Mathematical Architects · Pacing Guide

Pre-Calculus Pacing

Module by module across the Beta four-day calendar — ~144 instructional days, mapped to Texas TEKS §111.42 and grading periods. A two-semester bridge into Calculus.

31GP1 Days

Aug 19 – Oct 8

36GP2 Days

Oct 12 – Dec 17

36GP3 Days

Jan 5 – Mar 4

40GP4 Days

Mar 15 – May 20

Teaching Approach · Foundation-First, Gradual Release Pre-Calculus is the bridge year into Calculus — it has no state EOC, so the goal is calculus-readiness, not a test. Inside that arc I teach foundation-first: activate the Algebra II / Geometry skill the new topic leans on, work several examples together before independent practice, then release gradually. Function fluency in the fall (M1–M2) is the floor that trigonometry, analytic geometry, and the limit preview all stand on, so the pacing leaves room to slow down, check for understanding, and review before each unit test.

1 · Activate prior knowledge 2 · Guided worked examples 3 · Gradual release 4 · Check & review before the test

How This Pacing Was Built

Pre-Calculus has no publisher-fixed day count and no state EOC — the prerequisites are Algebra I, Geometry, and Algebra II, and the year paces toward calculus-readiness across two semesters. The Beta four-day calendar provides approximately 144 instructional days (GP1 31 + GP2 36 + GP3 36 + GP4 40, per the 2026–2027 calendar). Days are weighted toward trigonometry — Modules 3–4 together hold 62 days, the structural heart of the course. Module totals: M1 24 · M2 30 · M3 32 · M4 30 · M5 28 = 144. Day spans below are cumulative across the year. The process standards P.1A–P.1G are embedded in every module, every day.

Core Load-bearing for Calculus — heavily revisited Supporting Reinforces / extends a core strand No state EOC for Pre-Calculus — every assessment is teacher-built and locally assessed.

Topic	Days	Cumulative	TEKS §111.42	Emphasis	Target GP
Module 1 — Functions: Composition, Inverses & Symmetry 24 days Module resources Visual Lab 🧱 Foundations
Function Attributes, Domain & Transformations	13	1–13	P.1A, P.2A, P.2B, P.2C	Core	GP1
Composition, Inverses & Symmetry	11	14–24	P.2D, P.2E, P.1C, P.1F	Core	GP1
Module 2 — Analyzing Function Families 30 days Module resources Visual Lab 🧱 Foundations
Power, Polynomial & Rational Functions	16	25–40	P.2F, P.2G, P.2H, P.2I, P.2J	Core	GP1 → GP2
Exponential, Logarithmic & Piecewise Families	14	41–54	P.2K, P.2L, P.2M, P.2N	Supporting	GP2
Module 3 — Trigonometric Functions & the Unit Circle 32 days Module resources Visual Lab 🧱 Foundations
Angles, Radian Measure & the Unit Circle	15	55–69	P.4A, P.4B, P.2O	Core	GP2
Graphing Trig Functions & Inverses	17	70–86	P.2P, P.4C, P.4E	Core	GP3
Module 4 — Trig Identities, Equations, Laws & Vectors 30 days Module resources Visual Lab 🧱 Foundations
Identities & Trigonometric Equations	17	87–103	P.5A, P.5B, P.5C	Core	GP3
Laws of Sines & Cosines, Vectors	13	104–116	P.4D, P.5D, P.3H	Supporting	GP3 → GP4
Module 5 — Analytic Geometry, Polar & Series: The Edge of Calculus 28 days Module resources Visual Lab 🧱 Foundations
Conics, Parametric & Polar Coordinates	16	117–132	P.3A–P.3E, P.3I	Core	GP4
Sequences, Series & the Limit / Rate Preview	12	133–144	P.5B, P.5C, P.5D	Core	GP4

Emphasis (Core vs. Supporting) reflects how load-bearing each topic is for first-semester Calculus, not a state classification — because there is no EOC, the local assessment plan determines final weighting. Grading-period targets are planning guides — actual transitions shift slightly with the live calendar (make-up Fridays, breaks). One first-day scholar session (Aug 18) sits outside the four grading-period windows, so the four GP budgets sum to 143 while the year totals 144 instructional days.

Module 5 · The Edge of Calculus The year closes by looking over the edge. After series, the final days preview the two ideas Calculus is built on — the limit and the instantaneous rate of change. Scholars estimate a slope by letting a secant line approach a tangent, watching the average rate \[ \frac{f(x+h)-f(x)}{h} \quad\text{as}\quad h \to 0 \] settle toward a single number. No formal differentiation — just the intuition that \( \lim_{h\to 0} \) turns a family of secants into one tangent. That is the doorway into Calculus M1 (Limits & Continuity) and M2 (Derivatives), and it is exactly where this course is meant to leave them.

Assessment Calendar

Daily Do Now, mid-module checkpoints, end-of-module unit tests, and a mid-year benchmark — mapped to the calendar. Pre-Calculus has no state EOC, so every assessment is teacher-built and locally assessed, weighted toward the function and trigonometry fluency that Calculus depends on.

Daily

Do Now · warm-up

A 3–5 minute spiral warm-up opens every class — one item on yesterday's skill, one on a prior core standard (often an Algebra II prerequisite). It doubles as the daily check-for-understanding and flags re-teach needs early.

Mid-module

Checkpoint · low-stakes

A short formative checkpoint at each module's midpoint (between topics). Lightly weighted — it tells us whether to keep moving or add a review-game day before the unit test.

End of module

Unit Test · graded

A cumulative unit test closes each module, scheduled so the day before is a deliberate review-game / re-teach day — honoring the “more time before assessments” request.

Module · Unit Test	Recommended test window	Mid-module checkpoint	Grading period
M1 · Functions: Composition, Inverses & Symmetry	Week of Oct 5–8	~Sep 21 (after Attributes & Transformations)	GP1 · before Oct 8 close
M2 · Analyzing Function Families	Week of Nov 30–Dec 3	~Nov 9 (after Power & Rational)	GP1→GP2 · test in GP2
Benchmark · Mid-year diagnostic	Week of Feb 1–4	Cumulative M1–M3 (functions + trig foundations)	GP3 · local diagnostic
M3 · Trig Functions & the Unit Circle	Week of Jan 26–29	~Dec 14 (after Unit Circle)	GP2→GP3 · test in GP3
M4 · Identities, Equations, Laws & Vectors	Week of Mar 22–25	~Mar 1 (after Identities & Equations)	GP3→GP4 · test in GP4
M5 · Analytic Geometry, Polar & Series	Week of May 17–20	~May 3 (after Conics & Polar)	GP4 · closes the year

Test windows land in the last days of each module so the prior session can be a review-game / re-teach day. The mid-year benchmark (early Feb) is a cumulative diagnostic over functions and the trig foundations; M3's longer trigonometry span means its unit test sits just inside GP3. The final M5 window deliberately follows the limit / rate-of-change preview, leaving scholars pointed straight at Calculus. All windows are planning targets — shift them a few days with make-up Fridays and breaks on the live calendar.

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