Grade 7 · secular · Common Core-aligned
This is the year math stops being "follow the recipe" and starts being "here's the rule, and here's why it's true." Your kid will spend the fall pinning down what "proportional" really means and learning to compute with negative numbers, fractions, and decimals the same way. In winter they turn that into algebra — expressions and equations they can solve and explain. In spring they point all of it at geometry (scale drawings, angles, circles, 3D shapes) and finish with probability and sampling, which is really just ratios and rates wearing a different hat. By June they should be able to look at a table, a graph, or a word problem and immediately ask "is this proportional?" and "what's actually equal to what here?" — and answer both.
The whole year, in plain English. Tap any unit to see every skill inside, nothing is hidden.
This unit is about one question asked five different ways: is the ratio between two quantities always the same? Your kid learns to check that using fraction unit rates, tables, graphs, and equations, then applies it to real percent problems like tax, tip, and discount.
Given a rate involving fractional quantities (e.g. 3/4 cup per 2/3 hour), compute the unit rate.
Given a table of paired values, determine the constant of proportionality k by computing y/x for each row.
Given two representations of the same context (a table and a graph, or a table and a verbal description) that are NOT both provided directly, determine whether the underlying relationship is proportional by checking whether the ratio y/x is constant across all given pairs, not just the first pair or the visual shape of the graph.
Explain why a straight-line graph that does not pass through the origin represents a non-proportional relationship, using the constant-ratio definition rather than the visual shape alone.
Write the equation y = kx for a proportional relationship given a real-world context, a table, or a graph, identifying k correctly in each case.
Interpret the point (1, r) on a graph of a proportional relationship as showing the unit rate r.
Given a multi-step context involving tax, tip, markup, or discount, solve for the final amount, correctly identifying the original/base amount before calculating the percent.
Given a two-step scenario where an item is marked up then discounted (or discounted then marked up) by the same percent, determine whether the final price is the same in both orders and justify the answer using the structure of percent change, without having been shown this specific comparison during instruction.
Given a completely unfamiliar real-world dataset (e.g. a utility bill with a flat fee plus a per-unit rate, presented as a table), determine whether it is proportional and, if not, identify what would need to change about the pricing structure to make it proportional.
This unit extends everything your kid knows about adding, subtracting, multiplying, and dividing to negative numbers, fractions, and decimals together. Every new move gets shown first as a movement on a number line before it becomes symbols. It ends with problems that deliberately mix all four operations, which will feel harder than anything before it — that's expected.
Given a point on a number line, state its additive inverse and explain why the two points are the same distance from zero.
Compute the sum of two rational numbers with the same or different signs using a number-line movement model.
Explain why subtracting a rational number is equivalent to adding its additive inverse, using two contrasted number-line diagrams.
Derive the rule for the sign of a product of two rational numbers by extending the pattern of repeated addition to negative factors.
Apply the derived sign rules to compute products and quotients of rational numbers including fractions and decimals.
Convert a fraction to its decimal form, determining whether the result terminates or repeats, using long division.
Solve a multi-step word problem involving all four operations on rational numbers in a context not used during instruction (e.g., elevation change across multiple unrelated stops, or combined temperature and time-of-day shifts).
Justify a chosen sign rule (for addition, subtraction, multiplication, or division) by constructing an original number-line diagram for a rational-number pair the student has not seen used with that rule before.
Distinguish problems that require finding a difference in distance (absolute value of a difference) from problems that require finding a signed change, given a set of contextual word problems.
Here arithmetic becomes algebra. Your kid learns that an equation is a statement that two things are equal, and every legal move has to keep both sides equal — like a balance scale. They simplify expressions first, then solve increasingly complex equations, then translate word problems into equations, then do the same with inequalities.
Given a linear expression with rational coefficients, combine like terms correctly, including terms with negative coefficients.
Apply the distributive property to expand an expression like -3(2x - 5), including when the multiplier is negative.
Explain why two differently-written expressions, one expanded and one factored, represent the same quantity for every value of the variable.
Solve a two-step equation with rational coefficients by undoing operations in reverse order, recording each step as a balance move on both sides.
Solve multi-step equations that require distributing and combining like terms before undoing operations, including equations with the variable on both sides.
Given a verbal description of a real situation, decide which quantity is unknown and write an equation of the form px + q = r that models it.
Compare an arithmetic (guess-check-reason) solution and an algebraic (equation) solution to the same word problem and judge which reveals the general relationship more clearly.
