CCSS.Math.Content.8.G.B.8
The standard
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to use the Pythagorean Theorem to find the straight-line distance between two points on a coordinate grid. They should see the horizontal and vertical changes as the legs of a right triangle, then calculate the hypotenuse as the distance.
Mastery looks like choosing the correct x-change and y-change, squaring them, adding them, and taking the square root. Students often mix up signs, subtract coordinates in the wrong order, or stop at the squared distance instead of finding the square root.
Ways to teach it
- Have students plot two points on graph paper, draw the right triangle, count the legs, then calculate the diagonal distance.
- Ask students to explain why the distance from A to B is the same as from B to A, even if the subtractions look different.
- Give three point pairs and ask students to find which two are exactly 13 units apart.
- Use a map grid of the school and ask students to find the straight-line distance from the gym to the cafeteria.
Plan a lesson for CCSS.Math.Content.8.G.B.8
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Related standards
- CCSS.Math.Content.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to fi...
- CCSS.Math.Content.8.G.B
Understand and apply the Pythagorean Theorem.
- CCSS.Math.Content.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- CCSS.Math.Content.HSG-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.