NY Next Generation Math NY-8.G.8

Math8th GradeUnderstand and apply the Pythagorean Theorem.

The Standard

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students use the Pythagorean Theorem to find the distance between two coordinate points. They treat horizontal and vertical changes as perpendicular leg lengths.
What Mastery Looks Like: The student computes coordinate differences, draws the related right triangle, and finds its hypotenuse. The student gives an exact radical or appropriate decimal distance.
Common Misconceptions: Students may add coordinate differences directly or keep negative changes as negative lengths. They may confuse coordinate distance with slope.
How to Assess It: Ask students to find the distance between (-2, 1) and (4, 9) by drawing a right triangle and showing the Pythagorean calculation.

Lesson moves

Plot two points on grid paper and draw horizontal and vertical legs connecting them through a right triangle.
Ask students why coordinate differences become leg lengths before using the theorem.
Play Distance Match by pairing point pairs with right-triangle calculations.
Find straight-line distances between locations on a coordinate map.

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