Algebra-Based Physics: Modeling Matter, Motion, and Energy

This unit is about building a precise way to talk about motion, position, velocity, acceleration, and vectors, using graphs and real rolling objects, before ever asking why something moves. Think of it as vocabulary-building: every later unit's diagrams and graphs assume your child can read this language fluently.

1. Relative motion and reference frames+

   Given a described scenario (e.g., a person walking on a moving train observed from the platform and from inside the train), state the velocity of the object in each named reference frame and explain why both are correct.

2. Scalar vs. vector quantities+

   Classify given quantities (e.g., 5 m, 5 m north, 30 mph, 30 mph east, -9.8 m/s^2) as scalar or vector based on whether direction is specified.

3. The relationship between slope of a position-time graph and velocity+

   Given a position-time graph, determine the sign and relative magnitude of velocity across different segments by computing slope.

4. The correspondence between position-time and velocity-time graph features+

   Given a position-time graph with curvature, construct the corresponding velocity-time graph, and explain what feature of each graph (slope vs. height) represents velocity in the other.

5. Average vs. instantaneous velocity+

   Distinguish average velocity from instantaneous velocity by computing both from a data table and explaining when they differ.

6. Constant-acceleration kinematics equations+

   Execute the constant-acceleration (kinematics) equations to solve for an unknown quantity (position, velocity, acceleration, or time) given the other three, in one-dimensional motion problems.

7. Selection among constant-acceleration kinematics equations based on known/unknown quantities+

   Given a real-world one-dimensional motion word problem with no explicit labeling of which kinematics equation applies, select and apply the correct equation and justify the choice based on which quantities are known and unknown.

8. Independence of horizontal and vertical components of projectile motion+

   Decompose a projectile's initial velocity vector into independent horizontal and vertical components using right-triangle trigonometry, and explain why horizontal and vertical motion can be analyzed independently.

9. Physical plausibility of graphed motion+

   Given a set of graphed motions (position-time or velocity-time) not seen during instruction, identify which represent physically impossible motion and justify the judgment using vector and rate reasoning rather than formula-matching.

10. Prediction of future motion from experimentally derived velocity-time data+

    Using position-time data collected from a rolling-ball lab, generate a velocity-time graph and use it to predict the ball's position at a future time beyond the collected data, then evaluate the accuracy of that prediction against a real re-run one week later.

This is where 'how something moves' turns into 'why it moves that way.' Your child will spend real time on free-body diagrams, simple sketches of every force acting on an object, and use Newton's three laws to explain motion instead of just describing it. Most of this unit's difficulty is not the math; it's unlearning a very natural but wrong idea that moving things need a constant push to keep going.

1. Free-body diagrams representing forces acting on a single object+

   Given a labeled scenario (object at rest, constant velocity, or accelerating), draw a correct free-body diagram showing all forces acting on the object as vectors with appropriate relative lengths and directions.

2. Newton's first law (inertia) as it applies to motion without a sustaining force+

   Explain, using Newton's first law, why an object in motion with no net force continues at constant velocity rather than slowing down on its own.

3. Newton's first law applied to scenarios engineered to trigger impetus misconceptions+

   Predict the outcome of a force scenario that conflicts with impetus reasoning (e.g., a ball leaving a curved tube) and justify the prediction using Newton's first law rather than surface features of the scenario.

4. The F = ma relationship as a proportional statement linking net force, mass, and acceleration+

   Calculate the acceleration, net force, or mass of an object given the other two quantities using F = ma, including cases with multiple forces that must first be combined into a net force.

5. The proportional (not merely computational) relationship between force, mass, and acceleration+

   Explain why doubling the net force on an object doubles its acceleration but doubling its mass at constant force halves its acceleration, using the proportional structure of F = ma rather than only computing numbers.

