⚛️ 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
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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
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Use the web guide's approved unit assignment.

UnitPhysics big ideaIntegration anchor
01 Kinematics & MotionMotion models require initial conditions and a reference frame.Use Galileo's ramp investigation: from rest at constant acceleration, displacement follows time squared. Position-time slope gives velocity; distance-time slope gives speed.
02 Dynamics & Newton’s LawsA net force changes motion; with no net force, motion never changes at all (inertia).Newton’s Principia and the three laws of motion — and the free-body diagram becomes the physicist’s core tool.
03 Circular Motion & GravitationTurning and orbiting need a center-seeking force; gravity falls off with the square of the distance.Kepler’s planetary data and Newton uniting the heavens with the falling apple; pair with Longitude — one inverse-square law holds the Moon and drops a stone.
04 Energy & WorkWork transfers energy; energy is never lost, only moved from one form into another.Joule, Watt, and the age of the steam engine — measuring energy and power; the horsepower that drove the Industrial Revolution.
05 Momentum & CollisionsA system's momentum is conserved when net external impulse is zero or negligible.Rocketry and recoil: define the system, include expelled mass where appropriate, and justify the conservation model.
06 Simple Harmonic MotionIdeal SHM has a restoring force proportional and opposite to displacement; the simple-pendulum model requires small angles.Galileo, Huygens, and timekeeping; test how the period depends on length, mass, and the model assumptions.
07 Torque & Rotational MotionTorque turns things; a lever trades force for distance about a pivot point.Levers from Archimedes’ “give me a place to stand” to the machine age; pair with The Way Things Work — every machine is a handful of these ideas combined.
08 Fluids & PressurePressure pushes in every direction; buoyancy and flow follow simple, predictable laws.Archimedes in the bath, Pascal on pressure, and Bernoulli on flow — from crowns to hydraulics to the physics of flight.
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
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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 KinematicsConstant acceleration: displacement = initial velocity × time + ½at². From rest, a displacement-versus-time-squared slope is a/2. Position-time slope gives velocity; speed-time area gives distance.
02 Dynamics & Newton’s LawsNet F = ma in an inertial frame for constant mass; vector components and free-body diagrams.
03 Circular Motion & GravitationUniform circular a = v²/r; Newtonian point/spherical-mass gravity; Kepler ratios for the same central mass with negligible orbiting mass.
04 Energy & WorkConstant-force work W = Fd cos(angle); area under a force-component versus displacement graph; kinetic energy and conservation bookkeeping.
05 Momentum & CollisionsVector momentum and net external impulse; impulse from force-time area or average net force times the interval. State when momentum conservation applies.
06 Simple Harmonic MotionLinear spring, constant k and negligible damping: T = 2π√(m/k). Ideal small-angle pendulum: T = 2π√(L/g).
07 Torque & Rotational MotionTorque = force × perpendicular lever arm, or rF sin(angle); balanced moments, mechanical advantage, and rotational analogs of linear laws.
08 Fluids & PressurePressure P = perpendicular F/A; buoyancy from displaced fluid; steady mass continuity (constant density: A1v1 = A2v2). Bernoulli along a streamline assumes steady incompressible flow and negligible viscosity.
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
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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◯◯◯______

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.