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?
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| 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. |
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Equation of Line through y=x^2
| Level:
| 10th grade (Algebra 2)
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| 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?
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| Goal:
| Utilize and reinforce basic techniques from Algebra 1 in a visually and mathematically understandable process.
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| When:
| After teaching quadratics.
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| Format:
| Webpage (html) by Students!
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| Author:
| Robert Fant
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| 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)!
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Please contribute your thoughts, suggestions and - of course - your good guestions! LFS
