Canonical combined lesson MATH30B-L013 · week 3 day 3 · CURRICULUM_BASELINE

MATH30B-L013 - Combined translations and stretches; add/subtract rationals; reflections

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L013
• Calendar: Week 3 Day 3 of 18 weeks × 5 days (lesson 13 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-04-010, MATH30-2-LOGICALR-02-010, MATH30-3-X-03-004

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)

Clock is shared. Prompts are not. Combined function transforms are not 30-3 object reflections.

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-04-010	REQUIRED - Apply translations and stretches to the graphs and equations of functions
30-2	MATH30-2-LOGICALR-02-010	REQUIRED - Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials)
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

30-1 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-04-010

Official text: Apply translations and stretches to the graphs and equations of functions

Worked example (unique to this hour, this strand, this SO): Apply, in named order: horizontal stretch by 1/6, then translation 2 left and 8 down, to f(x)=|x|. Write the final equation and sketch parent and image.

Level	Prompt (inside the home strand)
FOUNDATION	Apply one translation and one stretch numerically.
CORE	Write the combined equation.
PROFICIENT	Graph parent and image.
ADVANCED	Reverse-order contrast.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Combined transform visual: translate then stretch (order named).

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 010: Applying stretch and translation in an unnamed order and claiming uniqueness. 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-02-010

Official text: Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Compute (x/8) + (6/(x+2)) with LCD x(x+2), x≠0, x≠−2. Then multiply (x/6)·((x+8)/x) and state restrictions.

Level	Prompt (inside the home strand)
FOUNDATION	Multiply two monomial rationals.
CORE	Add with LCD (binomials).
PROFICIENT	Complex fraction light.
ADVANCED	All restrictions after operations.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Common-denominator layout for rational operations.

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 010: Adding numerators and denominators separately. 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-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 8 m east and 6 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.05 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).

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 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.

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-L013.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-04-010	CORE exit: Apply, in named order: horizontal stretch by 1/6, then translation 2 left and 8 down, to f(x)=|x|. Write the final equation and sketch parent and image. FOUNDATION alternate: Apply one translation and one stretch numerically. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-02-010	CORE exit: Compute (x/8) + (6/(x+2)) with LCD x(x+2), x≠0, x≠−2. Then multiply (x/6)·((x+8)/x) and state restrictions. FOUNDATION alternate: Multiply two monomial rationals. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-03-004	CORE exit: Translate a 2-D tank rectangle 8 m east and 6 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.05 from a centre; state the inverse scale as 1/k. FOUNDATION alternate: Name T/R/Rf/D on a picture. 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.