NY Next Generation Math NY-8.G.7
The Standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students apply the Pythagorean Theorem to find unknown side lengths in right triangles. They solve mathematical and real-world problems in two and three dimensions.
What Mastery Looks Like
- The student identifies the hypotenuse, writes the correct equation, and solves for an unknown leg or hypotenuse. The answer includes suitable units and a reasonable approximation when needed.
Common Misconceptions
- Students may add side lengths instead of their squares or solve for the wrong side. They may use the theorem on triangles that are not right triangles.
How to Assess It
- Ask students to find an unknown leg of a right triangle with hypotenuse 13 and leg 5. Then have them find the space diagonal of a 3-by-4-by-12 rectangular prism by using the theorem twice.
Lesson moves
Ways to Teach It
Build right triangles on grid boards and measure sides before checking the theorem.
Ask students how the equation changes when the unknown is a leg instead of the hypotenuse.
Play Right Triangle Solve with cards showing two side lengths and a marked right angle.
Find a ladder length needed to reach a wall height from a stated ground distance.
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Printable NY-8.G.7 Worksheet
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Related Standards
- NY-8.G.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
- NY-7.G.6
Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids.
- NY-3.MD.8.a
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths or finding one unknown side ...
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