6. Newton's third law interaction pairs versus balanced forces acting on one object+

   Identify the Newton's-third-law interaction pair for a given force (e.g., table pushing up on book) and distinguish it from a same-object balanced-force pair that happens to look similar.

7. Static and kinetic friction and the transition between them, evidenced by measured force and acceleration data+

   Given measured data on force applied and acceleration produced while dragging a household object across an untaught surface, determine the coefficient of kinetic friction and evaluate whether the object's behavior is consistent with the static-then-kinetic friction model.

8. The distinction between mass (invariant) and weight (dependent on local gravitational field)+

   Distinguish weight from mass by explaining what would happen to each quantity for the same object on the Moon, and generalize the relationship W = mg to a hypothetical planet with a stated gravitational field strength never discussed in class.

9. Argumentation defending a Newtonian prediction against an explicitly stated impetus-theory counterclaim+

   Construct a written argument, citing specific evidence from a force scenario, defending a prediction that conflicts with a stated impetus-theory justification offered by a hypothetical student.

This unit is about a rule that holds no matter how violent or gentle a collision is: total momentum before equals total momentum after, as long as nothing outside the system interferes. Your child will derive this themselves from Newton's third law, then test it against real, messy collision data, learning to tell the difference between 'the law failed' and 'my measurement was off.'

1. Momentum as the product of mass and velocity+

   Given an object's mass and velocity vector, calculate its momentum and state its direction.

2. Impulse-momentum theorem (J = FΔt = Δp)+

   Given force-vs-time data for an interaction, calculate impulse as the area under the curve and relate it to the resulting change in momentum using the impulse-momentum theorem.

3. Derivation of momentum conservation from Newton's third law+

   Explain why total momentum is conserved in an isolated two-object collision by reasoning from Newton's third law applied over the same time interval.

4. Conservation of momentum applied to real, imperfect experimental data+

   Given before-and-after velocity data for a two-object collision, determine whether total momentum was conserved within reasonable measurement error and identify plausible sources of any discrepancy.

5. The qualitative distinction between elastic and inelastic collisions+

   Distinguish elastic from inelastic collisions by comparing whether total kinetic energy, as well as total momentum, is conserved across the same before/after data set.

6. The isolated-system criterion for conservation of momentum+

   Predict, without calculating, whether momentum will be conserved in a described everyday collision scenario the class has not analyzed (e.g., a shopping cart bumping a wall, a meteor striking a planet, a person jumping off a stationary skateboard), and justify the prediction using the definition of an isolated system.

7. Impulse-momentum reasoning applied to injury-reduction engineering (crumple zones, airbags)+

   Construct a written argument, using impulse-momentum reasoning and no new numerical calculation, for why increasing the time of a collision (e.g., a crumple zone or airbag) reduces the force experienced without changing the total impulse required.

8. System definition and its effect on whether conservation applies+

   Given a novel three-object or multi-stage collision/explosion scenario, determine whether treating different subsets of objects as 'the system' changes the conclusion about momentum conservation.

This unit builds a second way of accounting for what happens in a collision or a moving system, energy, and immediately sets it side by side with momentum from Unit 3 so your child has to tell them apart on purpose. They'll work through kinetic energy, potential energy, conservation of energy in ideal setups, and where energy actually goes in real ones (heat, sound, deformation), ending with power.

1. Work as force times displacement, with angle/component consideration+

   Given a force applied at an angle to displacement, calculate the work done using W = Fd cos(theta), and correctly identify when work done is zero, positive, or negative.

2. Kinetic energy (1/2 mv^2) and gravitational potential energy (mgh)+

   Calculate kinetic energy and gravitational potential energy for an object given mass, velocity, and/or height, and correctly apply units (Joules) throughout.

3. Conservation of mechanical energy and energy dissipation as heat/sound/deformation+

   Explain why mechanical energy is conserved in an idealized frictionless system but not in a real system, identifying where the 'missing' energy goes.

