Geometry

Seventh grade geometry sits in a strange spot. Most of what students do this year — angle reasoning, scale work, pi, volume — they’ve seen pieces of before. What’s new is the expectation that they reason about why it works, not just plug numbers into a formula. That’s the gap this 9-week program is built to close, and it starts by teaching the concept before drilling the practice.

Every week opens with a short passage that explains the idea in plain language, followed by a worked example that walks through a typical problem step by step. Only then do the worksheets begin. So when a student sees “a triangle has sides of 3, 5, and 9 cm — can it exist?” they’re not guessing — they’ve already read about the triangle inequality theorem and seen it applied to a similar problem.

What the Weeks Cover

Week 1 starts with angle pairs — supplementary, complementary, vertical, adjacent — and the missing-angle problems built on top of them. The reasoning that vertical angles must be equal (because each one is 180° minus the same neighbor angle) sets the tone for the whole year: geometry rules are not arbitrary.

Weeks 2 and 3 cover scale drawings. Reading them first (W2): converting between drawing and real-world measurements on maps, blueprints, and models, and recognizing that area changes by the square of the scale factor — a classic test trap. Then creating them (W3): picking a scale that fits on the page, drawing enlargements and reductions, computing scale factors between figures.

Week 4 is the most hands-on. Students use ruler and protractor (have both ready) to construct triangles from SSS, SAS, and ASA conditions, and figure out when a set of conditions produces exactly one triangle, infinitely many, or none at all. The triangle inequality theorem comes in as the gatekeeper — sides have to actually be able to close into a triangle in the first place.

Weeks 5 and 6 are the circle weeks. Pi and circumference first, with a teaching passage that explains why C/d is the same constant for every circle (it’s worth doing the string-and-can demo once at home). Then area: A = πr², working backward from area to find radius, semicircles and quarter circles, and composite shapes where students break a figure into pieces they recognize.

Week 7 covers cross-sections of 3D figures — predicting the 2D shape that results when a plane slices through a prism, cylinder, pyramid, or cone. Week 8 moves to volume and surface area of prisms, including the V = Bh generalization that covers both rectangular and triangular prisms with one formula.

Week 9 is the capstone. Problems no longer hand students one skill at a time; instead they layer scale reasoning, circle formulas, and volume into a single multi-step question — the format that shows up on end-of-year state assessments.

How It Works

Five worksheets per week, full answer keys with worked solutions for word problems, one passage and one worked example per week before the practice begins. Aligned to Common Core 7.G standards across the full geometry strand. Works as daily practice alongside any math curriculum, or as a self-contained unit for homeschool families.