Florida B.E.S.T. MA.8.GR.1.2
The Standard
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the horizontal and vertical changes between two plotted points. They treat those changes as legs of a right triangle and use a² + b² = c² to find the direct distance.
What Mastery Looks Like
- A student can find the horizontal and vertical changes and use them correctly in the Pythagorean Theorem. They can give an exact radical or reasonable decimal, include units, and explain why the distance is the hypotenuse.
Common Misconceptions
- Students may add the coordinate changes instead of squaring them, or forget to take the square root. They may mishandle negative differences, round too early, or report the squared distance.
How to Assess It
- Give students the points (-2, 3) and (4, -5). Ask them to sketch the right triangle and find the exact distance and a decimal approximation.
Lesson moves
Ways to Teach It
Plot two taped points on a floor grid, measure both coordinate changes, then calculate and verify the direct distance with a tape measure.
Explain why horizontal and vertical changes form the legs of a right triangle when finding the distance between two plotted points.
Play Coordinate Distance Match by pairing point cards with triangle-leg cards and distance cards, then justify each match.
Use a city grid map to compare the straight-line distance between two landmarks with the walking route along blocks.
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Related Standards
- MA.912.GR.3.4
Use coordinate geometry to solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
- MA.912.T.1.2
Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
- MA.8.GR.1.1
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
- MA.6.GR.1.3
Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle.
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