The plan

How to read this

Moves, not items. The 45 questions collapse into 14 moves. A move is one thing the student has to be able to do; the test asks it two to six ways. Teach the move, then let the items show the shape repeating.

The order is the order things feed each other. Reasoning feeds Triangles feeds Polygons/Circles/Solids. When a late item is missed, the plan says which earlier move to go back to, and that is where you go — not to more of the same item.

Every session has the same five-part shape (at the bottom of this page) and every problem has the same three doors: a nudge that is a question, the bare answer, and the work one step at a time. The tutor layer on each session page carries the answer key, what each wrong choice means, and the check for that item.

Tomorrow — Day 1 · The grammar

Conditional statements: hypothesis and conclusion, the converse and its relatives, what follows from what, and one symbolic argument. It is the root of the whole test — every theorem is an if-then — and it needs no arithmetic, so the first hour is about thinking rather than about calculation. It also carries a three-question placement so the month starts from the right place.

• 0:00Placement. #2 (slope of a parallel line), #24 (right-triangle sides), #32 (cone scaled ×3). One per category. Nothing explained, nothing marked. The tutor layer records what each wrong answer means.
• 0:08The map. Three parts, why the order matters, why we start at the root.
• 0:12If, then. Hypothesis and conclusion; the converse; a counterexample (5, 5, 8); inverse and contrapositive; which relative agrees with the original. Three inline checks.
• 0:20Worked in five moves — #8, the converse. Fully worked: duplicate, transcribe, rearrange, collapse, meaning.
• 0:32Faded — #1, the Venn diagram. Same control in pictures; the middle two moves are left for the student to fill.
• 0:42Bare — #6, the logical conclusion. Then a solution that goes wrong: the student finds the step that breaks.
• 0:50Build the argument — #3, the drag-and-drop. p → ~q, q, ∴ ~p.
• 0:57Close. What the hour meant, in one rule. Seed: say the converse of the parallel-lines theorem out loud.

Open the Day 1 console. Press Start when the hour begins, T for your layer, Notes to take notes as you go, Summary at the end to copy the record.

Next week

Three sessions finish the first category and open the second. If you meet fewer than three times, take them in order and let the fourth week absorb the slip; the order matters more than the calendar.

The four-week form

Three sessions a week is the assumption; the shape survives two. Each week ends with the student re-doing the placement's three items plus three new ones, so the month has four measurements, not one.

Fading runs across the month as well as within a session: Week 1 problems are worked in full; by Week 3 the five moves are a strip the student fills in themselves; by Week 4 the strip is gone.

How the moves feed each other

Mother on the left, child on the right. When a child is weak, the plan sends you to the mother.

The check that comes before the answer (the ke of each move) is on the session page, in the tutor layer, one line per item. The commonest across the whole test: a reversed statement is a new statement; true is not follows; the largest side is the hypotenuse; what dimension is this quantity?; a model's number cannot equal the real-world number.

Item → move map

All forty-five, with the key. 001 Reasoning, Lines, and Transformations · 002 Triangles · 003 Polygons, Circles, and Three-Dimensional Figures.

The key column is the Virginia Department of Education's released answer key, not ours. One caution for #30: the figure's (2x + 4)° label sits close to two different angles; the key's answer of 12 treats it as the angle between the diagonal and the vertical side, so the two acute angles of the right triangle are complementary (62 + 28 = 90). Read that one with the student rather than at them.

The shape of one session

Every hour has the same five parts, and every problem the same five moves. The names are the ones this project already uses; the geometry is the first thing outside chemistry to be put through them, and the fit is being watched.

• 0–8Measure first. Two or three questions, no teaching, no marking. The tutor layer records. (Day 1's is the placement; later days re-use a miss from the last session.)
• 8–12Where we are on the map. One minute on what feeds today and what today feeds.
• 12–45The move, faded. One item worked fully in five moves — duplicate the figure, transcribe it to symbols, rearrange, collapse to the one relation that decides it, say what the number means. Then one item with the middle missing. Then one bare.
• 45–55A solution that goes wrong. A wrong worked answer, and the student finds the step that breaks. (Booth et al.: explaining a wrong step teaches more than being shown the right one.)
• 55–60Close and seed. The hour in one rule; the next hour's theorem said aloud before leaving.

Three doors under every problem, all closed until opened: Nudge (a question, never the answer), Check my answer (the answer alone), The work, one step at a time. The tutor layer (press T on a session page) adds the key, what each wrong choice means, the check for that item, where to go if it is missed, and a mark satisfied button for when it was said aloud and typing it would only slow things down.