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Geometry Lesson

Tower Grids & Fiber Routes: From Segment Addition to Distance & Midpoint on the Coordinate Plane

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High SchoolBTC Vertical Whiteboard FramingHSG.CO.A.1 / HSG.GPE.B.6 / HSG.GPE.B.750 min
Learning Objective

Students will apply the Segment Addition Postulate to find unknown lengths algebraically, derive and apply the coordinate distance formula from the Pythagorean theorem, and use the midpoint formula — including solving for a missing endpoint — in the context of fiber-optic cable routing between telecom towers.

Lesson Overview

Students progress from 1D segment addition on a number line to 2D coordinate distance and midpoint formulas, using a telecom tower placement context. Groups work at vertical non-permanent surfaces (VNPS) in a BTC flow, changing one variable at a time across 7 thin-sliced tasks.

Materials

  • Vertical whiteboards or chart paper mounted on walls
  • Dry-erase markers (multiple colors per group)
  • Erasers or paper towels
  • Random grouping cards (pre-made)
  • Printed coordinate grids (integer bounds -20 to 20) for consolidation notes
  • Four-Quadrant note sheets (one per student)

Scaffolded Task Progression

1Task 1
Tower A, Tower B, and Tower C are placed in a straight line along a service road (treat the road as a number line). Tower A is at position , Tower C is at position . Tower B is between A and C, and . Find the position of Tower B and the lengths and .
2Task 2
Now Tower B's position is unknown. Tower A is at position and Tower C is at position on the number line. Tower B is between them, and . Find the position of Tower B.

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