1. Class Greeting

2. Objective: The student will be able to solve Cross Topic Mathematical Problems.

3. What’s the problem?

4. You are an electronic engineer…

5. You are designing a Printed Circuit Board (PCB)
PCBs are used in electronics to connect electrical components using conductive pathways Since the wires are not insulated, they must not cross

6. This is an example of a Planarity Problem

7. Another example
Utilities companies (gas, water, electricity) trying to lay pipes that do not cross each other…

8. Planarity Problems A graph is planar if it can be drawn in a plane
so that no two edges meet
(except at a vertex)

10. You have designed the circuit that you want, but some of the wires cross

11. Redraw this PCB in such a way that no wires cross.
*** Notice you do not have to connect points A and C; C and F; and D and F. A B C D E F
*** You cannot move points A, B, C, D, E and F.

12. A B C D E F
Hint: A, B, C, D, E and F are components. Add more points to your circuit that are not components that allow you to connect your components in multiple steps using more than one line from one component to the next.

13. Solution: A B D F E C

14. Lesson Summary:
Objective: The student will be able to solve Cross Topic Mathematical Problems.

15. Preview of the Next Lesson:
Objective: The student will be able to solve Cross Topic Mathematical Problems.

16. Mathematical Skills and Processes - HW 1
Homework
Mathematical Skills and Processes - HW 1