Canonical combined lesson MATH30B-L076 · week 16 day 1 · CURRICULUM_BASELINE

MATH30B-L076 - Reteach: function operations and transforms; rationals; measure/transforms

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L076
• Calendar: Week 16 Day 1 of 18 weeks × 5 days (lesson 76 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-03-009, MATH30-1-TRIGONOM-04-010, MATH30-1-TRIGONOM-05-011, MATH30-1-TRIGONOM-06-012, MATH30-2-LOGICALR-01-009, MATH30-2-LOGICALR-02-010, MATH30-2-LOGICALR-03-011, MATH30-3-X-01-001, MATH30-3-X-03-004

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)

Weak-outcome reteach from strand tickets. FOUNDATION inside home strand if needed.

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-03-009	REQUIRED - Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations
30-1	MATH30-1-TRIGONOM-04-010	REQUIRED - Apply translations and stretches to the graphs and equations of functions
30-1	MATH30-1-TRIGONOM-05-011	REQUIRED - Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: • x-axis • y-axis • line y = x
30-1	MATH30-1-TRIGONOM-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-2	MATH30-2-LOGICALR-01-009	REQUIRED - Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials)
30-2	MATH30-2-LOGICALR-02-010	REQUIRED - Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials)
30-2	MATH30-2-LOGICALR-03-011	REQUIRED - Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)
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-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)=8x+4, 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-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 8 up: y=(x−4)²+8. The point (0,0) maps to (4,8). Match a graphed image to y=f(x+1)−8.

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-03-009

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

Worked example (unique to this hour, this strand, this SO): From y=√x, write y=8√(x/4) and describe the vertical stretch by 8 and horizontal stretch by 4. A data “all values ×1.2” heard from 30-2 is exposure, not this SO.

Level	Prompt (inside the home strand)
FOUNDATION	Identify a vertical stretch from a sketch.
CORE	Write y=af(bx).
PROFICIENT	Distinguish horizontal vs vertical stretch.
ADVANCED	Stretch then translate with order.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Stretch graphs: y=af(x) and y=f(bx) on the same axes as the parent.

MATH30-1-TRIGONOM-04-010

Official text: Apply translations and stretches to the graphs and equations of functions

Worked example (unique to this hour, this strand, this SO): Apply, in named order: horizontal stretch by 1/4, then translation 1 left and 8 down, to f(x)=|x|. Write the final equation and sketch parent and image.

Level	Prompt (inside the home strand)
FOUNDATION	Apply one translation and one stretch numerically.
CORE	Write the combined equation.
PROFICIENT	Graph parent and image.
ADVANCED	Reverse-order contrast.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Combined transform visual: translate then stretch (order named).

MATH30-1-TRIGONOM-05-011

Official text: Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: • x-axis • y-axis • line y = x

Worked example (unique to this hour, this strand, this SO): Given y=f(x) through (2,8), find images under y=−f(x), y=f(−x), and y=f⁻¹ related reflection in y=x. Write −f(x−1) as a composition of reflection and translation.

Level	Prompt (inside the home strand)
FOUNDATION	Reflect a point in the x-axis.
CORE	Write y=−f(x) and y=f(−x).
PROFICIENT	Reflection in y=x vs inverse language.
ADVANCED	Compose reflection with translation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Reflections through x-axis, y-axis, and y=x.

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)=8x−4. 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 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 009: Swapping the roles of a and b in y=af(bx). Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 010: Applying stretch and translation in an unnamed order and claiming uniqueness. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 011: Reflecting in y=x by negating y only. 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-LOGICALR-01-009

Official text: Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Simplify (x²−64)/(x−8) for x≠8. State the equivalent form and the restriction. Numerators/denominators limited to monomials and binomials.

Level	Prompt (inside the home strand)
FOUNDATION	Cancel a monomial factor.
CORE	Binomial over binomial with restriction.
PROFICIENT	State all non-permissible values.
ADVANCED	Equivalent form used later in an equation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Expression tiles showing cancelled factors and restrictions.

MATH30-2-LOGICALR-02-010

Official text: Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Compute (x/8) + (4/(x+1)) with LCD x(x+1), x≠0, x≠−1. Then multiply (x/4)·((x+8)/x) and state restrictions.

Level	Prompt (inside the home strand)
FOUNDATION	Multiply two monomial rationals.
CORE	Add with LCD (binomials).
PROFICIENT	Complex fraction light.
ADVANCED	All restrictions after operations.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Common-denominator layout for rational operations.

MATH30-2-LOGICALR-03-011

Official text: Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Solve 8/x + 4/(x+1) = 8/(x(x+1)) with x≠0, x≠−1. Check for extraneous roots. Context option: two work rates filling a tank.

Level	Prompt (inside the home strand)
FOUNDATION	Clear a single-term rational equation.
CORE	Binomial denominators + check.
PROFICIENT	Work-rate context.
ADVANCED	Explain an extraneous root.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Rate table that becomes a rational equation; restrictions boxed.

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 009: Cancelling terms (not factors), or dropping restrictions. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 010: Adding numerators and denominators separately. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 011: Clearing denominators then keeping a restricted x as a root. 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 116 mL. State precision, a reasonable uncertainty interval, and whether a ±8 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-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 8 m east and 4 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 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 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.

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-L076.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-007	CORE exit: f(x)=8x+4, 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-LOGICALR-01-009	CORE exit: Simplify (x²−64)/(x−8) for x≠8. State the equivalent form and the restriction. Numerators/denominators limited to monomials and binomials. FOUNDATION alternate: Cancel a monomial factor. 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 116 mL. State precision, a reasonable uncertainty interval, and whether a ±8 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.