Bootcamp overlay (weeks 1-2 only): session-10.html. Full course continues through week 18. Overlay does not shrink 30-1/30-2/30-3 to ten outcomes.

Canonical combined lesson MATH30B-L010 · week 2 day 5 · ENHANCED_BOOTCAMP_OVERLAY

MATH30B-L010 - Strand-specific exit tickets and calendar check

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L010
• Calendar: Week 2 Day 5 of 18 weeks × 5 days (lesson 10 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: B
• Bootcamp overlay: sessions/session-10.md (weeks 1-2 start maps; this file is still a full pack lesson with three workshops)
• 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-06-012, MATH30-1-TRIGONOM-07-013, MATH30-1-TRIGONOM-08-014, MATH30-1-TRIGONOM-01-021, MATH30-1-TRIGONOM-02-022, MATH30-2-X-01-001, MATH30-2-LOGICALR-02-004, MATH30-2-LOGICALR-04-006, MATH30-2-LOGICALR-05-007, MATH30-2-LOGICALR-06-008, MATH30-2-LOGICALR-04-012, MATH30-2-RELATION-05-013, MATH30-2-RELATION-06-014, MATH30-2-MATHEMAT-01-017, MATH30-3-X-01-001, MATH30-3-X-03-004, MATH30-3-X-01-005, MATH30-3-X-02-006, MATH30-3-X-03-007, MATH30-3-ALGEBRA-01-008, MATH30-3-ALGEBRA-01-011

Calendar honesty: This is week 2 day 5 of 18×5. It is not “the whole course.” Remaining 30-1 (24), 30-2 (17), and 30-3 (11) specific outcomes continue in weeks 3-18.

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)

Display three remaining-outcome lists. Each learner ticks home strand only. Exposure items stay on the D register. Weeks 1-2 started maps; they did not finish 24+17+11.

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-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-1	MATH30-1-TRIGONOM-07-013	REQUIRED - Demonstrate an understanding of logarithms
30-1	MATH30-1-TRIGONOM-08-014	REQUIRED - Demonstrate an understanding of the product, quotient and power laws of logarithms
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
30-2	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-02-004	REQUIRED - Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events
30-2	MATH30-2-LOGICALR-04-006	REQUIRED - Solve problems that involve the fundamental counting principle
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
30-2	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-MATHEMAT-01-017	REQUIRED - Research and give a presentation on a current event or an area of interest that involves mathematics
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
30-3	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
30-3	MATH30-3-X-03-007	REQUIRED - Critique the viability of small business options by considering: • expenses • sales • profit or loss
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
30-3	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-01-007

Official text: Demonstrate an understanding of operations on, and compositions of, functions

Worked example (unique to this hour, this strand, this SO): f(x)=5x+3, g(x)=x²−3. Compute (f∘g)(8) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−3).

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 3 right and 5 up: y=(x−3)²+5. The point (0,0) maps to (3,5). Match a graphed image to y=f(x+3)−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-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)=5x−3. 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.

MATH30-1-TRIGONOM-07-013

Official text: Demonstrate an understanding of logarithms

Worked example (unique to this hour, this strand, this SO): Rewrite 5^8=390625 in log form. Evaluate log_5(125) exactly. Explain log_51=0 and why log_5(−3) is not real.

Level	Prompt (inside the home strand)
FOUNDATION	log_10 1000.
CORE	Convert b^x=a to log form.
PROFICIENT	Exact log of a power of the base.
ADVANCED	Change-of-base preview.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG: y=b^x and y=log_b x as inverse graphs.

MATH30-1-TRIGONOM-08-014

Official text: Demonstrate an understanding of the product, quotient and power laws of logarithms

Worked example (unique to this hour, this strand, this SO): Expand log_5(x^3 y) for x,y>0: 3 log_5 x + log_5 y. Condense log_5 8 − log_5 3 + 3 log_5 5. Reject the illegal step log u + log v = log(u+v) with a counter-example using 5 and 3.

Level	Prompt (inside the home strand)
FOUNDATION	One law: log(xy).
CORE	Expand or condense mixed laws.
PROFICIENT	Justify each step.
ADVANCED	Counter-example to log(u+v).

