Boat-Landing 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, distance-rate-time formula, visually finding the minimum from a graph of a function

Format: Complete resource page
Author: Linda Fahlberg-Stojanovska
Comments: Resource page includes - Ready-to-use-simulator 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 geo-exercise for your work.
Q3. Can you find simpler formulas for the slope and y-intercept?
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 slope-intercept form of a line. Further investigation allows trial-and-error 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


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Page last modified on January 25, 2009, at 12:47 AM