Proofs & logical reasoning
Two-column and paragraph proofs, postulates, theorems, and how to structure an argument.
Geometry tutoring
Online Geometry Tutor: proofs, shapes, and reasoning.
Geometry asks students to justify their thinking as well as compute answers. Northstar works on that reasoning using a shared digital whiteboard, so diagrams and proofs are drawn and discussed together in real time.
$50 / 60 minutes · No long-term commitments · No required prepaid packages · 12-hour cancellation policy
What we cover
What geometry sessions can cover
Angles, lines & triangles
Parallel lines, triangle congruence and similarity, and the classic angle relationships.
Circles
Arcs, chords, tangents, inscribed angles, and circle equations.
Coordinate geometry
Distance, midpoint, slope, and proving geometric facts using the coordinate plane.
Area, surface area & volume
Two- and three-dimensional measurement, including composite and rotated solids.
Right-triangle trigonometry
The Pythagorean theorem, special right triangles, and sine, cosine, and tangent.
Founded by a mathematics specialist
Northstar was founded by Joshua Lizardi, who holds an M.S. in Applied Mathematics, an M.S. in Data Analytics, a B.S. in Mathematics, and a Graduate Certificate in Applied Statistics, with 9+ years of teaching mathematics, including college and graduate-level instruction.
- Live one-to-one sessions through Zoom
- $50 per 60-minute session
- No long-term commitments or required prepaid packages
- 12-hour cancellation policy
- Flexible scheduling
- Payment through Zelle
Family cancellation policy, effective November 1, 2026
Cancel or reschedule with at least 12 hours' notice without charge. With less notice, the full $50 session fee may be charged. Student no-shows are generally charged the full scheduled fee. If Northstar cancels, you are not charged; any payment collected for that session is refunded or credited as appropriate. Rescheduling depends on mutual availability. Previously agreed individual exceptions are honored, and this policy does not apply to earlier sessions.
Private tutoring is $50 per 60-minute session. Invoices are typically issued after 4 tutoring sessions and paid through Zelle. Late-cancellation or no-show fees may appear on an invoice. No required prepaid packages or long-term commitments.
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