Canonical combined lesson MATH30B-L070 · week 14 day 5 · CURRICULUM_BASELINE

MATH30B-L070 - Counting cumulative; explog/sinusoidal review; 009-011 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-L070
• Calendar: Week 14 Day 5 of 18 weeks × 5 days (lesson 70 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-01-021, MATH30-1-TRIGONOM-02-022, MATH30-1-TRIGONOM-03-023, MATH30-1-TRIGONOM-04-024, MATH30-2-LOGICALR-04-012, MATH30-2-RELATION-05-013, MATH30-2-RELATION-06-014, MATH30-2-RELATION-08-016, MATH30-3-ALGEBRA-01-009, MATH30-3-ALGEBRA-02-010, MATH30-3-ALGEBRA-01-011

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)

Every 30-3 SO 001-011 has now appeared as REQUIRED in weeks 1-14.

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-01-021	REQUIRED - Apply the fundamental counting principle to solve problems
30-1	MATH30-1-TRIGONOM-02-022	REQUIRED - Determine the number of permutations of n elements taken r at a time to solve problems
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
30-1	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-LOGICALR-04-012	REQUIRED - Demonstrate an understanding of logarithms and the laws of logarithms
30-2	MATH30-2-RELATION-05-013	REQUIRED - Solve problems that involve exponential equations
30-2	MATH30-2-RELATION-06-014	REQUIRED - Represent data, using exponential and logarithmic functions, to solve problems
30-2	MATH30-2-RELATION-08-016	REQUIRED - Represent data, using sinusoidal functions, to solve problems
30-3	MATH30-3-ALGEBRA-01-009	REQUIRED - Solve problems that involve measures of central tendency, including: • mean • median • mode • weighted mean • trimmed mean
30-3	MATH30-3-ALGEBRA-02-010	REQUIRED - Analyze and describe percentiles
30-3	MATH30-3-ALGEBRA-01-011	REQUIRED - Analyze and interpret problems that involve probability

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-01-021

Official text: Apply the fundamental counting principle to solve problems

Worked example (unique to this hour, this strand, this SO): A lock uses 2 digits (0-9) then 3 letters (26). Count codes if repetition is allowed, then if digits cannot repeat. Add a restriction: first digit not 0.

Level	Prompt (inside the home strand)
FOUNDATION	Two-stage menu count.
CORE	Multi-stage FCP.
PROFICIENT	FCP with a restriction.
ADVANCED	Justify an overcount.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Tree diagram VIS-M30B-FCP.

MATH30-1-TRIGONOM-02-022

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

Worked example (unique to this hour, this strand, this SO): Compute P(15,4) = n!/(n−r)!. Schedule 4 distinct speakers from 15 where order of speaking matters. Contrast a case with a repeated identical role (preview only if ADVANCED).

Level	Prompt (inside the home strand)
FOUNDATION	List permutations of 3 letters.
CORE	P(n,r) formula.
PROFICIENT	Restrictions (cannot be first).
ADVANCED	Identical items preview.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered-arrangement visual VIS-M30B-PERM.

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(15,4). Choose 4 test kits from 15 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.

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+2)^5 using the binomial theorem (natural exponent). Give the general term and the term containing x^3.

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 021: Adding choices instead of multiplying stages. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 022: Using nCr when order matters. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.
• 30-1 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-LOGICALR-04-012

Official text: Demonstrate an understanding of logarithms and the laws of logarithms

Worked example (unique to this hour, this strand, this SO): Users grow from 60 at annual factor 1.08. Write a log to find years to reach 180. Apply one product or power law in the setup, then a technology check. Not 30-1 exact-only demand.

Level	Prompt (inside the home strand)
FOUNDATION	Meaning of log in a growth sentence.
CORE	One law in a story.
PROFICIENT	Tech check after setup.
ADVANCED	Reasonableness limits.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG in a growth story (not 30-1 exact-only demand).

MATH30-2-RELATION-05-013

Official text: Solve problems that involve exponential equations

Worked example (unique to this hour, this strand, this SO): Solve 1.08^t = 4 using logs or tech after a table guess. State what the solution means for the water-enterprise users and one model limit.

Level	Prompt (inside the home strand)
FOUNDATION	Guess-check table for a^t=k.
CORE	Log or tech solve.
PROFICIENT	Model limits.
ADVANCED	Compare two growth models.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Table-to-equation growth model.

MATH30-2-RELATION-06-014

Official text: Represent data, using exponential and logarithmic functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Given points (0,12), (1,12), (2,13), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 2.

Level	Prompt (inside the home strand)
FOUNDATION	Table to graph.
CORE	Choose exp vs linear.
PROFICIENT	Fit language.
ADVANCED	Residual talk.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + exponential/log model VIS-M30B-DATA.

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 3, amplitude 1.2, period 12 months, max in month 5. 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 012: Applying 30-1 exact-only demands as if they were this SO, or illegal log sums. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 013: Reporting a negative time without checking the model. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 014: Forcing a linear model on clearly exponential data. 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-ALGEBRA-01-009

Official text: Solve problems that involve measures of central tendency, including: • mean • median • mode • weighted mean • trimmed mean

Worked example (unique to this hour, this strand, this SO): Chlorine residual data (mg/L): 1.1, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 2:3. 15% trimmed mean after ordering.

Level	Prompt (inside the home strand)
FOUNDATION	Mean of a small list.
CORE	Mean, median, mode together.
PROFICIENT	Weighted mean.
ADVANCED	Trimmed mean after ordering.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Dot plot with mean/median/mode markers.

MATH30-3-ALGEBRA-02-010

Official text: Analyze and describe percentiles

Worked example (unique to this hour, this strand, this SO): Ordered times (min) to fill a jerry-can: eight values around 50. Find the percentile rank of 45 min and interpret (“percent of observations ≤ this value” in the school’s stated definition).

Level	Prompt (inside the home strand)
FOUNDATION	Percentile as “at or below” in words.
CORE	Percentile from an ordered list.
PROFICIENT	Interpret a percentile rank.
ADVANCED	Contrast percentile vs percent score.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered list or ogive for percentile.

MATH30-3-ALGEBRA-01-011

Official text: Analyze and interpret problems that involve probability

Worked example (unique to this hour, this strand, this SO): A poster: “There is a 90% chance the water is safe.” Critique: 90% of what? Sample size? Given P(fail)=2/100, interpret in words. Do not compute nPr as evidence for this SO.

Level	Prompt (inside the home strand)
FOUNDATION	Likely/unlikely from a given P.
CORE	Interpret a given P in the story.
PROFICIENT	Critique a claim.
ADVANCED	Sample-space talk without nPr.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Probability-statement cards (interpret, do not run 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):

• 30-3 SO 009: Reporting the mean when an outlier makes the median the better centre, without comment. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 010: Treating “80th percentile” as “80% correct on a test.” Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 011: Computing nPr or a 30-1 counting proof as if it were 011. 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-L070.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-021	CORE exit: A lock uses 2 digits (0-9) then 3 letters (26). Count codes if repetition is allowed, then if digits cannot repeat. Add a restriction: first digit not 0. FOUNDATION alternate: Two-stage menu count. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-04-012	CORE exit: Users grow from 60 at annual factor 1.08. Write a log to find years to reach 180. Apply one product or power law in the setup, then a technology check. Not 30-1 exact-only demand. FOUNDATION alternate: Meaning of log in a growth sentence. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-ALGEBRA-01-009	CORE exit: Chlorine residual data (mg/L): 1.1, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 2:3. 15% trimmed mean after ordering. FOUNDATION alternate: Mean of a small list. 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.