MTTC Earth/Space Science (020) cheat sheet

Scientific method cycle: observation → question → hypothesis → prediction → experiment → analysis → revision; hypotheses must be testable and falsifiable, and results can support or refute but never prove a hypothesis.

Controlled experiment: one independent variable manipulated, dependent variable measured, all other variables held constant; a control group receives no treatment or a placebo to isolate the variable's effect.

Accuracy is closeness to the true value; precision is repeatability of measurements. Random error reduces precision and averages out with repetition; systematic error shifts all readings the same way and biases accuracy.

Significant figures: nonzero digits count; captive zeros between nonzero digits count; leading zeros never count; trailing zeros count only with a decimal point. In multiplication/division, report the fewest sig figs; in addition/subtraction, report the fewest decimal places.

Density = mass ÷ volume (D = m/V), typically g/cm³ or g/mL; density is an intensive property independent of sample size and useful for identifying minerals and substances.

Percent error = |measured − accepted| ÷ accepted × 100%. Slope on a linear graph equals the rate of change of the dependent variable per unit of the independent variable.

Theory vs. law: a theory is a well-tested explanatory framework (plate tectonics, evolution); a law is a concise description of a consistent relationship (Newton's laws, superposition). Neither becomes the other.

Metric prefixes: kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹). Convert with dimensional analysis so unwanted units cancel.

Earth's interior layers by composition: crust (oceanic basaltic, ~5–10 km; continental granitic, ~30–70 km), mantle (ultramafic silicate rock), and core (iron-nickel). By physical state: lithosphere (rigid plates), asthenosphere (plastic, partially molten), mesosphere, outer core (liquid, generates the magnetic field by dynamo action), inner core (solid due to pressure).

Plate boundaries: divergent (mid-ocean ridges, seafloor spreading, normal faults), convergent (subduction zones, trenches, volcanic arcs, reverse/thrust faults; continental collision builds mountains), and transform (strike-slip faults such as the San Andreas). Hotspots form intraplate island chains like Hawaii.

Rock cycle: igneous rocks crystallize from magma (intrusive = coarse-grained, extrusive = fine-grained); sedimentary rocks form by weathering, erosion, deposition, compaction, and cementation; metamorphic rocks recrystallize under heat and pressure (foliated vs. nonfoliated).

Relative dating principles: superposition (youngest on top), original horizontality, lateral continuity, cross-cutting relationships (a feature cutting another is younger), inclusions, and faunal succession. Absolute dating uses radioactive decay, e.g., half-life of carbon-14 ≈ 5,730 years, uranium-lead for ancient rocks.

Hydrologic cycle fluxes: evaporation and transpiration → condensation → precipitation → runoff and infiltration → groundwater flow. Watershed divides separate drainage basins; porosity is void space, permeability is connectivity of pores.

Carbon cycle: photosynthesis removes CO₂; respiration, decomposition, and combustion release it. Reservoirs include the atmosphere, oceans (largest exchangeable reservoir), biomass, soils, and fossil fuels. Ocean acidification follows CO₂ dissolution forming carbonic acid.

Rock and nutrient cycles: nitrogen fixation by bacteria and lightning converts N₂ to usable forms; nitrification, assimilation, denitrification, and ammonification complete the cycle. Phosphorus cycles mainly through rock weathering with no significant atmospheric phase.

Climate vs. weather: climate is long-term statistical behavior (30-year normals); weather is short-term atmospheric state. Greenhouse gases (H₂O, CO₂, CH₄, N₂O) absorb outgoing infrared radiation; albedo and cloud cover affect energy balance.

Earthquakes and volcanoes: focus is the subsurface rupture point, epicenter the surface point above it; P waves (compressional, fastest, travel through solids and liquids) precede S waves (shear, only solids) and surface waves. Magnitude (Richter/moment) measures energy; intensity (Mercalli) measures observed effects.

Kepler's laws: (1) orbits are ellipses with the Sun at one focus; (2) equal areas are swept in equal times, so orbital speed is greatest at perihelion; (3) P² ∝ a³ when P is in years and a in astronomical units. Newton's law of gravitation explains these as a balance of gravity and inertia.

Solar system structure: terrestrial planets (Mercury, Venus, Earth, Mars) are small, dense, rocky, and close to the Sun; Jovian planets (Jupiter, Saturn, Uranus, Neptune) are large, low-density, gas/ice giants with rings and many moons. Asteroids lie mainly between Mars and Jupiter; the Kuiper Belt and Oort Cloud supply comets.

Earth's seasons result from axial tilt (~23.5°) and the resulting change in solar angle and day length-not from distance to the Sun. Solstices mark maximum tilt toward/away; equinoxes have equal day and night. The Moon's phases arise from its orbital geometry relative to the Sun and Earth.

Eclipses: solar eclipse = Moon between Earth and Sun, occurs only at new moon; lunar eclipse = Earth between Sun and Moon, occurs only at full moon. They are rare because the Moon's orbit is inclined about 5° to the ecliptic, so alignment occurs only near nodes.

Tides: the Moon's gravity produces two bulges (near and far sides), giving semidiurnal tides; spring tides occur at new and full moons when Sun and Moon align; neap tides at quarter moons when they are at right angles.

Electromagnetic spectrum order (long to short wavelength): radio, microwave, infrared, visible (red→violet), ultraviolet, X-ray, gamma ray. Wien's law: hotter objects peak at shorter wavelengths. Doppler shift reveals motion: redshift = receding, blueshift = approaching.

Hertzsprung-Russell diagram: stars plotted by luminosity vs. temperature/spectral class; main sequence runs diagonally, red giants upper right, white dwarfs lower left. Star life cycle depends on mass: nebula → protostar → main sequence → red giant or supergiant → planetary nebula/white dwarf (low mass) or supernova/neutron star/black hole (high mass).

Big Bang evidence: cosmic microwave background radiation, Hubble's law (recessional velocity proportional to distance, v = H₀d), and the abundance of light elements. The solar nebula theory explains the Sun and planets forming from a rotating cloud of gas and dust.

NGSS three dimensions: Disciplinary Core Ideas (content), Science and Engineering Practices (inquiry behaviors), and Crosscutting Concepts (patterns, cause and effect, scale, systems, energy and matter, structure and function, stability and change). Effective instruction integrates all three.

5E instructional model: Engage, Explore, Explain, Elaborate, Evaluate. Exploration with materials precedes formal explanation so students build concepts from evidence rather than from lecture alone.

Inquiry levels: structured (teacher provides question and procedure), guided (teacher provides question, students design procedure), and open (students generate question and procedure). Lab safety must be established before any hands-on activity.

Formative assessment is ongoing and diagnostic (exit tickets, concept maps, questioning, whiteboards); summative assessment evaluates learning at the end of a unit (tests, projects, performance tasks). Rubrics and exemplars make expectations transparent.

Common misconceptions to target: seasons caused by Earth's distance from the Sun; phases caused by Earth's shadow; heavier objects falling faster; groundwater existing as underground lakes; the Sun being a planet or burning by combustion.

Assessment item quality: align each item to a specific standard, avoid ambiguous or double-negative stems, use plausible distractors based on known misconceptions, and ensure one clearly best answer. Interpretation should reference validity and reliability.

Data literacy instruction: students construct and interpret graphs, identify variables, distinguish correlation from causation, and evaluate sources. Error analysis and repeated trials build understanding of measurement uncertainty.

Differentiation and equity: use multiple representations (models, diagrams, simulations, kinesthetic activities), scaffold language for multilingual learners, and connect content to local phenomena and students' lived experience.