BoatLanding Problem
Level: 
10th grade ( Algebra ) 
Problem:^{ } 
Problem setting: A man with a boat at point S at sea wants to get to point Q inland. Point S is distance d1 from the closest point P on the shore, point Q is distance d2 from the closest point T on the shore and point P and T are at a distance of d.
Question: If the man rows with a speed of vr and walks with a speed of vw at what point R should he beach the boat in order to get from point S to point Q in the least possible time?

Goal: 
Utilize and reinforce basic techniques from Algebra 1 in a visually and mathematically understandable process.
Students build their own simulator using the free and extremely versatile and easy to use program: GeoGebra 
Requires: 
Pythagoras' theorem, distanceratetime formula, visually finding the minimum from a graph of a function 
Format: 
Complete resource page 
Author: 
Linda FahlbergStojanovska 
Comments: 
Resource page includes  Readytousesimulator with animated directions, Mathcast for teachers/students to build and understand the simulator, starter geogebra file and Worksheet with Good Questions. 


Equation of Line through y=x^2
Level:
 10th grade (Algebra 2)

Problem:
 Q1. Find the equation of a line through two points on the parabola y=x2.
Q2. Make an interactive geoexercise for your work.
Q3. Can you find simpler formulas for the slope and yintercept?
Q4. Can you prove these formulas?

Goal:
 Utilize and reinforce basic techniques from Algebra 1 in a visually and mathematically understandable process.

When:
 After teaching quadratics.



Format:
 Webpage (html) by Students!

Author:
 Robert Fant

Comments:
 (LFS) Students use basic techniques from understanding coordinate values of a point on a function and then finding the slopeintercept form of a line. Further investigation allows trialanderror testing for a formula. Finally  for your best students  going back to find a proof by actually using factoring of the difference of two squares and drawing conclusions.
At any point, students can design a corresponding interactive geogebra exercise  an amazingly good question (and a wonderful result from these two students)!



Please contribute your thoughts, suggestions and  of course  your good guestions! LFS