4. The distinction between conditions for momentum conservation (always, isolated system) versus mechanical energy conservation (only without dissipation)+

   For a given collision or mechanical scenario, determine whether momentum, mechanical energy, both, or neither is conserved, and justify the determination using the physical conditions of the event (elastic vs. inelastic, presence of external force, presence of dissipation).

5. Power as rate of energy transfer (P = W/t = ΔE/t)+

   Calculate power as the rate of energy transfer or work done over time, and interpret what a given power rating means in terms of energy transferred per second.

6. Experimental verification of conservation of mechanical energy using height and speed measurements+

   Design and carry out a household-materials investigation (ramp-and-cart or pendulum) to test whether height-related potential energy converts to kinetic energy in a pattern consistent with conservation of mechanical energy, and identify sources of measured energy loss.

7. Application of energy and momentum conservation reasoning to novel multi-stage mechanical systems+

   Given a novel machine or system description not discussed in class (e.g., a roller coaster loop, a bungee jump, a ballistic pendulum), predict and justify which conservation law(s) apply at each stage and identify where energy transformations occur.

8. Quality of justification for conservation-law selection in mechanical scenarios+

   Critique a peer's or sample's written justification of which conservation law applies to a given scenario, identifying whether the justification confuses momentum and energy conservation or omits a necessary condition (e.g., ignoring an external force or dissipation).

9. Real-world energy transformation processes described in technical/informational text+

   Interpret a technical text or video (e.g., on regenerative braking or roller coaster engineering) describing an energy transformation process, and synthesize it with the class's conservation-of-energy model to explain the process in the student's own words.

This unit breaks the idea that 'traveling' always means an object changing location. A wave moves energy through a medium while each point in that medium just oscillates in place and ends up back where it started. Your child will build wave vocabulary, amplitude, wavelength, period, frequency, from watching a rope or slinky before ever seeing the formula v = fλ, then use interference to show that two waves can cross each other and keep going unchanged, which is the real evidence that a wave isn't a moving object.

1. The parts of a transverse wave (amplitude, wavelength, crest, trough)+

   Given a labeled snapshot of a transverse wave, identify and label amplitude, wavelength, crest, and trough.

2. The distinction between transverse and longitudinal wave motion+

   Classify a given wave demonstration (rope shake, slinky push-pull, sound in air, water ripple) as transverse or longitudinal based on the relationship between particle motion and wave travel direction.

3. The wave equation v = fλ and its relationship to T = 1/f+

   Calculate wave speed, frequency, wavelength, or period given the other two quantities using v = fλ and T = 1/f.

4. Wave speed as a property of the medium, independent of amplitude or frequency of the source+

   Explain why wave speed is a property of the medium rather than a property of the disturbance producing the wave, citing a specific medium property (tension, density, temperature) as evidence.

5. Superposition of two overlapping wave pulses+

   Predict the resulting displacement pattern when two wave pulses of given shape and amplitude meet, applying the principle of superposition.

6. Constructive and destructive interference as outcomes of superposition+

   Distinguish constructive from destructive interference in a given two-source scenario and predict resulting amplitude at a point.

7. The difference between a medium particle's local oscillation and the wave's propagation+

   Explain, using the motion of one specific labeled point on a medium over one full period, why that point's motion is not the same as the wave's motion.

8. Superposition reasoning applied to an untaught interference context+

   Given an unfamiliar two-wave scenario (e.g., two speakers producing a quiet spot in a room, described but not previously modeled), infer whether interference is occurring and justify using superposition reasoning.

9. An experimental procedure for measuring wavelength, frequency, and computing wave speed from household materials+

   Design and carry out a measurement procedure using household materials (string/rope or water tray) to determine wavelength and frequency, then calculate and compare predicted vs. measured wave speed.

10. Wave-based energy transport vs. object-based energy transport+

    Compare the mechanism of energy transport by a wave to the mechanism of energy transport by a moving object (from Unit 4), identifying what is conserved and what is transferred in each case.

