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 07 — Counting and probability shared launch
Time: 75 minutes
Labels: ALL STRANDS test story · 30-1 REQUIRED FCP · 30-2 REQUIRED FCP and mutually exclusive start · 30-3 REQUIRED probability interpretation
Braid class: B
Official outcome codes
| Strand | Codes |
|---|---|
| 30-1 | MATH30-1-TRIGONOM-01-021 REQUIRED start |
| 30-2 | MATH30-2-LOGICALR-04-006; MATH30-2-LOGICALR-02-004 start (003 later) |
| 30-3 | MATH30-3-ALGEBRA-01-011 REQUIRED start |
Shared portion (14 min) — ALL STRANDS
Story: a water sample can test positive/negative; a second independent check exists. Also: choosing a delivery day and a neighbourhood. Shared tree sketch without forcing nPr on 30-3.
30-1 pathway (24 min) — 30-1 REQUIRED
FCP toward combinatorics. Restrictions: “no two routes the same.”
| Level | Task |
|---|---|
| FOUNDATION | 3 neighbourhoods × 4 time slots |
| CORE | FCP with one restriction (cannot use Sunday) |
| PROFICIENT | Two-stage then three-stage; explain overcount |
| ADVANCED | Restriction that is not independent (preview permutations) |
30-2 pathway (24 min) — 30-2 REQUIRED
FCP in chance context. Mutually exclusive: “positive vs negative” vs overlapping “positive or high-turbidity.”
| Level | Task |
|---|---|
| FOUNDATION | 3×4 FCP |
| CORE | FCP + P(A or B) for exclusive events with given P |
| PROFICIENT | Non-exclusive: subtract overlap in words + numbers |
| ADVANCED | Critique a newspaper odds claim (preview 003) |
30-3 pathway (24 min) — 30-3 REQUIRED
Interpret: “There is a 5% chance this test flags a safe sample.” What does that mean? What does it not mean?
| Level | Task |
|---|---|
| FOUNDATION | Likely / unlikely on a number line of P |
| CORE | Interpret 0.05 in the story |
| PROFICIENT | Critique “5% means 5 of our 5 samples are bad” |
| ADVANCED | Sample space in words without nPr |
Cross-strand exposure
D-S07-P: 30-1 may hear probability language. Not a 30-1 probability SO.
30-3 must not receive nPr.
Visuals
VIS-M30B-FCP trees · Venn exclusive vs overlap (30-2) · probability statements (30-3)
Tutor boundaries
Route by profile. 30-3 interpretation bank. 30-1 FCP bank. 30-2 FCP+exclusive bank.
Exit tickets
30-1: Number of routes: 5 days × 3 sites, then minus a forbidden pair; show FCP.
30-2: FCP for 4×2; then P(A or B) if A,B exclusive, P(A)=0.2, P(B)=0.15.
30-3: Interpret P=0.05 in one correct and one incorrect sentence.
Teacher solutions
30-1 FOUNDATION: 12. CORE example: 5×3=15; subtract 1 forbidden =14 if restriction is one pair.
30-2 CORE: 8 ways; P(A or B)=0.35 if exclusive.
30-2 PROFICIENT: If overlap 0.05, P(A or B)=0.2+0.15-0.05=0.30.
30-3 CORE: About 5 in 100 safe samples might still flag (false positive framing) — accept equivalent careful wording.
30-3 PROFICIENT: Incorrect: “exactly 5 of our next 5 tests fail.”
Misconception: 30-3 doing 30-2 exclusive-event algebra as if it were 011 complete.
Visual task (AFTER_PRACTICE): Interpret the graph and state slope/intercept or trend.
MATH30B session 07 graph 097