Lesson plan

10. Use the Pythagorean Theorem to find the distance between points in 3D space (A)

teaches Common Core State Standards CCSS.Math.Content.8.G.B.7 http://corestandards.org/Math/Content/8/G/B/7
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8
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Lesson objective: Apply the Pythagorean Theorem to distance in 3D space.

This lesson provides an opportunity for students to apply their knowledge and understanding of calculating distance to a real-life situation. Students are asked to find the diagonal space in gift boxes to see if gifts with certain lengths will fit inside.

Key Concept students will use: 

  • We can use the relationships shown in the Pythagorean Theorem to solve problems given particular pieces of information about the problem.

Skills students will use:

  • Use rational approximations of irrational numbers to compare the size of irrational numbers. (8.NS.A.2)
  • 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.B.7)
  • Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.B.8)

​Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they develop a strategy to find distance in three dimensions, then apply that strategy to see if the gifts will fit in the boxes.

Key vocabulary: 

  • 3-dimensional space
  • diagonal
  • Pythagorean Theorem