Mathematics 30 (braided classroom)
One combined classroom for Mathematics 30-1, 30-2 and 30-3. Braiding adjusts the shared calendar. It does not shrink any strand to ten sessions.
MATH30B Session 03 — Transformations of graphs and objects
Time: 75 minutes
Labels: PARALLEL WORKSHOP · 30-1 REQUIRED translations · 30-2 data-stretch interpretation (glimpse) · 30-3 REQUIRED 2-D/3-D transformations
Braid class: C
See also: MATH30_PARALLEL_WORKSHOP_PLAN.md
Official outcome codes
| Strand | Codes |
|---|---|
| 30-1 | MATH30-1-TRIGONOM-02-008 REQUIRED |
| 30-2 | MATH30-2-RELATION-07-015 and MATH30-2-RELATION-08-016 glimpse only (not complete) |
| 30-3 | MATH30-3-X-03-004 REQUIRED |
Shared portion (12 min) — ALL STRANDS
Show: (1) a parent graph y=x² shifted, (2) a table whose values were multiplied by 1.2, (3) a rectangle slid and enlarged. Ask: “What moved? What stayed the same?” Do not force one vocabulary onto all three POS texts.
30-1 pathway (40 min) — 30-1 REQUIRED
PATHWAY_30_1: equation of translation.
- Given f, graph y=f(x-3)+2. State h,k in y=f(x-h)+k.
- Match four graphs to equations.
| Level | Task |
|---|---|
| FOUNDATION | Numeric: point (1,4) on f → where on f(x-3) |
| CORE | Write the translated equation from a graph |
| PROFICIENT | Horizontal vs vertical: “why minus 3 moves right” |
| ADVANCED | Two sequential translations as one |
Stretches (009) are not mastery today (D-S03-STRETCH if mentioned).
30-2 pathway (40 min) — data stretch
- Same water table. New column: all values ×1.2 (calibration). Interpret in context.
- Name this as data transformation, not 30-1 stretch SO.
- Glimpse: later we may fit polynomial or sinusoidal models (015/016) — one sentence only.
| Level | Task |
|---|---|
| FOUNDATION | Compute 1.2× column |
| CORE | Sentence: what 1.2 means in the story |
| PROFICIENT | Would a vertical shift +10 mean something different from ×1.2? |
| ADVANCED | Which future model family (linear/poly/sine) might fit a seasonal demand sketch? (preview, ungraded as 016) |
30-3 pathway (40 min) — 30-3 REQUIRED
- On grid: translate, rotate 90°, reflect, dilate a tank footprint (2-D).
- Describe one 3-D move of a crate (slide up a ramp / rotate).
| Level | Task |
|---|---|
| FOUNDATION | Translate 3 right, 2 up; draw image |
| CORE | One rotation and one reflection correctly |
| PROFICIENT | Dilation scale factor 2 from a centre |
| ADVANCED | Composition: translate then dilate; order matters |
Cross-strand exposure
Register D-S03-STRETCH. 30-1 must not tick 009. 30-2 must not tick 008. 30-3 must not tick 008.
Visuals
VIS-M30B-TRANS (parent/image) · VIS-M30B-3DTRANS · data table overlay
Tutor boundaries
Three banks. Parallel workshop mode. No silent swap.
Exit tickets (13 min)
30-1: Point on f is (2,5). Give the image on y=f(x+1)-4 and the equation in h,k language.
30-2: In one sentence, 1.2× all readings means ___. Optional: shift vs stretch in the story.
30-3: Draw the image of a given triangle after a named dilation; state scale factor.
Teacher solutions
30-1 CORE: (2,5) on f → on y=f(x+1)-4: x replaced by x+1 means shift left 1, then down 4 → image (1,1).
30-1 FOUNDATION: For y=f(x-3), point (1,4) on f corresponds to x-3=1 ⇒ x=4, same y=4.
30-2 CORE: Every measurement is 20% higher (calibration or extra shift demand).
30-3 CORE: Image vertices multiplied from centre by k=2.
30-3 ADVANCED: Dilate then translate ≠ translate then dilate in general.
Misconception: “Left/right from the sign in f(x-h) is the same as sliding a cardboard tank.” Kill it in the 5-minute synthesis: function translation vs object translation share a word, not a POS outcome.
Visual task (BEFORE_WORKED_EXAMPLE): Inspect the visual, notice labels, and answer the lesson prompt.
Open table abv-math30b-0093 - MATH30B session 03 table 093
Open full table (lazy). Alt: MATH30B session 03 table 093. Full instructional table for MATH30B.