Introduction To Problem Solving

Understand the problem from multiple perspectives to grow your understanding. Apply the four phases: understand, plan, do, and review, by planning a solution, executing it, and reviewing the results.

Apply what you’ve learned to solve the diagonal problem. Find the diagonal of a rectangular figure with known length, width, and height.

Phase one guides you to understand the diagonal problem in a rectangular parallelepiped, using drawing diagrams, recognizing right triangles, and applying the Pythagorean theorem to identify knowns and unknowns.

Execute the plan to derive the space diagonal X from A, B, C, showing X = sqrt(A^2 + B^2 + C^2) using A^2 + B^2 = Y^2.

Examine the solution by double-checking steps and validating the diagonal formula with right triangles. Consider extensions to parallelograms and rooms, and recall the four-phase process: understand, plan, execute, examine.

Solve the handshake problem by applying four steps, counting handshakes in pairs, and embracing motivation and persistence to learn mathematics.

Phase 1 focuses on understanding the handshake problem by examining handshakes among two, three, and four people, laying the groundwork before planning a solution.

Apply a phase 2 problem solving plan by using a counting strategy that builds on the previous handshake count to find the new total as each person joins the room.

The lecture derives the handshake problem, showing how handshakes tally to one plus two plus three, forming triangular numbers, and culminates in the formula n(n-1)/2 for n people.

Examine the handshake solution to verify triangular numbers and their link to Pascal's triangle, then extend the idea by checking results and exploring problem-solving connections.

Apply a four-step problem-solving method: understand, plan, execute, and review; use figures and symbolic representations, including the Pythagorean theorem, to solve problems from two to three dimensions and extend ideas.