Canonical combined lesson MATH30B-L078 · week 16 day 3 · CURRICULUM_BASELINE

MATH30B-L078 - Reteach: polynomials radicals rationals; poly/sine data; triangles/polygons

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L078
• Calendar: Week 16 Day 3 of 18 weeks × 5 days (lesson 78 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-11-017, MATH30-1-TRIGONOM-12-018, MATH30-1-TRIGONOM-13-019, MATH30-1-TRIGONOM-14-020, MATH30-2-RELATION-07-015, MATH30-2-RELATION-08-016, MATH30-3-X-01-002, MATH30-3-X-02-003

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)

Show the relevant diagram after retrieval, before independent reteach practice.

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-11-017	REQUIRED - Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients)
30-1	MATH30-1-TRIGONOM-12-018	REQUIRED - Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 )
30-1	MATH30-1-TRIGONOM-13-019	REQUIRED - Graph and analyze radical functions (limited to functions involving one radical)
30-1	MATH30-1-TRIGONOM-14-020	REQUIRED - Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)
30-2	MATH30-2-RELATION-07-015	REQUIRED - Represent data, using polynomial functions (of degree ≤ 3), to solve problems
30-2	MATH30-2-RELATION-08-016	REQUIRED - Represent data, using sinusoidal functions, to solve problems
30-3	MATH30-3-X-01-002	REQUIRED - Solve problems by using the sine law and cosine law, excluding the ambiguous case
30-3	MATH30-3-X-02-003	REQUIRED - Solve problems that involve: • triangles • quadrilaterals • regular polygons

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-11-017

Official text: Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients)

Worked example (unique to this hour, this strand, this SO): Factor P(x)=x³−3x²−6x+18 by testing possible rational roots ±1,±3,±6. Show synthetic division and write linear/quadratic factors over the reals if possible. Degree ≤5, integer coefficients.

Level	Prompt (inside the home strand)
FOUNDATION	Factor x³−x.
CORE	Synthetic division with a given root.
PROFICIENT	Full factorization deg 4.
ADVANCED	Explain a non-rational root remaining.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Factor tree / synthetic division layout for a cubic or quartic.

MATH30-1-TRIGONOM-12-018

Official text: Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 )

Worked example (unique to this hour, this strand, this SO): For y=(x+3)²(x−3), state zeros, multiplicities, x-intercepts, and end behaviour. Sketch, marking whether the graph touches or crosses at x=−3.

Level	Prompt (inside the home strand)
FOUNDATION	Read zeros from a factored cubic.
CORE	Multiplicity touch vs cross.
PROFICIENT	End behaviour from leading term.
ADVANCED	Link zeros, roots, intercepts in words.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Polynomial graph with zeros, multiplicity, and end behaviour.

MATH30-1-TRIGONOM-13-019

Official text: Graph and analyze radical functions (limited to functions involving one radical)

Worked example (unique to this hour, this strand, this SO): Graph y=√(x−3)+3. Domain x≥3. Show the translation from y=√x. Evaluate y(7) exactly.

Level	Prompt (inside the home strand)
FOUNDATION	Domain of √(x−1).
CORE	Graph a translated radical.
PROFICIENT	Match equation to graph.
ADVANCED	One radical only - reject a second nested radical.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Radical graph with domain ray and transform from √x.

MATH30-1-TRIGONOM-14-020

Official text: Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)

Worked example (unique to this hour, this strand, this SO): Analyse y=(x²−9)/(x−3). Factor; identify the hole at x=3 vs any vertical asymptote. State horizontal behaviour and sketch with the hole marked, not as a VA.

Level	Prompt (inside the home strand)
FOUNDATION	Vertical asymptote of 1/x.
CORE	Hole vs VA on a cancelled factor.
PROFICIENT	Horizontal behaviour.
ADVANCED	Full analysis of a proper/improper rational.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Rational graph with holes vs vertical asymptotes labelled.

