Canonical combined lesson MATH30B-L014 · week 3 day 4 · CURRICULUM_BASELINE

MATH30B-L014 - Reflections including y=x; multiply/divide rationals; dilations

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L014
• Calendar: Week 3 Day 4 of 18 weeks × 5 days (lesson 14 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-05-011, 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)

y=x reflection previews inverse language. 30-3 dilation is an enlargement of a shape, not f(−x).

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-05-011	REQUIRED - Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: • x-axis • y-axis • line y = x
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-05-011

Official text: Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: • x-axis • y-axis • line y = x

Worked example (unique to this hour, this strand, this SO): Given y=f(x) through (2,2), find images under y=−f(x), y=f(−x), and y=f⁻¹ related reflection in y=x. Write −f(x−3) as a composition of reflection and translation.

Level	Prompt (inside the home strand)
FOUNDATION	Reflect a point in the x-axis.
CORE	Write y=−f(x) and y=f(−x).
PROFICIENT	Reflection in y=x vs inverse language.
ADVANCED	Compose reflection with translation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Reflections through x-axis, y-axis, and y=x.

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 011: Reflecting in y=x by negating y only. 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/2) + (7/(x+3)) with LCD x(x+3), x≠0, x≠−3. Then multiply (x/7)·((x+2)/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 2 m east and 7 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.06 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-L014.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-05-011	CORE exit: Given y=f(x) through (2,2), find images under y=−f(x), y=f(−x), and y=f⁻¹ related reflection in y=x. Write −f(x−3) as a composition of reflection and translation. FOUNDATION alternate: Reflect a point in the x-axis. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-02-010	CORE exit: Compute (x/2) + (7/(x+3)) with LCD x(x+3), x≠0, x≠−3. Then multiply (x/7)·((x+2)/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 2 m east and 7 m north. Rotate 90° about a labelled corner. Reflect across a site axis. Dilate by scale 1.06 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.