Solve a one-variable inequality of form px + q > r or px + q < r, correctly reversing the inequality symbol when multiplying or dividing by a negative number.
Graph the solution set of a one-variable inequality on a number line and explain what the shading and endpoint mean about which numbers satisfy it.
Given a completely unfamiliar multi-step scenario with extraneous numeric information, decide whether it calls for an equation or an inequality, then solve it and justify the choice.
Given a real-world balance scenario never used in instruction (e.g., a chemistry mixture or a multi-currency exchange), construct and solve an equation or inequality that models it and explain why the balance principle still applies.
This is Unit 1's proportional relationships applied to shapes: a scale factor is just the constant of proportionality, applied to every length in a figure at once. The second half shifts to building triangles by hand with a compass, straightedge, and protractor, and figuring out when the given information locks in exactly one triangle.
Given a scale drawing and its stated scale, compute the actual length of a labeled segment.
Given a scale drawing, compute the actual area of a region by first finding actual side lengths, then applying an area formula.
Explain why area scales by the square of the linear scale factor, using a grid-square count as evidence.
Distinguish a true scaled copy of a figure from a figure that has been distorted (e.g., stretched in one direction, or altered by addition rather than multiplication).
Given a scale drawing at one scale, produce an accurate redrawing of the same figure at a specified different scale.
Given two maps or drawings of the same unfamiliar region at different, unstated scales with no shared labeled reference length, determine the scale relationship between them using only measured distances.
Construct a triangle from three given side lengths using a compass and straightedge, and determine whether the construction is possible.
Given two side lengths and the included angle (SAS), or two angles and the included side (ASA), construct the triangle with a protractor and ruler and state whether the given conditions determine a unique triangle.
Given an unfamiliar set of three conditions on a triangle (a mix of side and angle constraints, including an SSA case not previously modeled), determine whether zero, one, or infinitely many triangles satisfy them, and justify the conclusion.
Given a scale-drawing redrawing task and a triangle-construction task presented in mixed, unlabeled order, select and apply the correct procedure for each.
Four angle relationships — complementary, supplementary, vertical, adjacent — become sources of equations to solve, using the same balance idea from Unit 3. Then area work extends from grade-6 polygons to circles and composite shapes, ending with surface area of solids made from triangles and quadrilaterals.
Given a diagram of two angles labeled as complementary or supplementary, write an equation using a variable for the unknown angle and solve it.
Given an unlabeled diagram of two lines crossing, identify which angle pairs are vertical and which are adjacent, and state the relationship (equal vs. sums to 180) that applies to each.
Given a multi-angle diagram with several lines crossing at one point and only one angle measure provided, write and solve a chain of equations to find every unknown angle, citing the specific relationship used for each step.
Explain why the sum of the interior angles of any triangle is 180 degrees, using a torn-corner or parallel-line demonstration, rather than stating the rule as a memorized fact.
Calculate the area and circumference of a circle given its radius or diameter, choosing the correct formula for what is asked.
Given a composite figure combining a circle with triangles and/or quadrilaterals, decompose it into named component shapes two different valid ways and compute the total area from either decomposition.
Calculate the surface area of a three-dimensional figure composed of triangular and quadrilateral faces by identifying and summing the area of each distinct face.
Given a real-world scenario not resembling any diagram used in instruction (e.g. the angle between clock hands, or a compass bearing problem), determine which angle relationship applies and solve for the unknown angle.
Given a novel composite solid combining a scaled copy of a shape from Unit 4 with new triangular faces, and no formula provided, determine a strategy to find its total surface area and justify why that strategy is valid for any solid built the same way.
This unit treats every geometry formula as a description of a physical action — going around a shape, wrapping it, or filling it up. It moves from circles (reconnecting pi to Unit 1's constant-ratio idea) through surface area built from actual paper nets, to volume with fractional dimensions, and closes with why volume scales by the cube of the scale factor for similar solids.
Given the radius or diameter of a circle, calculate its circumference and area using the correct formula for each.
Explain why pi is the same fixed ratio for every circle, regardless of size, by connecting it to the constant-of-proportionality idea from Unit 1.
Given a net of a rectangular prism or triangular prism, calculate its total surface area by finding and summing the area of each face.
Given a net of a pyramid, calculate its total surface area, distinguishing the base from the lateral (triangular) faces.
Given a rectangular prism with fractional edge lengths, calculate its volume by multiplying length, width, and height.
