Canonical combined lesson MATH30B-L086 · week 18 day 1 · CURRICULUM_BASELINE

MATH30B-L086 - Buffer: functions catch-up; logic/sets catch-up; measurement catch-up

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L086
• Calendar: Week 18 Day 1 of 18 weeks × 5 days (lesson 86 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: C
• 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-02-008, MATH30-1-TRIGONOM-06-012, MATH30-2-X-01-001, MATH30-2-LOGICALR-02-002, MATH30-3-X-01-001, MATH30-3-X-01-005

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)

Authorized catch-up. Learner stays on home strand.

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-02-008	REQUIRED - Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations
30-1	MATH30-1-TRIGONOM-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-2	MATH30-2-X-01-001	REQUIRED - Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies
30-2	MATH30-2-LOGICALR-02-002	REQUIRED - Solve problems that involve the application of set theory
30-3	MATH30-3-X-01-001	REQUIRED - Demonstrate an understanding of the limitations of measuring instruments, including: • precision • accuracy • uncertainty • tolerance and solve problems
30-3	MATH30-3-X-01-005	REQUIRED - Analyze puzzles and games that involve logical reasoning, using problem-solving strategies

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)=4x+4, g(x)=x²−3. Compute (f∘g)(6) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−3).

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-02-008

Official text: Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations

Worked example (unique to this hour, this strand, this SO): Parent f(x)=x². Write the equation of the image after shift 4 right and 4 up: y=(x−4)²+4. The point (0,0) maps to (4,4). Match a graphed image to y=f(x+3)−6.

Level	Prompt (inside the home strand)
FOUNDATION	Shift a table of values up 2.
CORE	Write y=f(x−h)+k.
PROFICIENT	Equation from a graphed image.
ADVANCED	Composition with a translation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Parent-to-image graphs for y=f(x−h)+k.

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)=4x−4. Restrict if needed so the inverse is a function. Show (f∘f⁻¹)(x)=x on that domain. Numeric undo: f(6) 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 008: Writing y=f(x−h) as a shift left when h>0, or sliding a 30-3 shape and calling it SO 008. 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-X-01-001

Official text: Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies

Worked example (unique to this hour, this strand, this SO): KenKen-style or “exactly one of these three statements is true” puzzle using numbers 4,4,6. Name the strategy (eliminate / work backward / guess-check) and transfer it to a second mini-puzzle.

Level	Prompt (inside the home strand)
FOUNDATION	Attempt the puzzle with hints.
CORE	Solve and name a strategy.
PROFICIENT	Transfer to a second puzzle.
ADVANCED	Write a false-friend statement.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Puzzle card with a named strategy box (guess-check, eliminate, work backward).

MATH30-2-LOGICALR-02-002

Official text: Solve problems that involve the application of set theory

Worked example (unique to this hour, this strand, this SO): In a class of 31, 18 like chlorine tablets, 11 like filters, 6 like both. Draw the Venn. Find only-tablets, only-filters, neither, and n(A∪B).

Level	Prompt (inside the home strand)
FOUNDATION	Place two numbers in a Venn.
CORE	Compute union with overlap.
PROFICIENT	Three-set or complement.
ADVANCED	Word problem with “neither”.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Venn diagram VIS-M30B-SET (two or three sets) 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):

• 30-2 SO 001: Guessing without naming a strategy, or claiming a unique solution when two remain. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 002: Adding n(A)+n(B) without subtracting the intersection. 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-01-001

Official text: Demonstrate an understanding of the limitations of measuring instruments, including: • precision • accuracy • uncertainty • tolerance and solve problems

Worked example (unique to this hour, this strand, this SO): A cylinder scale is marked every 2 mL. A reading looks like 126 mL. State precision, a reasonable uncertainty interval, and whether a ±4 mL tolerance is met. Accuracy still needs a true value - do not call a precise reading accurate by default.

Level	Prompt (inside the home strand)
FOUNDATION	Read to nearest mark; copy precision vs accuracy.
CORE	Uncertainty interval.
PROFICIENT	Tolerance met/not.
ADVANCED	Choose an instrument for the job.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ruler/scale photos VIS-M30B-MEAS (precision vs accuracy).

MATH30-3-X-01-005

Official text: Analyze puzzles and games that involve logical reasoning, using problem-solving strategies

Worked example (unique to this hour, this strand, this SO): Logic grid: three pumps and three flow rates including 4 L/min. Use elimination. Name the strategy. This is 30-3 005, not 30-2 001 mastery for 30-3 learners (they own 005).

Level	Prompt (inside the home strand)
FOUNDATION	Attempt with hints.
CORE	Solve and name strategy.
PROFICIENT	Transfer.
ADVANCED	Create a variant.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Logic-puzzle card (30-3 wording, not 30-1 diploma).

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 001: Calling a precise instrument accurate, or writing uncertainty as a single point. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 005: Random guessing with no elimination trail. 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 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-L086.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-007	CORE exit: f(x)=4x+4, g(x)=x²−3. Compute (f∘g)(6) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−3). FOUNDATION alternate: Numeric f(3). Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-X-01-001	CORE exit: KenKen-style or “exactly one of these three statements is true” puzzle using numbers 4,4,6. Name the strategy (eliminate / work backward / guess-check) and transfer it to a second mini-puzzle. FOUNDATION alternate: Attempt the puzzle with hints. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-001	CORE exit: A cylinder scale is marked every 2 mL. A reading looks like 126 mL. State precision, a reasonable uncertainty interval, and whether a ±4 mL tolerance is met. Accuracy still needs a true value - do not call a precise r… FOUNDATION alternate: Read to nearest mark; copy precision vs accuracy. 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.