This unit takes everything just learned about waves and asks: does light follow the same rules? Some things carry over, wavelength, frequency, v=fλ, and one big thing doesn't: light needs no medium at all. Your child will build the electromagnetic spectrum as the same v=fλ relationship at different scales, learn to draw reflection and refraction ray diagrams, and meet the idea of a 'field', a way of describing influence that exists at every point in space, whether or not anything is sitting there to feel it.

1. The wave equation v=fλ applied to electromagnetic waves+

   Given a wave's frequency and the speed of light in vacuum, calculate its wavelength using v=fλ, and vice versa.

2. The electromagnetic spectrum and the energy-frequency relationship+

   Order a set of electromagnetic waves (radio, microwave, infrared, visible, UV, X-ray, gamma) by increasing frequency and explain that photon energy increases with frequency.

3. The law of reflection and ray-diagram notation+

   Construct a ray diagram showing an incident ray, normal line, and reflected ray for a plane mirror, correctly applying the law of reflection.

4. Refraction as a consequence of a wave's speed change at a boundary+

   Predict the qualitative direction a ray bends when passing from a faster to a slower optical medium, using the change-in-speed explanation rather than a 'crowding' account.

5. The set of wave properties that generalize across mechanical and electromagnetic waves versus those that do not+

   Compare light and the mechanical waves studied in Unit 5 (water, rope) to determine which properties (wavelength, frequency, v=fλ relationship, transverse oscillation, need for a medium) transfer to light and which do not, citing evidence from the vacuum-jar contrast and reflection lab data.

6. The field model as a description of influence at every point in space independent of whether a test object occupies that point+

   Explain why a field model (defining a value at every point in space, including points with no object present) resolves the 'action at a distance with nothing there' problem raised by light traveling through a vacuum.

7. Prediction of interference behavior for untaught EM-wave scenarios using the field model+

   Given a novel scenario (a wave phenomenon not discussed in class, e.g., two flashlight beams crossing in a dark room), predict whether the beams will show interference effects like water waves or pass through unaffected, and justify the prediction using the field model rather than memorized examples.

8. Inference of relative wave speed in an unknown medium from observed refraction angle+

   Given an unfamiliar transparent material's approximate refractive behavior (e.g., a novel gemstone bending light more sharply than glass), infer whether light travels faster or slower in that material than in air, without being told the speed directly.

9. Scattering versus specular reflection as distinct light-matter interaction mechanisms+

   Distinguish frequency-dependent scattering (why the sky is blue) from wavelength-independent reflection (why a mirror image is not colored) as two different light-matter interactions, given a written explanation containing both phenomena.

10. The student's own reflection lab data and its relationship to the law of reflection+

    Summarize the household ray-diagram lab procedure and results in a lab report that states the measured angle relationship and the predicted image location, with the claim supported by the specific angle measurements collected.

This unit treats circuits as a new home for two ideas your child already trusts: charge in equals charge out, and energy supplied equals energy dissipated. Voltage gets introduced as energy per unit charge, the field idea from Unit 6 made measurable, rather than as a brand-new mystery quantity. Your child builds real circuits with batteries and bulbs before formalizing Ohm's law, then applies everything to a sealed 'mystery box' they have to figure out using only a multimeter.

1. Conservation of charge in a single-loop series circuit+

   Given a simple series circuit diagram, a student identifies the direction of conventional current flow and states the value of current at any two points in the loop.

2. The proportional relationship V=IR among voltage, current, and resistance+

   Given a circuit diagram with a battery and one resistor, a student calculates current using V=IR when voltage and resistance are given, and calculates the missing quantity when either of the other two is given instead.

3. The structural difference between series and parallel circuit topology and its effect on current and voltage distribution+

   A student compares a series and a parallel circuit built from identical bulbs and batteries and explains why bulb brightness changes differently as bulbs are added to each configuration, referencing current and voltage separately.

