Bootcamp overlay (weeks 1-2 only): session-05.html. Full course continues through week 18. Overlay does not shrink 30-1/30-2/30-3 to ten outcomes.

Canonical combined lesson MATH30B-L005 · week 1 day 5 · ENHANCED_BOOTCAMP_OVERLAY

MATH30B-L005 - Exponential growth in the water 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-L005
• Calendar: Week 1 Day 5 of 18 weeks × 5 days (lesson 5 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: B
• Bootcamp overlay: sessions/session-05.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, MATH30-2-LOGICALR-04-012, MATH30-2-RELATION-05-013, MATH30-2-RELATION-06-014, MATH30-3-X-03-007

Calendar honesty: This is week 1 day 5 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)

Water-enterprise users grow. 30-1 starts log definition; 30-2 models with laws/tech; 30-3 critiques expense vs sales.

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
30-2	MATH30-2-LOGICALR-04-012	REQUIRED - Demonstrate an understanding of logarithms and the laws of logarithms
30-2	MATH30-2-RELATION-05-013	REQUIRED - Solve problems that involve exponential equations
30-2	MATH30-2-RELATION-06-014	REQUIRED - Represent data, using exponential and logarithmic functions, to solve problems
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 7^9=40353607 in log form. Evaluate log_7(49) exactly. Explain log_71=0 and why log_7(−3) 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.

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.

30-2 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 65 at annual factor 1.09. Write a log to find years to reach 195. 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).

MATH30-2-RELATION-05-013

Official text: Solve problems that involve exponential equations

Worked example (unique to this hour, this strand, this SO): Solve 1.09^t = 5 using logs or tech after a table guess. State what the solution means for the water-enterprise users and one model limit.

Level	Prompt (inside the home strand)
FOUNDATION	Guess-check table for a^t=k.
CORE	Log or tech solve.
PROFICIENT	Model limits.
ADVANCED	Compare two growth models.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Table-to-equation growth model.

MATH30-2-RELATION-06-014

Official text: Represent data, using exponential and logarithmic functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Given points (0,17), (1,18), (2,20), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 7.

Level	Prompt (inside the home strand)
FOUNDATION	Table to graph.
CORE	Choose exp vs linear.
PROFICIENT	Fit language.
ADVANCED	Residual talk.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + exponential/log model VIS-M30B-DATA.

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.
• 30-2 SO 013: Reporting a negative time without checking the model. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 014: Forcing a linear model on clearly exponential data. 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 $1000, sales $1225, so profit/loss = sales − expenses. Second scenario: sales drop 15%. 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.

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: model users, kits, or committees with today’s relation/counting SO. 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-L005.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-07-013	CORE exit: Rewrite 7^9=40353607 in log form. Evaluate log_7(49) exactly. Explain log_71=0 and why log_7(−3) is not real. FOUNDATION alternate: log_10 1000. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-04-012	CORE exit: Users grow from 65 at annual factor 1.09. Write a log to find years to reach 195. 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 $1000, sales $1225, so profit/loss = sales − expenses. Second scenario: sales drop 15%. 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.