Bootcamp overlay (weeks 1-2 only): session-04.html. Full course continues through week 18. Overlay does not shrink 30-1/30-2/30-3 to ten outcomes.

Canonical combined lesson MATH30B-L004 · week 1 day 4 · ENHANCED_BOOTCAMP_OVERLAY

MATH30B-L004 - Inverse and composition intro

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L004
• Calendar: Week 1 Day 4 of 18 weeks × 5 days (lesson 4 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: E
• Bootcamp overlay: sessions/session-04.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-01-007, MATH30-1-TRIGONOM-06-012, MATH30-2-RELATION-06-014, MATH30-3-X-03-004

Calendar honesty: This is week 1 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)

Undo and compose as shared language. Only 30-1 is assessed on algebraic inverse and composition today.

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-01-007	REQUIRED - Demonstrate an understanding of operations on, and compositions of, functions
30-1	MATH30-1-TRIGONOM-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-2	MATH30-2-RELATION-06-014	REQUIRED - Represent data, using exponential and logarithmic functions, to solve problems
30-3	MATH30-3-X-03-004	REQUIRED - Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including: • translations • rotations • reflections • dilations

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-01-007

Official text: Demonstrate an understanding of operations on, and compositions of, functions

Worked example (unique to this hour, this strand, this SO): f(x)=6x+7, g(x)=x²−1. Compute (f∘g)(8) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−1).

Level	Prompt (inside the home strand)
FOUNDATION	Numeric f(3).
CORE	(f∘g)(x) algebraic.
PROFICIENT	Domain of a composition.
ADVANCED	(f∘f⁻¹)(x)=x justification.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Mapping diagrams for f and g; composition arrows.

MATH30-1-TRIGONOM-06-012

Official text: Demonstrate an understanding of inverses of relations

Worked example (unique to this hour, this strand, this SO): Find the inverse of f(x)=6x−7. Restrict if needed so the inverse is a function. Show (f∘f⁻¹)(x)=x on that domain. Numeric undo: f(8) then invert.

Level	Prompt (inside the home strand)
FOUNDATION	Numeric undo.
CORE	Swap coordinates on a table.
PROFICIENT	Algebraic inverse with domain.
ADVANCED	Prove composition identity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Inverse visual: points swapped; y=x mirror.

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 007: Computing (f∘g) as f(x)·g(x), or ignoring domain of the inner function. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 012: Swapping a and b in y=ax+b incorrectly, or claiming every inverse is a function. 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-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 (0,16), (1,17), (2,18), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 6.

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 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-03-004

Official text: Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including: • translations • rotations • reflections • dilations

Worked example (unique to this hour, this strand, this SO): Translate a 2-D tank rectangle 6 m east and 7 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.08 from a centre; state the inverse scale as 1/k.

Level	Prompt (inside the home strand)
FOUNDATION	Name T/R/Rf/D on a picture.
CORE	Perform one 2-D transform.
PROFICIENT	3-D or composition.
ADVANCED	Inverse of a dilation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-3DTRANS: 2-D footprint and 3-D crate (T/R/Rf/D).

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 004: Calling a function translation y=f(x−h) evidence for this object-transform SO. 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.
• 30-2/30-3 may see inverse/undo language (D). Not 30-1-012 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-L004.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-007	CORE exit: f(x)=6x+7, g(x)=x²−1. Compute (f∘g)(8) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−1). FOUNDATION alternate: Numeric f(3). Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-06-014	CORE exit: Given points (0,16), (1,17), (2,18), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 6. FOUNDATION alternate: Table to graph. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-03-004	CORE exit: Translate a 2-D tank rectangle 6 m east and 7 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.08 from a centre; state the inverse scale as 1/k. FOUNDATION alternate: Name T/R/Rf/D on a picture. 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.