Mathematics 30 (braided classroom)
One combined classroom for Mathematics 30-1, 30-2 and 30-3. Braiding adjusts the shared calendar. It does not shrink any strand to ten sessions.
MATH30B Session 06 — Log laws workshop
Time: 75 minutes
Labels: 30-1 REQUIRED algebraic depth · 30-2 CORE log laws in context · 30-3 CROSS-STRAND EXPOSURE orders of magnitude only
Braid class: A (30-1/30-2) · D (30-3)
Official outcome codes
| Strand | Codes |
|---|---|
| 30-1 | MATH30-1-TRIGONOM-08-014 REQUIRED (continues 013) |
| 30-2 | MATH30-2-LOGICALR-04-012 CORE |
| 30-3 | none for mastery |
Shared portion (8 min) — ALL STRANDS
Write on board: log(ab), log(a/b), log(a^n). Say: 30-3 will not be tested on these laws. 30-3 gets a ppm / order-of-magnitude card.
30-1 pathway (40 min) — 30-1 REQUIRED
PATHWAY_30_1: expand/condense; name each law; reject illegal “log(a+b)=log a + log b”.
| Level | Task |
|---|---|
| FOUNDATION | log(xy) as sum |
| CORE | Mix product/quotient/power on a numeric exact example |
| PROFICIENT | Justify each step; flag illegal sum-inside |
| ADVANCED | Change of base to compute log_2 10 (preview) |
Example CORE: expand log_2(8x^3/y).
30-2 pathway (40 min) — 30-2 CORE
Use laws in the growth story: e.g. log of both sides of 80(1.15)^t=200 after S05, or condense a modelled expression. Technology check after the law setup.
| Level | Task |
|---|---|
| FOUNDATION | log(A^t)=t log A in the user model |
| CORE | Apply power law then solve with tech |
| PROFICIENT | Interpret the t they get; reasonableness |
| ADVANCED | Why the illegal sum law would break the model |
30-3 pathway (40 min) — CROSS-STRAND EXPOSURE
Orders of magnitude: 1 ppm vs 1000 ppm vs 10^6 (ppb confusion). Which is more concentrated? No log_b algebra.
| Level | Task (EXPOSURE) |
|---|---|
| FOUNDATION | 1000 is 10×100 |
| CORE | 10^3 vs 10^6 in a water-quality sentence |
| PROFICIENT | Why “0.001 vs 1” can be a safety issue |
| ADVANCED | Optional listen to 30-1 law names — still EXPOSURE |
Cross-strand exposure
D-S06-OOM, D-S06-TECH. 30-3 exposure log. 30-1 may see 30-2 calculator use; 30-1 still exact-first.
Visuals
VIS-M30B-LOGLAW cards · VIS-M30-EXPLOG · ppm place-value strip (30-3)
Tutor boundaries
30-1: law-justification items, no illegal-law accept.
30-2: context+law+tech check.
30-3: magnitude cards ungraded as 014/012.
Refuse 30-3 log-algebra.
Exit tickets
30-1: Expand log(a^2 b / c) with laws named; mark one false statement about log(a+b).
30-2: From 80(1.15)^t=200, show the power-law step then the value of t.
30-3: EXPOSURE: which is more dilute, 1 ppm or 100 ppm? One sentence. Label EXPOSURE.
Teacher solutions
30-1 CORE: log_2(8x^3/y)=log_2 8 + log_2(x^3) − log_2 y = 3 + 3 log_2 x − log_2 y (for x,y>0).
30-1 PROFICIENT: log(a+b)≠log a + log b in general.
30-2: t log(1.15)=log(2.5) ⇒ t=log(2.5)/log(1.15)≈6.55.
30-3: 1 ppm is more dilute than 100 ppm.
Misconception: Silent 30-3 log worksheet. Forbidden.
Visual task (DURING_LAB_ANALYSIS): Inspect the visual, notice labels, and answer the lesson prompt.
MATH30B session 06 trigonometry 096