Math practice · first semester · both grades

Data or it didn't happen.

One core sheet per unit, plus occasional focused add-ons. No lab required — just a pencil, a brain, and the numbers the phenomenon is hiding. Print one, show your work on the dotted lines, and check yourself against the key at the bottom.

7th grade: 7 sheets 8th grade: 9 sheets answer keys included print-friendly

How these work: each sheet rides its unit's phenomenon — the beetle's dash, the green statue, the willow that ate the air. Parts A–D build from warm-up to the good stuff. The answer key lives in the folded section at the bottom of each sheet (and prints on its own page). Second-semester sheets arrive as the units do. Every worksheet Part now has a Learn How doorway with a worked example, an interactive model, and a self-check before students tackle the practice.

7th grade · chapter one

First semester — foundations in motion

From the scientific method to the solar system: rates, integers, equations, and scale.

#03 · Scientific method ⇄

Data or It Didn't Happen

Expected vs. observed on a coin, mean vs. median against a gust, three graphs caught lying.

expected vs. observedmean & mediangraph literacy Open the sheet →
#03 · Graphing Studio · add-on

Graph It. Read It. Defend It.

Choose the graph, build a bar or line graph, and read a scatter plot without confusing correlation for cause.

bar / line / scatteraxes + scaledata claims Open the graphing sheet →
#03 · Graphing word problems · add-on

Eight stories. Eight graphs.

Read each story and type into its table on the computer. Draw six graphs on grid paper and two pie graphs on the 50-dot circles.

bar / line / scatterpie graphstables + percent Open the 8 interactive tables →
#04 · Measurement & graphing ⇄

Honest Numbers

Time Trial statistics, the percent-error leaderboard, conversion reflexes, the estimated digit.

statisticspercent errorconversions Open the sheet →
#05 · Motion

Can a Graph Tell You Who Won?

Interval speeds from the beetle dash, unit-rate comparisons, sprint splits, story-to-graph.

unit ratesd–t graphsaverages Open the sheet →
#06 · Forces

Tug-of-War Arithmetic

Signed-integer net force, friendly-number F = ma, and your weight on four worlds.

integersnet forceF = ma Open the sheet →
#07 · Newton's laws

F = ma, No Appeals

The triangle drill, the inverse-mass table, stopping distance by the square, crumple-zone math.

equationsinverse patternsnonlinear Open the sheet →
#08 · Energy

The Energy Ledger

The v² discovery, PE = mgh on the beetle shelf, 100-joule bookkeeping, the First Hill Rule.

squaresPE = mghconservation Open the sheet →
#09 · Solar system & light

Marble Math

Earth as a marble, scientific notation in the wild, light-time tables, the Jupiter volume trap.

scale modelsscientific notationunit rates Open the sheet →

8th grade · chapter one

First semester — matter & chemistry

From atoms to reactions: exponents, percents, piecewise graphs, and the algebra of balancing.

#05 · Matter: it's everything

Thirty Cuts

The 2ⁿ halving table to the atom, powers of ten, mystery metals by density, atom ratios.

exponentspowers of tendensity Open the sheet →
#06 · Matter is made of particles

The Smell Race

Diffusion rates, the 500 m/s paradox, coin-flip random walks, hot vs. cold.

ratesestimationprobability Open the sheet →
#07 · States of matter

Reading the Curve

Heating-curve plateaus, below-zero integers, the price of melting vs. boiling, the mirror curve.

piecewise graphsnegativesrate of change Open the sheet →
#08 · Compounds, elements & mixtures

89% Oxygen

Percent composition by mass, cereal-label iron math, the two-way sort, the air pie.

percentratiostwo-way tables Open the sheet →
#09 · Meet the periodic table

Mendeleev's Report Card

Percent error on a never-seen element, the periodic wave as a scatter plot, weighted isotopes.

percent errorscatter patternsweighted averages Open the sheet →
#10 · Physical & chemical changes

The Green Skin

Fermi-estimate the statue's copper, rust's mass gain, where the candle goes, evidence scorecards.

estimationpercent changedensity Open the sheet →
#11 · Intro to chemical reactions

Nothing Is Lost

Missing-mass equations, the steel-wool ledger, balancing as algebra, the campfire budget.

solving for xconservationbalancing Open the sheet →
#12 · Synthetic materials ⇄

The Materials Tournament

Strength-per-gram brackets, the plastic curve, recycling percents, the bottle scaling chain.

ratiosfold-changescaling Open the sheet →
#13 · Chemistry in nature

The Tree That Ate Air

Van Helmont's 1,240× ratio, the photosynthesis atom inventory, calorie math, a tree in kg of CO₂.

conversionsratiosatom accounting Open the sheet →