Bootcamp overlay (weeks 1-2 only): session-06.html. Full course continues through week 18. Overlay does not shrink 30-1/30-2/30-3 to ten outcomes.

Canonical combined lesson MATH30B-L006 · week 2 day 1 · ENHANCED_BOOTCAMP_OVERLAY

MATH30B-L006 - Log laws workshop

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L006
• Calendar: Week 2 Day 1 of 18 weeks × 5 days (lesson 6 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: A
• Bootcamp overlay: sessions/session-06.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-08-014, MATH30-2-LOGICALR-04-012, MATH30-3-X-03-007

Calendar honesty: This is week 2 day 1 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)

Same log-law object, different depth. 30-3 hears orders of magnitude only as exposure, then continues business arithmetic as REQUIRED.

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-08-014	REQUIRED - Demonstrate an understanding of the product, quotient and power laws of logarithms
30-2	MATH30-2-LOGICALR-04-012	REQUIRED - Demonstrate an understanding of logarithms and the laws of logarithms
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-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_8(x^4 y) for x,y>0: 4 log_8 x + log_8 y. Condense log_8 4 − log_8 3 + 4 log_8 8. Reject the illegal step log u + log v = log(u+v) with a counter-example using 8 and 4.

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 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-LOGICALR-04-012

Official text: Demonstrate an understanding of logarithms and the laws of logarithms

Worked example (unique to this hour, this strand, this SO): Users grow from 70 at annual factor 1.04. Write a log to find years to reach 210. Apply one product or power law in the setup, then a technology check. Not 30-1 exact-only demand.

Level	Prompt (inside the home strand)
FOUNDATION	Meaning of log in a growth sentence.
CORE	One law in a story.
PROFICIENT	Tech check after setup.
ADVANCED	Reasonableness limits.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG in a growth story (not 30-1 exact-only demand).

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 012: Applying 30-1 exact-only demands as if they were this SO, or illegal log sums. 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 $1020, sales $1250, so profit/loss = sales − expenses. Second scenario: sales drop 16%. 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.
• 30-3 hears orders of magnitude only. Not 30-1-014 / 30-2-012 mastery.

Project or clean math

Project overlay today: none. Use a clean math prompt on the home-strand tray. Do not force Sustainable Community Water & Hygiene onto work that is not genuinely that mathematics.

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-L006.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-08-014	CORE exit: Expand log_8(x^4 y) for x,y>0: 4 log_8 x + log_8 y. Condense log_8 4 − log_8 3 + 4 log_8 8. Reject the illegal step log u + log v = log(u+v) with a counter-example using 8 and 4. FOUNDATION alternate: One law: log(xy). Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-04-012	CORE exit: Users grow from 70 at annual factor 1.04. Write a log to find years to reach 210. Apply one product or power law in the setup, then a technology check. Not 30-1 exact-only demand. FOUNDATION alternate: Meaning of log in a growth sentence. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-03-007	CORE exit: Month expenses $1020, sales $1250, so profit/loss = sales − expenses. Second scenario: sales drop 16%. 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.