Bootcamp overlay (weeks 1-2 only): session-09.html. Full course continues through week 18. Overlay does not shrink 30-1/30-2/30-3 to ten outcomes.

Canonical combined lesson MATH30B-L009 · week 2 day 4 · ENHANCED_BOOTCAMP_OVERLAY

MATH30B-L009 - Project day: water/hygiene micro-enterprise

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L009
• Calendar: Week 2 Day 4 of 18 weeks × 5 days (lesson 9 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: B
• Bootcamp overlay: sessions/session-09.md (weeks 1-2 start maps; this file is still a full pack lesson with three workshops)
• Labels: ALL STRANDS launch → 30-1 REQUIRED / 30-2 REQUIRED / 30-3 REQUIRED workshops → CROSS-STRAND EXPOSURE ≠ mastery
• Source: Alberta Mathematics 10-12 Program of Studies, https://open.alberta.ca/publications/mathematics-grades-10-12
• Official outcome IDs today: MATH30-1-TRIGONOM-07-013, MATH30-1-TRIGONOM-08-014, MATH30-2-MATHEMAT-01-017, MATH30-3-X-03-007

Calendar honesty: This is week 2 day 4 of 18×5. It is not “the whole course.” Remaining 30-1 (24), 30-2 (17), and 30-3 (11) specific outcomes continue in weeks 3-18.

Labels (post on the board)

1. ALL STRANDS - shared launch only.
2. 30-1 REQUIRED - MAT3791 tray; mastery evidence for 30-1 SOs listed below.
3. 30-2 REQUIRED - MAT3792 tray; mastery evidence for 30-2 SOs listed below.
4. 30-3 REQUIRED - MAT3793 tray; mastery evidence for 30-3 SOs listed below.
5. CROSS-STRAND EXPOSURE ≠ mastery - hearing another tray is logged as EXPOSURE, never as an SO tick, never as a silent enrolment change.

ALL STRANDS launch (~10-14 min)

Shared project hour. Strand-specific math tasks. 30-2 owns SO 017; 30-1 and 30-3 do not tick 017.

Clock ~75 min unless the school uses 60; cut the workshop block first, never the strand exit ticket. Class C parallel workshops are the default when one strand is on exclusive work.

Official outcomes (REQUIRED on home strand)

Strand	Official ID	Role today
30-1	MATH30-1-TRIGONOM-07-013	REQUIRED - Demonstrate an understanding of logarithms
30-1	MATH30-1-TRIGONOM-08-014	REQUIRED - Demonstrate an understanding of the product, quotient and power laws of logarithms
30-2	MATH30-2-MATHEMAT-01-017	REQUIRED - Research and give a presentation on a current event or an area of interest that involves mathematics
30-3	MATH30-3-X-03-007	REQUIRED - Critique the viability of small business options by considering: • expenses • sales • profit or loss

30-1 workshop - 30-1 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-1.

MATH30-1-TRIGONOM-07-013

Official text: Demonstrate an understanding of logarithms

Worked example (unique to this hour, this strand, this SO): Rewrite 4^7=16384 in log form. Evaluate log_4(16) exactly. Explain log_41=0 and why log_4(−7) is not real.

Level	Prompt (inside the home strand)
FOUNDATION	log_10 1000.
CORE	Convert b^x=a to log form.
PROFICIENT	Exact log of a power of the base.
ADVANCED	Change-of-base preview.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG: y=b^x and y=log_b x as inverse graphs.

MATH30-1-TRIGONOM-08-014

Official text: Demonstrate an understanding of the product, quotient and power laws of logarithms

Worked example (unique to this hour, this strand, this SO): Expand log_4(x^7 y) for x,y>0: 7 log_4 x + log_4 y. Condense log_4 7 − log_4 2 + 7 log_4 4. Reject the illegal step log u + log v = log(u+v) with a counter-example using 4 and 7.

Level	Prompt (inside the home strand)
FOUNDATION	One law: log(xy).
CORE	Expand or condense mixed laws.
PROFICIENT	Justify each step.
ADVANCED	Counter-example to log(u+v).

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Log-law cards (product, quotient, power) posted after retrieval.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-1 SO 013: Writing log_b a = b^a, or logging a negative as if it were real. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 014: log u + log v = log(u+v), or bringing an exponent across a sum inside a log. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-2 workshop - 30-2 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-2.

