2518.8	− 2436	82.8	× 54 / 312	14.3
4	80,264	2558.2	− 2485	73.2	× 53 / 312	12.4
5	80,265	2603.8	− 2528	75.8	× 51 / 312	12.4
6	80,266	2618.7	− 2552	66.7	× 57 / 312	12.2
7	80,267	2663.2	− 2567	96.2	× 51 / 312	15.7
8	80,268	2677.3	− 2586	91.3	× 46 / 312	13.5
Sum, rounded to a whole point						81

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	80,225	2536.7	− 2436	100.7	× 52 / 324	16.2
4	80,226	2552.7	− 2485	67.7	× 58 / 324	12.1
5	80,227	2593.4	− 2528	65.4	× 59 / 324	11.9
6	80,228	2633.7	− 2552	81.7	× 53 / 324	13.4
7	80,229	2664.1	− 2567	97.1	× 54 / 324	16.2
8	80,230	2707.5	− 2586	121.5	× 48 / 324	18
Sum, rounded to a whole point						88

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	80,247	2512.1	− 2436	76.1	× 50 / 309	12.3
4	80,248	2588.4	− 2485	103.4	× 48 / 309	16.1
5	80,249	2597.0	− 2528	69	× 58 / 309	13
6	80,250	2610.8	− 2552	58.8	× 47 / 309	8.9
7	80,251	2677.1	− 2567	110.1	× 54 / 309	19.2
8	80,252	2696.0	− 2586	110	× 52 / 309	18.5
Sum, rounded to a whole point						88

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,911	2518.9	− 2436	82.9	× 61 / 313	16.2
4	79,912	2562.1	− 2485	77.1	× 49 / 313	12.1
5	79,913	2615.2	− 2528	87.2	× 49 / 313	13.7
6	79,914	2633.3	− 2552	81.3	× 51 / 313	13.2
7	79,915	2638.5	− 2567	71.5	× 49 / 313	11.2
8	79,916	2714.8	− 2586	128.8	× 54 / 313	22.2
Sum, rounded to a whole point						89

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 75, 79, 76, 79, 84, 72, 81, 88, 88, 89 → 81.1
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: 3 · 2017→2018: 3 · 2018→2019: 5 · 2019→2021: 12 · 2021→2022: 9 · 2022→2023: 7 · 2023→2024: 0 · 2024→2025: 1 → average 4.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 4.9 × 2.66 = 13. Upper limit 94.1, lower limit 68.1.

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 — for a district, the total across its schools. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.