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 017: Stopping after one synthetic-division step when a quadratic factor remains. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 018: Calling a touch-at-axis zero “no intercept,” or mixing degree with number of turning points blindly. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 019: Including x-values inside the radical that make the radicand negative. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 020: Labelling a hole as a vertical asymptote after cancelling. 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-07-015

Official text: Represent data, using polynomial functions (of degree ≤ 3), to solve problems

Worked example (unique to this hour, this strand, this SO): Weekly demand looks curved: (0,13), (1,16), (2,22), (3,31). Argue for a polynomial of degree ≤3 (here quadratic-like second differences). Do not invoke 30-1 factor theorem.

Level	Prompt (inside the home strand)
FOUNDATION	Plot deg ≤3 data.
CORE	Choose quadratic vs cubic in words.
PROFICIENT	Reasonableness.
ADVANCED	Do not factor-theorem the data.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + polynomial (deg ≤ 3) with a reasonableness comment.

MATH30-2-RELATION-08-016

Official text: Represent data, using sinusoidal functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Tank level (m): midline 2, amplitude 1.5, period 12 months, max in month 1. Write a sinusoidal model and predict month 8. This is data modelling, not 30-1 identity proof.

Level	Prompt (inside the home strand)
FOUNDATION	Read amplitude from a graph.
CORE	Write midline/period/amp from data.
PROFICIENT	Predict a future month.
ADVANCED	Discuss a poor sine fit.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Sine data graph: amplitude, period, midline labelled from 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 015: Invoking the factor theorem on a scatter plot. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 016: Proving a trig identity instead of fitting amplitude/period/midline. 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-01-002

Official text: Solve problems by using the sine law and cosine law, excluding the ambiguous case

Worked example (unique to this hour, this strand, this SO): Triangle: angle A=43°, angle B=46°, side a=15 m (AAS). Use sine law (no ambiguous case). Second item: sides 13, 18, included angle 53° - cosine law for the third side. Never assign 30-1 radian identities as this SO.

Level	Prompt (inside the home strand)
FOUNDATION	Identify AAS vs SAS from a sketch.
CORE	Sine law numerical (no ambiguous case).
PROFICIENT	Cosine law numerical.
ADVANCED	Choose the law from given parts.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Oblique triangle with sides/angles labelled; sine or cosine law choice boxed.

MATH30-3-X-02-003

Official text: Solve problems that involve: • triangles • quadrilaterals • regular polygons

Worked example (unique to this hour, this strand, this SO): Regular 7-gon with side 3 m. Interior angle sum and one interior angle. A quadrilateral site plot with sides 11,12,9,7 and one diagonal 14 - split into triangles if needed.

Level	Prompt (inside the home strand)
FOUNDATION	Name the polygon.
CORE	Interior angle of a regular polygon.
PROFICIENT	Composite quadrilateral area/angles.
ADVANCED	Regular polygon in a site plan.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Polygon / quadrilateral diagram with interior-angle marks.

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 002: Using sine law when SAS needs cosine law, or entering the ambiguous case (excluded). Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 003: Using (n−2)×90° for interior sum, or treating a non-regular polygon as regular. 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-L078.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-11-017	CORE exit: Factor P(x)=x³−3x²−6x+18 by testing possible rational roots ±1,±3,±6. Show synthetic division and write linear/quadratic factors over the reals if possible. Degree ≤5, integer coefficients. FOUNDATION alternate: Factor x³−x. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-07-015	CORE exit: Weekly demand looks curved: (0,13), (1,16), (2,22), (3,31). Argue for a polynomial of degree ≤3 (here quadratic-like second differences). Do not invoke 30-1 factor theorem. FOUNDATION alternate: Plot deg ≤3 data. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-002	CORE exit: Triangle: angle A=43°, angle B=46°, side a=15 m (AAS). Use sine law (no ambiguous case). Second item: sides 13, 18, included angle 53° - cosine law for the third side. Never assign 30-1 radian identities as this SO. FOUNDATION alternate: Identify AAS vs SAS from a sketch. 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.