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EdEx - Good Questions for Algebra
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=x2
| Level: |
10th grade (Algebra 1) |
| 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. |
| Format: |
Webpage (html) by Students! |
| Author: |
Educator Portfolio - 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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EdEx - Educator to Educator Exchange
Please contribute your thoughts, suggestions and - of course - your good guestions! LFS
Ed2Ed-Math247 (Links to all Ed2Ed links on this site.)
Comments (1)
Dani said
at 12:29 pm on Jul 10, 2008
I just watched these two examples and they are inspiring. I plan to use them with my students in the Fall and hopefully develop my own intuition. The web page by Robert's students shows how we can empower students to do exploration/research.
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