Mississippi Math FA.G.36

MathGrades 9–12Geometry (G) Geometry

The Standard

Explain and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (8.G.7)

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What This Standard Means

What Students Need to Do: Students find missing sides of right triangles using the lengths of the other two sides. They explain why the squares of those lengths are related, then use two right triangles to find a diagonal inside a box.
What Mastery Looks Like: A student identifies the right angle and the longest side before calculating. They can find a missing leg or diagonal, show their steps, and give a length in the correct units.
Common Misconceptions: Students may use the rule on a triangle with no right angle, or add side lengths instead of their squares. When finding a missing leg, some add the squares instead of subtracting. In a box, they may mistake a face diagonal for the diagonal through the box.
How to Assess It: Draw a rectangular box measuring 3 cm by 4 cm by 12 cm. Ask students to find its 5 cm base diagonal, then its 13 cm diagonal through the box, and mark both right triangles.

Lesson moves

Ways to Teach It

Give pairs a shoebox and string to measure its edges, face diagonal, and diagonal through the box, then compare measurements with calculations.
Ask students to sketch and explain the two right triangles needed to find a box's corner-to-corner distance.
Hand out triangle and box cards; partners race to mark the right angle, find the missing length, and check each other's work.
Ask whether a 125 cm dowel fits inside a 30 cm by 40 cm by 120 cm shipping box; students calculate its longest diagonal.

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