Students will find the distance between two cities on a U.S. map using the Pythagorean Theorem. Labeled map and worksheet included: Distances Between Cities.
Math Commerical – IBM
Quick 30 second IBM ad on the uses of math:
Linear Inequalities – Online Activities
For the Classroom
Inequalities Demo
See how slope, y-intercept and inequality symbol changes the shaded area of a linear inequality. Mr. Kibbe’s Linear Inequalities.
Google Earth and Volume and Surface Area
Here is another project by realworldmath.org. Real World Math projects integrate Google Earth with various math topics, this one on Volume and Surface Area. Below is a very brief excerpt from their site, but you need to visit the site itself for the full project:
Volume and Surface Area – Real World Math
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Objectives
•Find the volume of geometric solids using a formula
•Find the surface area of geometric solids using a formula
Lesson Description
Volume and Surface Area problems appear three dimensionally in this collection of Google Earth locations. With the “3D Buildings” mode in Google Earth’s “Layers” selected, the students will be able to view and pan around these solids. Each place-mark icon includes the necessary dimensions students need to complete the Geometric Solids Worksheet.
Functions – Online Activities
For the Classroom
Function Machine
This is one of the nicest function machine interactive boards that I have come across: Function machine.
End of Year Review (Algebra) – Online Activities
For the classroom
Algebra Bits
Jeopardy 1
Jeopardy 2
Very nice Jeopardy Power Point. However, it doesn’t seem to keep track of which questions have already been used, but maybe it was because I wasn’t using IE.
For the classroom or Students
Jefferson Lab
Virginia State SOL
Multiple choice, Virginia SOL question bank.
Pendulum Dance
This is an absolutely amazing video. Fifteen pendulums, each with a period of one swing more per minute than the previous pendulum, produces magnificent designs from snakes to spirals to near chaos and back to a swinging line once again. What would be interesting is to see the graphs of each position in time of all the pendulums – this would have to be 3 dimensional, with pendulum number, distance from center and time. Or with a sinusoidal equation. I’m wondering what to do with this in regards to middle school students, and what could be seen on a two dimensional graph. I can’t think of anything. Here’s the video Krulwich Wonders: A Pendulum Dance
Olympics and Systems of Equations
Using data from the Olympic games, students can compare the performances of men vs. women. Men have outperformed women, but the data suggests that women are rapidly improving and improving at a faster rate than men. Using scatterplots, regression and solving systems, students will predict if and when women will outperform men. This is originally supposed to be an Algebra 2 project, here is the original Algebra 2 version. But Algebra 1 students should be able complete the project once they have learned how to solve systems of equations. Here is the modified version: Olympic Regression for Algebra 1 students.
All the World’s Water – Volume of a Sphere Project
This picture inspires a wonderful volume project, and can easily have scientific notation and proportions integrated into the project as well.
(1) Have students calculate the volume of the Earth.
(2) Research the amount of water that’s on the Earth (about 326 million trillion gallons according to science.howstuffworks.com)
(3) Have students calculate what size sphere would hold that volume of water
(4) Either with a computer drawing program or just on a piece of paper, have students use proportions to show the size of the Earth compared to the sphere that would hold the world’s water.
** The same thing can be done with air (atmosphere), though I couldn’t find a specific number as to the exact volume of air. But considering the atmosphere extends (very roughly) out to about 300 km (there’s more atmosphere, I’m sure, but the density of the molecules would be very negligible), simply take the radius of the Earth (6,378.1 km) to figure out the volume of the Earth, then draw another sphere around the Earth that has a radius of 6,678.1 (radius of Earth + 300) and calculate the volume of that sphere, and the difference would be the volume of the atmosphere … albeit a very rough estimation. Students shouldn’t be told this, of course!
Here’s a site with more information about the Amount of Water in/on/above the Earth.
Teaching Slope
If there’s one thing I’ve figured out about teaching the basics of slope, it’s that there’s not one single method that will reach every single student. (This is true of any topic). However, it is still possible to reach every student since different methods work for different students. Here’s a few slope memory tricks that I’ve used when remediating students, if they just don’t get it after being shown the traditional ways:
Mr. Slope Guy
This was actually the favorite method of my below-level high school students. On every assessment relating to linear equations, the first thing most students did was sketch this on the top page as a guide. This isn’t my creation, but I can’t remember where and when I came across this to give the proper credit.
Writing “slope”
Since we write from left to write, people inherently will write the word “slope” from left to write, and this gives students a visual. Without moving the paper around, write the word “slope” on the line and if you find yourself writing upwards, it’s positive. Writing down is negative. Straight across is zero. And since there’s not really a place to write the word “slope” on a vertical line (without moving the paper), that’s undefined.
Tracing
This only works for distinguishing positive from negative slopes, but simply tracing the line with a fingertip from left to right lets students physically feel the direction of the line as to whether it’s going up or down. I prefer that students write the word “slope” as mentioned above since writing is inherently left to right and tracing is not, but some students prefer this method.
Verbal
One test asked “what is the slope of a horizontal line,” and a student told me that she couldn’t decide whether to write zero or undefined until she remembered that I had told them horiZontal has “z” for zero. Whatever works…
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Concordia University
