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.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

CCSS.Math.Content.HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Hint: Use right triangle trigonometry, Pythagorean theorem, and/or similarity.

This task asks students to complete real-world and multiple application problems. These problems require students to use multiple concepts to complete the work and analyze constraints to find relationships that allow them to solve the problems.

This task forces students to apply basic skills to higher level applications. This activity forces students to apply more than one concept to completely solve the problem. This problem will likely cause some students to struggle to find different values within the problems. The students may also struggle to recognize the mathematical concepts they should apply to the problem as they are not shown as a single standard triangle.

To assist students with these problems we could rewrite the problem in a scaffold manner so that it hints toward which parts of the triangles can be solved for more easily as the first ones to solve for. This could require breaking the diagrams into parts or just modifying the language in which they are presented.

This task asks students to find errors within work. This is not something students are accustomed to doing and promotes students to consider common errors in solving equations. I would suspect that within the speed dating activity students will struggle to agree on arguments of properties of equality as well as methods for solving equations. For higher level thinkers the KC-46/A-10 airplanes problem could be extended to say that the angle of the arm can be between 20 and 70 degrees and to find the largest and smallest distances in each direction possible.