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 08 — Parallel workshop: permutations vs vehicle cost
Time: 75 minutes
Labels: PARALLEL WORKSHOP · 30-1 REQUIRED permutations · 30-2 REQUIRED permutations/combinations intro · 30-3 REQUIRED buying vs leasing
Braid class: C
30-3 provenance: satellite Lesson 1 (do not overwrite satellite files). Reuse comparison table pattern from math30_3_vehicle.json.
Official outcome codes
| Strand | Codes |
|---|---|
| 30-1 | MATH30-1-TRIGONOM-02-022 REQUIRED start |
| 30-2 | MATH30-2-LOGICALR-05-007 REQUIRED start; MATH30-2-LOGICALR-06-008 intro |
| 30-3 | MATH30-3-X-02-006 REQUIRED start |
Shared portion (10 min) — ALL STRANDS
Two Grade 12 jobs today: (1) when order matters in counting; (2) when total cost over time matters in acquiring a vehicle. Do not convert one into the other.
30-1 pathway (45 min) — 30-1 REQUIRED
nPr; why order matters; simple restriction.
| Level | Task |
|---|---|
| FOUNDATION | List permutations of 3 letters |
| CORE | P(8,3) for ordered volunteer shifts |
| PROFICIENT | Restriction: first slot is a trained tester |
| ADVANCED | Contrast with P(n,n)=n! |
30-1 combinations (023) not complete today.
30-2 pathway (45 min) — 30-2 REQUIRED
Permutations in context; introduce combinations: committee of 3 from 8 (order does not matter).
| Level | Task |
|---|---|
| FOUNDATION | List ordered pairs from 4 names |
| CORE | P(6,2) story |
| PROFICIENT | C(6,2) vs P(6,2) — which for a 2-person team with no roles? |
| ADVANCED | One sentence: when to use which |
30-3 pathway (45 min) — 30-3 REQUIRED
Buying vs leasing vs lease-to-own. Compare monthly payment and total cost; ownership at end. (Satellite Lesson 1 numbers may be simplified for one period.)
Example numbers (teacher may substitute local CAD figures):
- Buy (loan): price 12000, down 2000, 24 months, interest as a simple add-on or given PMT 480 — be explicit which model. Prefer: given table of total paid and residual, not an unexplained formula dump.
- Lease: 24×350 + fees; no ownership.
- Lease-to-own: 24×400 then balloon.
| Level | Task |
|---|---|
| FOUNDATION | Define buy / lease / lease-to-own |
| CORE | Total cost vs monthly for two options |
| PROFICIENT | Recommend for “need 2 years then none” vs “keep 8 years” |
| ADVANCED | Residual / mileage penalty in words |
Cross-strand exposure
D-S08-VEH, D-S08-PERM. Optional 2-minute listen. No mastery swap.
Visuals
VIS-M30B-PERM · VIS-M30B-VEH comparison table (TABLE working object)
Tutor boundaries
30-1/30-2: permutation/combination banks.
30-3: vehicle bank only.
Do not clone satellite Python engine.
Exit tickets
30-1: Compute P(7,2) and state why order matters in the story.
30-2: P(5,2) and C(5,2); which for unordered pairs?
30-3: Two-row table: monthly and total for buy vs lease; one recommendation.
Teacher solutions
30-1 CORE: P(8,3)=8×7×6=336.
30-1 FOUNDATION: ABC, ACB, BAC, BCA, CAB, CBA — 6.
30-2 CORE: P(6,2)=30. PROFICIENT: C(6,2)=15 for unordered team.
30-3 CORE (illustrative): Lease 24×350=8400, no asset; buy totals depend on given PMT×24+down — mark from the issued table. Recommendation must cite time horizon.
If using PMT 480, 24 months, down 2000: total paid 2000+11520=13520 plus they own the vehicle (ignore remaining book value unless given).
Misconception: Scoring a 30-1 learner on a lease residual. Forbidden.
Visual task (ASSESSMENT_STIMULUS): Inspect the visual, notice labels, and answer the lesson prompt.
MATH30B session 08 strand map 098