Montana Math MT.8.G.7
The Standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangle problems, including problems in context in two and three dimensions. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the side opposite the right angle and use squared side lengths to find a missing length. For a box, they find a face diagonal first, then use it to find a diagonal through the box.
What Mastery Looks Like
- Given legs of 6 cm and 8 cm, a student finds a 10 cm diagonal. Given a 13 cm diagonal and a 5 cm leg, they find the other leg is 12 cm. They can show the two right triangles needed to find a corner-to-corner distance through a box.
Common Misconceptions
- Students may add side lengths instead of squaring them. They may treat the longest given side as the hypotenuse when the unknown side is opposite the right angle. For a box, they may leave out one dimension.
How to Assess It
- Exit ticket: A box is 3 cm long, 4 cm wide, and 12 cm high. Draw and label the two right triangles needed to find its corner-to-corner distance, then calculate it.
Lesson moves
Ways to Teach It
Measure a shoebox's length, width, and height; calculate its base diagonal, then its corner-to-corner diagonal.
A student says the diagonal of a 5 cm by 12 cm rectangle is 17 cm; write two sentences checking the claim.
Give pairs right-triangle cards marked 5, 12, x or 9, 15, x; have them circle the hypotenuse before solving.
On a scaled map of the Confederated Salish and Kootenai Tribes' reservation, draw 3 cm and 4 cm perpendicular legs; calculate distance using the scale.
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