⚛️ Integration & Spine — printable binder packet (Physics). Print 8.5×11 portrait. The integration method, the eight-unit anchor map, the applied-math lane, and a cross-year integration score sheet — the spine that ties the whole course together.
← Back to resources Integration guide (web)
▲ Page 1 — The integration spine & method
Bright Minds Physics · Course Pack
Integration & Spine — The Method
Spine
Page 1 of 4

Use the science to investigate a real source, explain the evidence, and communicate a defensible conclusion. The guide supplies the actual reading, data, task, and chosen level before the unit begins.

The integration spine

StrandRequired evidence
History, Reading, WritingUse an approved source in context and a student-authored response. Separate the original evidence from later explanations; do not force a single-hero story.
Geography and ethicsInclude location, social context, or ethical trade-offs where they genuinely support the scientific question.
Elective extensionsChoose additional depth in data, technology, economics, or art. Extensions do not replace the core work.
Quantitative scienceUse the unit's mathematical lane at the agreed level. Supply units, denominators, and model conditions; required science is assessed as science.

Four steps

Separate assessment

Integration is reported separately and cannot lower the science grade or block a science demonstration pass. Science and practical criteria determine that pass.

Use the same approved task in both formats. The web guide explains the source, data, assumptions, student work, and evidence checklist; this packet is its portable summary, not a different assignment.

▲ Page 2 — Eight-unit anchor map
Integration & Spine · The Map
Integration Anchors — All Eight Units
Anchors
Page 2 of 4

Use the web guide's approved unit assignment.

UnitPhysics big ideaIntegration anchor
01 KinematicsMotion depends on a stated frame, initial conditions and a model checked against the actual record.MacTutor: Galileo. Compare a sourced Galileo claim with the motion model; distinguish history from synthetic data. Full task and data.
02 Dynamics & Newton’s LawsThe selected system determines which forces are external; diagrams and components make the model testable.MacTutor: Newton. Use Newton’s source and body diagrams; distinguish a general law from a particular force model. Full task and data.
03 Circular Motion & GravitationAn actual interaction supplies the radial force; circular-state comparisons are not unpowered transfer histories.MacTutor: Newton. Cite gravitational history; compare separate circular states, not an unpowered orbit transfer. Full task and data.
04 Energy & WorkEnergy accounting depends on a system boundary, while signed work and thermal conversion preserve the total ledger.OpenStax: Joule, work and heat. Connect Joule’s work/heat account to the fictional friction ledger; identify what is not measured. Full task and data.
05 Momentum & CollisionsA system changes momentum by net external impulse; internal collisions need not preserve kinetic energy.MacTutor: Newton. Connect historical mechanics to system and external-impulse conditions; do not invent trials. Full task and data.
06 Simple Harmonic MotionA restoring model predicts phase, energy and period only within its stated linear or small-angle regime.MacTutor: Galileo. Compare the sourced timing question with the model; repeat spread alone does not establish accuracy. Full task and data.
07 Torque & Rotational MotionAxis-specific torque, inertia, angular impulse and energy distinguish equilibrium, acceleration, rolling and contraction.MacTutor: Archimedes. Separate historical attribution from our torque data; distinguish equilibrium from rotating models. Full task and data.
08 Fluids & PressurePressure, displaced volume and flow are constrained by force, volume and energy balances with explicit references.MacTutor: Archimedes. Distinguish cited works, later stories and modern buoyancy models; retain evidence and a limitation. Full task and data.
Worked example — Galileo’s inclined plane (Unit 01)

Test constant-acceleration motion released from rest. Measure displacement from the release point and plot it against time squared; the fitted slope represents a/2, not a. State the effects of initial motion, rolling inertia, and losses. Connect the measurement to an approved Galileo excerpt without claiming that a ramp changes gravity itself.

▲ Page 3 — Applied-math lane
Integration & Spine · Quantitative
The Applied-Math Lane — Unit by Unit
Math lane
Page 3 of 4

Math never drives a unit, but physics uses it constantly — always anchored to the reaction or measurement at the bench. Here is the quantitative skill each unit actually uses, done inside the lab context rather than as a parallel curriculum.

UnitApplied math at the agreed level
01 KinematicsSigned slopes/areas and zero-crossing distance; constant-acceleration relations with stated initial velocity; relative frames and perpendicular projectile components.
02 Dynamics & Newton’s LawsMass-weighted center; component force balances, tension and incline acceleration; static inequality versus kinetic friction.
03 Circular Motion & Gravitationv^2/r; inverse-square field; v = sqrt(mu/r), T proportional to r^(3/2); circular L and signed energy ratios.
04 Energy & WorkF d cos(angle), m v^2/2, mgh for constant g, k x^2/2 for a linear spring and average power; require a physically possible final kinetic energy.
05 Momentum & CollisionsSigned force-time areas and vector components; conserve system momentum only with negligible net external impulse; distinguish elastic from sticking energy accounts.
06 Simple Harmonic MotionT = 2pi sqrt(m/k) for a linear spring; T = 2pi sqrt(L/g) for a small-angle pendulum; phase, energy exchange, timing mean and sample SD.
07 Torque & Rotational MotionTorque uses the perpendicular lever arm; fixed-axis I alpha and radian kinematics; rolling energy with sufficient static friction; angular impulse and same-axis L/energy.
08 Fluids & Pressurerho g depth plus reference pressure; piston and buoyancy balances; continuity A v and Bernoulli for steady incompressible flow with negligible viscosity along a streamline, retaining height and no-pump assumptions.
Math in service of the science

Students read the slope off their own motion graph, resolve the force vector inside the inclined-plane lab, and work the pendulum’s period at the bench. The number always means something because it is attached to a result they produced — never a worksheet detached from the physics.

▲ Page 4 — Cross-year integration score sheet
Integration & Spine · Record
Cross-Year Integration Score Sheet
Score sheet
Page 4 of 4

Integration is its own strand. Track each unit’s integration level across the year — Developing, Proficient, or Mastery — separate from the science-mastery rubric. Record the evidence reference and date in the final column.

UnitDevelopingProficientMasteryEvidence / date
01 Kinematics & Motion◯◯◯______
02 Dynamics & Laws◯◯◯______
03 Circular & Gravitation◯◯◯______
04 Energy & Work◯◯◯______
05 Momentum & Collisions◯◯◯______
06 Simple Harmonic Motion◯◯◯______
07 Torque & Rotation◯◯◯______
08 Fluids & Pressure◯◯◯______

Original investigation designs and evidence records and current AP topic mapping with explicit limits. Public practice is not performed-lab evidence or a secure assessment.

What each level means

The goal of the strand

A student who walks through all eight anchors finishes understanding that physics is how humans learned to measure and predict the moving world, and that every formula on the page was once a discovery someone fought for — the version of the subject a student keeps.