Given two solids with equal volume but different dimensions, determine whether their surface areas are also equal and justify the conclusion by relating it to how each formula depends on the arrangement of faces.
Given the volume of a rectangular prism and two of its three dimensions, solve an equation to find the missing dimension.
Given the surface area of a rectangular prism and all but one dimension, solve an equation to find the missing dimension.
Given two similar solids and their scale factor, predict the ratio of their volumes and explain why it is the cube of the scale factor rather than the scale factor itself.
Given a real-world composite figure (e.g., a grain silo as cylinder-plus-cone-like shape simplified to prism-plus-pyramid), plan and carry out a multi-step solution combining surface area, volume, and equation-solving from this unit.
Probability here is just a proportion — a long-run rate of favorable outcomes over all outcomes — which is why it leans hard on Unit 1's rate language and Unit 2's fractions. It moves from single-event probability to experimental probability (and why it doesn't match theory with small samples) to compound events using sample spaces and tree diagrams.
Given a context with a stated ratio of outcomes, state the theoretical probability of a specified outcome as a fraction, decimal, and percent.
Explain, using a specific numeric example from a class simulation, why an experimental probability computed from 20 trials can differ from the theoretical probability of the same event.
Develop a uniform or non-uniform probability model for a given chance process by assigning probabilities to each outcome so they sum to 1.
Compare a theoretical probability model against long-run relative frequencies collected from repeated trials of a chance process, and judge whether the model is a good fit.
Construct a complete sample space for a two-stage compound event using a tree diagram or organized list.
Calculate the probability of a compound event from its sample space by counting favorable outcomes over total outcomes.
Differentiate between a compound-event context that requires multiplying stage probabilities and one that has been miscombined by adding them.
Design and carry out a simulation (using coins, number cubes, spinners, or a random-number generator) to estimate the probability of a compound event described in an unfamiliar real-world scenario.
Given two proposed probability models for the same context, judge which better matches collected experimental data and justify the choice using the size of the sample.
The year's closing unit. Instead of computing a known probability, your kid now uses sample data to make a claim about a whole population — and learns that a sample is only as trustworthy as the process that produced it. They generate multiple samples, watch estimates bounce around, and use that bounce to judge whether two groups are really different.
Given a description of a sampling method (e.g. survey students exiting the gym after a game, vs. survey every 20th name on the school roster), classify it as likely to produce a representative sample or a biased sample, and name which group is over- or under-represented.
State, from memory, the definitions of population, sample, and random sample using a given scenario.
Given one random sample's data (e.g. proportion of tagged fish, mean bag weight), compute a point estimate of the population characteristic and explain what the estimate does and does not tell you about the exact population value.
Given a set of 8-10 simulated sample estimates from the same population, describe the spread of the estimates and explain why no single sample estimate should be treated as the exact population value.
Generate multiple random samples of a stated size from a given population (physical or simulated), record each sample's estimate, and use the collection of estimates to state a plausible range for the population characteristic.
Given two numerical data sets (e.g. heights of two grade levels) with similar variability, compare their distributions by expressing the difference in means as a multiple of the mean absolute deviation (MAD).
Given two dot plots with visibly overlapping distributions, judge informally whether the groups differ meaningfully, and justify the judgment using both center and spread.
Design a complete sampling plan for a stated real-world question (define population, sampling method, sample size, and what will be measured) for a context never used during instruction.
Given a claim in a news-style headline about a survey result (e.g. "9 out of 10 dentists agree"), critique the sampling method implied by the claim and propose a specific improvement.
From the parent guide
This is the year math stops being "follow the recipe" and starts being "here's the rule, and here's why it's true." Your kid will spend the fall pinning down what "proportional" really means and learning to compute with negative numbers, fractions, and decimals the same way. In winter they turn that into algebra — expressions and equations they can solve and explain. In spring they point all of it at geometry (scale drawings, angles, circles, 3D shapes) and finish with probability and sampling, which is really just ratios and rates wearing a different hat. By June they should be able to look at a table, a graph, or a word problem and immediately ask "is this proportional?" and "what's actually equal to what here?" — and answer both.
Unit 1 · what to expect
This unit is about one question asked five different ways: is the ratio between two quantities always the same? Your kid learns to check that using fraction unit rates, tables, graphs, and equations, then applies it to real percent problems like tax, tip, and discount.
The full guide covers all 8 units: where kids get stuck, what to say, and how to tell it's working. Included with the course.
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