Canonical combined lesson MATH30B-L068 · week 14 day 3 · CURRICULUM_BASELINE

MATH30B-L068 - Binomial review; puzzles/sets review; 005-006 fill

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L068
• Calendar: Week 14 Day 3 of 18 weeks × 5 days (lesson 68 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-04-024, MATH30-2-X-01-001, MATH30-2-LOGICALR-02-002, MATH30-3-X-01-005, MATH30-3-X-02-006

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)

30-2 may review 001/002 after 017 is in. 30-3 vehicle numbers again 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-04-024	REQUIRED - Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)
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-01-005	REQUIRED - Analyze puzzles and games that involve logical reasoning, using problem-solving strategies
30-3	MATH30-3-X-02-006	REQUIRED - Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy

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-04-024

Official text: Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)

Worked example (unique to this hour, this strand, this SO): Expand (x+7)^8 using the binomial theorem (natural exponent). Give the general term and the term containing x^6.

Level	Prompt (inside the home strand)
FOUNDATION	(x+1)² by Pascal.
CORE	Full expansion natural n.
PROFICIENT	General term.
ADVANCED	Coefficient of a named power.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Pascal row / binomial expansion aligned to coefficients.

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 024: Writing binomial coefficients as n+r or expanding with subtraction signs ignored. 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 7,6,6. 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 28, 16 like chlorine tablets, 14 like filters, 4 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-01-005

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 7 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).

MATH30-3-X-02-006

Official text: Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy

Worked example (unique to this hour, this strand, this SO): Vehicle price $22000. Buy: tax 5% + $355 fees. Lease: $355/month for 60 months + $1480 due at signing, residual $7400. Lease-to-buy: add a stated buyout. Compare total cost vs monthly cash flow. Table after retrieval.

Level	Prompt (inside the home strand)
FOUNDATION	Define buy / lease / lease-to-buy.
CORE	Total cost vs monthly.
PROFICIENT	Choose with a cash-flow condition.
ADVANCED	Interest/residual sensitivity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Vehicle comparison table VIS-M30B-VEH (buy / lease / lease-to-buy).

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 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.
• 30-3 SO 006: Comparing monthly payment only, ignoring down payment, residual, or term length. 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-L068.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-04-024	CORE exit: Expand (x+7)^8 using the binomial theorem (natural exponent). Give the general term and the term containing x^6. FOUNDATION alternate: (x+1)² by Pascal. 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 7,6,6. 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-01-005	CORE exit: Logic grid: three pumps and three flow rates including 7 L/min. Use elimination. Name the strategy. This is 30-3 005, not 30-2 001 mastery for 30-3 learners (they own 005). FOUNDATION alternate: Attempt with hints. 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.