MATH30-2-MATHEMAT-01-017

Official text: Research and give a presentation on a current event or an area of interest that involves mathematics

Worked example (unique to this hour, this strand, this SO): Research question (30-2 only): “How does a published article use mathematics in a current water or hygiene issue?” Required product: question, two sources, one model or calculation, and a limits sentence. Do not tick this SO for 30-1 or 30-3.

Level	Prompt (inside the home strand)
FOUNDATION	Write a research question.
CORE	Math in the story named.
PROFICIENT	Sources + model.
ADVANCED	Limits of the model.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Project board: question, sources, model, limits - 30-2 only.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-2 SO 017: A poster with no mathematics, or copying a news claim with no sources. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-3 workshop - 30-3 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-3.

MATH30-3-X-03-007

Official text: Critique the viability of small business options by considering: • expenses • sales • profit or loss

Worked example (unique to this hour, this strand, this SO): Month expenses $1080, sales $1325, so profit/loss = sales − expenses. Second scenario: sales drop 12%. Critique viability (can this hygiene kiosk continue?).

Level	Prompt (inside the home strand)
FOUNDATION	Label expense vs revenue.
CORE	Compute profit or loss.
PROFICIENT	Critique viability.
ADVANCED	Two scenarios.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ledger: expenses, sales, profit or loss.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-3 SO 007: Calling revenue “profit,” or ignoring a category of expense. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

CROSS-STRAND EXPOSURE ≠ mastery

• CROSS-STRAND EXPOSURE ≠ mastery. Log D items. Do not tick another strand’s SO.
• AI Tutor must not treat an exposure card as proficiency.
• 30-1 and 30-3 do strand tasks during 017 hour. Do not mark 017 complete for them.

Project or clean math

Project (Sustainable Community Water & Hygiene) - genuine math only: 30-1: users, rates, or sampling paths - composition, logs, or FCP/nPr as today’s SO requires. 30-2: SO 017 research/presentation on a current event that uses mathematics (water/hygiene allowed if the math is real). Never tick 017 for 30-1/30-3. 30-3: site layout, vehicle if the enterprise needs one, ledger, linear fill-rate, or measurement of volume/chlorine - matching today’s SO.

AI Tutor

• Load the authorized home strand only: MAT3791 (Mathematics 30-1) or MAT3792 (Mathematics 30-2) or MAT3793 (Mathematics 30-3) from the authorized profile.
• Never silent-switch a struggling 30-1 learner into 30-2/30-3 banks (or the reverse) to “make it easier.”
• Serve today’s home-strand SOs. Exposure cards are read-only.
• Never dump diploma keys or released exam wording. Original items only.
• Wrong answers: name the error and repair; do not praise.

Human-tutor handoff

Call a human tutor when: the learner cannot complete CORE after two documented repairs; an identity proof (30-1 006) is stuck after the identity map; a 30-2 017 source is unsafe or empty; a 30-3 vehicle/business number is being faked to match a hoped-for answer; distress, disclosure, or a request to change official enrolment. Enrolment changes are an office/PASI process, not a tutor action.

Diagram / whiteboard

Approved starter math30-quadratic-shift. Strand workshops may add axes/tables. Never praise a translated parabola as a circle.

Strand exit ticket (~8-12 min)

Collect only the home-strand row. Exposure ≠ mastery. Lesson MATH30B-L009.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-07-013	CORE exit: Rewrite 4^7=16384 in log form. Evaluate log_4(16) exactly. Explain log_41=0 and why log_4(−7) is not real. FOUNDATION alternate: log_10 1000. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-MATHEMAT-01-017	CORE exit: Research question (30-2 only): “How does a published article use mathematics in a current water or hygiene issue?” Required product: question, two sources, one model or calculation, and a limits sentence. Do not tick … FOUNDATION alternate: Write a research question. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-03-007	CORE exit: Month expenses $1080, sales $1325, so profit/loss = sales − expenses. Second scenario: sales drop 12%. Critique viability (can this hygiene kiosk continue?). FOUNDATION alternate: Label expense vs revenue. Do not submit another strand’s ticket as 30-3 mastery.

Provenance

Official IDs/text: _official_math_calm_outcomes.json. Pacing: MATH30_COMBINED_CLASSROOM_PACING.md. Crosswalk: MATH30_1_30_2_30_3_OUTCOME_CROSSWALK.csv. Generated by oeom/core/training/rapid3/write_math30b_lessons.py.