Canonical combined lesson MATH30B-L060 · week 12 day 5 · CURRICULUM_BASELINE

MATH30B-L060 - 023 check; 007-008 complete; mixed applied 30-3

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L060
• Calendar: Week 12 Day 5 of 18 weeks × 5 days (lesson 60 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-03-023, MATH30-2-LOGICALR-05-007, MATH30-2-LOGICALR-06-008, MATH30-3-X-01-001, MATH30-3-X-02-006, MATH30-3-ALGEBRA-01-008

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)

Do not mark 30-1 combinations complete for 30-2 or 30-3.

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-03-023	REQUIRED - Determine the number of combinations of n different elements taken r at a time to solve problems
30-2	MATH30-2-LOGICALR-05-007	REQUIRED - Solve problems that involve permutations
30-2	MATH30-2-LOGICALR-06-008	REQUIRED - Solve problems that involve combinations
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-02-006	REQUIRED - Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy
30-3	MATH30-3-ALGEBRA-01-008	REQUIRED - Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating

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-03-023

Official text: Determine the number of combinations of n different elements taken r at a time to solve problems

Worked example (unique to this hour, this strand, this SO): Compute C(14,2). Choose 2 test kits from 14 where order does not matter. Show C(n,r)=P(n,r)/r! and why dividing by r! is required.

Level	Prompt (inside the home strand)
FOUNDATION	List combinations of 3 from 4.
CORE	C(n,r) formula.
PROFICIENT	Choose nCr vs nPr.
ADVANCED	Restriction on a committee.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Unordered-subset visual (nCr) distinct from nPr.

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 023: Using nPr when order does not matter. 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-05-007

Official text: Solve problems that involve permutations

Worked example (unique to this hour, this strand, this SO): Arrange 2 distinct volunteer shifts from 14 people (order matters). Compute nPr. List if n is small. One restriction: a named person cannot be first.

Level	Prompt (inside the home strand)
FOUNDATION	List orders of 3 people.
CORE	nPr in context.
PROFICIENT	Light restriction.
ADVANCED	Optional identical-order stretch.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered lists then nPr formula card.

MATH30-2-LOGICALR-06-008

Official text: Solve problems that involve combinations

Worked example (unique to this hour, this strand, this SO): Choose 2 people from 14 for a water-test committee (order does not matter). Compute nCr. Write one sentence on why this is not nPr.

Level	Prompt (inside the home strand)
FOUNDATION	List committees of 2 from 4.
CORE	nCr in context.
PROFICIENT	Choose nCr vs nPr.
ADVANCED	Optional harder restriction.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Committee diagram: order does not matter.

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 007: Using nCr for an ordered schedule. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 008: Using nPr for an unordered committee. 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 100 mL. State precision, a reasonable uncertainty interval, and whether a ±6 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-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 $18000. Buy: tax 5% + $370 fees. Lease: $370/month for 36 months + $1400 due at signing, residual $7000. 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).

MATH30-3-ALGEBRA-01-008

Official text: Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating • solving problems

Worked example (unique to this hour, this strand, this SO): Table: hours 0, 1, 2, 3 vs litres treated 0, 18, 36, 54. Graph, write litres = (rate)(hours), interpolate at 1.5 h, extrapolate to 5 h with a caution.

Level	Prompt (inside the home strand)
FOUNDATION	Complete a table.
CORE	Graph + equation.
PROFICIENT	Interpolate.
ADVANCED	Extrapolate with caution.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-LINEAR: table, graph, equation together.

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 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.
• 30-3 SO 008: Extrapolating far beyond the table with no caution. 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-L060.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-03-023	CORE exit: Compute C(14,2). Choose 2 test kits from 14 where order does not matter. Show C(n,r)=P(n,r)/r! and why dividing by r! is required. FOUNDATION alternate: List combinations of 3 from 4. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-05-007	CORE exit: Arrange 2 distinct volunteer shifts from 14 people (order matters). Compute nPr. List if n is small. One restriction: a named person cannot be first. FOUNDATION alternate: List orders of 3 people. 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 100 mL. State precision, a reasonable uncertainty interval, and whether a ±6 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.