4. Electrical power and energy dissipation using the P=IV relationship+

   A student calculates electrical power dissipated by a resistor using P=IV and, separately, energy delivered over a stated time interval, connecting the result to Unit 4's definition of power as energy transfer per unit time.

5. Inferring internal circuit structure from external voltage-current measurements+

   Given measurements of total voltage and current for an unknown combination of two resistors, a student infers whether the resistors are arranged in series or in parallel and estimates their individual resistances.

6. Circuit diagrams and free-body diagrams as structurally analogous modeling abstractions+

   A student draws an analogy between a circuit diagram and a free-body diagram from Unit 2, explaining what each abstracts away from the real system and why both are legitimate models despite the simplification.

7. A measurement-based strategy for characterizing an unknown circuit from external inputs and outputs only+

   Given a sealed mystery box with two external terminals and access only to a multimeter, a student designs a measurement sequence that will determine whether the internal components are in series, parallel, or a combination, and justifies why the sequence is sufficient.

8. The distinction between voltage (energy per charge) added by series batteries and current capacity added by parallel batteries+

   A student explains why doubling the number of identical batteries in series increases the energy delivered per unit charge while doubling identical batteries in parallel does not, without invoking the discredited notion that more batteries simply means more current under all conditions.

No new physics gets taught here. Your child picks (or is assigned) a constrained build, a mousetrap or rubber-band car that has to travel a set distance and stop in a target zone, or a circuit device that has to meet a power/resistance target, and has to figure out, without being told, which tools from the whole year apply. They predict performance on paper first, build it, test it, and use the gap between prediction and reality to figure out whether their physics reasoning or their construction was the problem. They do this twice.

1. Criteria versus constraints in an engineering design brief+

   Given a design brief, the student writes measurable criteria (e.g., stopping distance within a marked zone ±5 cm) and lists physical/material constraints (allowed materials, size, cost) separately from criteria.

2. Model selection among kinematics, force, energy, momentum, and circuit models+

   The student selects which prior-unit model (kinematics, Newton's second law, energy conservation, momentum conservation, or circuit rules) applies to a specific sub-question about their device, and states why the other models do not fit that sub-question.

3. Pre-build quantitative prediction using energy or circuit equations+

   The student calculates a predicted stopping distance (or predicted circuit power output) for their design using energy-conservation or circuit equations before construction, showing all given values and units.

4. Discrepancy between predicted and measured design performance+

   The student compares predicted performance data against measured test data for two design iterations and identifies specific sources of discrepancy (e.g., friction not modeled, energy lost to sound/heat, measurement error).

5. Diagnosis of design failure as reasoning error versus construction error+

   Given their own iteration-1 and iteration-2 data, the student explains whether a design failure was caused by an error in physics reasoning (wrong model or wrong equation) or an error in construction (build did not match the modeled assumptions), citing specific data as evidence.

6. Iterative redesign informed by discrepancy diagnosis+

   The student redesigns one specific component of their device in response to a diagnosed discrepancy and re-predicts performance using the same model, adjusting at least one input variable.

7. Integration of concepts from at least three prior units in a design rationale+

   In their written report, the student cites and correctly applies concepts from at least three prior units (e.g., kinematics prediction, energy-loss accounting, circuit power constraint) to justify their design's physics rationale.

8. Qualitative prediction of design outcome under an unrehearsed parameter change+

   During the oral defense, the student answers a novel 'what if we changed X' question (e.g., doubled the mass, halved the resistance) by reasoning from the underlying model rather than recalling a rehearsed answer, predicting the qualitative direction of the change in outcome.

9. Equation forms for KE, PE, F=ma, and P=IV from Units 2, 4, and 7+

   The student recalls the equation forms for kinetic energy, gravitational potential energy, Newton's second law, and electrical power without reference, in the context of a mixed retrieval warm-up.