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Log-law cards (product, quotient, power) posted after retrieval.

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 5 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(9,4) = n!/(n−r)!. Schedule 4 distinct speakers from 9 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.

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 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.
• 30-1 SO 013: Writing log_b a = b^a, or logging a negative as if it were real. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 014: log u + log v = log(u+v), or bringing an exponent across a sum inside a log. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.

30-2 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 5,3,8. 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-02-004

Official text: Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events

Worked example (unique to this hour, this strand, this SO): P(A)=5/10, P(B)=3/10, P(A∩B)=1/10. Decide mutually exclusive or not. Compute P(A∪B). Contrast a pair of events that cannot occur together.

Level	Prompt (inside the home strand)
FOUNDATION	Exclusive pair example.
CORE	P(A or B) exclusive.
PROFICIENT	Non-exclusive with overlap.
ADVANCED	Justify overlap from a story.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Venn overlay for exclusive vs overlapping events.

MATH30-2-LOGICALR-04-006

Official text: Solve problems that involve the fundamental counting principle

Worked example (unique to this hour, this strand, this SO): Outfit a sample kit: 5 bottle types × 3 labels × 8 cap colours. Count with FCP. Then forbid one labelled combination and recount.

Level	Prompt (inside the home strand)
FOUNDATION	Two-stage FCP.
CORE	Three-stage kit count.
PROFICIENT	Forbidden combo.
ADVANCED	Explain FCP vs listing.

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

MATH30-2-LOGICALR-05-007

Official text: Solve problems that involve permutations

Worked example (unique to this hour, this strand, this SO): Arrange 4 distinct volunteer shifts from 9 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 4 people from 9 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.

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 90 at annual factor 1.08. Write a log to find years to reach 270. 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 (0,15), (1,16), (2,17), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 5.

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-MATHEMAT-01-017

Official text: Research and give a presentation on a current event or an area of interest that involves mathematics

Worked example (unique to this hour, this strand, this SO): Research question (30-2 only): “How does a published article use mathematics in a current water or hygiene issue?” Required product: question, two sources, one model or calculation, and a limits sentence. Do not tick this SO for 30-1 or 30-3.

Level	Prompt (inside the home strand)
FOUNDATION	Write a research question.
CORE	Math in the story named.
PROFICIENT	Sources + model.
ADVANCED	Limits of the model.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Project board: question, sources, model, limits - 30-2 only.

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 004: Using P(A)+P(B) when events overlap. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 006: Listing a few outcomes and treating the list as complete. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.
• 30-2 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 017: A poster with no mathematics, or copying a news claim with no sources. 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 50 mL. State precision, a reasonable uncertainty interval, and whether a ±5 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 5 m east and 3 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).

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 5 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 $18000. Buy: tax 5% + $295 fees. Lease: $295/month for 48 months + $900 due at signing, residual $4500. 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-X-03-007

Official text: Critique the viability of small business options by considering: • expenses • sales • profit or loss

Worked example (unique to this hour, this strand, this SO): Month expenses $1100, sales $1350, so profit/loss = sales − expenses. Second scenario: sales drop 13%. Critique viability (can this hygiene kiosk continue?).

Level	Prompt (inside the home strand)
FOUNDATION	Label expense vs revenue.
CORE	Compute profit or loss.
PROFICIENT	Critique viability.
ADVANCED	Two scenarios.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ledger: expenses, sales, profit or loss.

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, 17, 34, 51. 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.

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)=5/100, 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 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.
• 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.
• 30-3 SO 007: Calling revenue “profit,” or ignoring a category of expense. 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.
• 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.
• 30-1 and 30-3 do strand tasks during 017 hour. Do not mark 017 complete for them.

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-L010.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-007	CORE exit: f(x)=5x+3, g(x)=x²−3. Compute (f∘g)(8) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−3). FOUNDATION alternate: Numeric f(3). 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 5,3,8. 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-01-001	CORE exit: A cylinder scale is marked every 2 mL. A reading looks like 50 mL. State precision, a reasonable uncertainty interval, and whether a ±5 mL tolerance is met. Accuracy still needs a true value - do not call a precise re… 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.