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…

Google Earth and Complex Area

Here is a project by realworldmath.org. Real World Math integrates Google Earth with various math topics, this one on Complex Area. Below is a very brief excerpt from their site, but you need to visit the site itself for the full project:

Complex Area Problems – Real World Math

 

Objectives
•Measure distances
•Find the area of complex polygons
•Solve word problems involving rates

Lesson Description
This lesson consists of two parts. The first requires students to find the area of a complex shape using … the area formulas for a parallelogram and triangle.

The second part … Students will need to be able to solve rate problems with a proportion for this section.

Data and Graphs – Online Activities

For the classroom

Circle Graphs
Thirteen Ed Online
Here is a ready-made online worksheet for circle graphs. Work can be done on a piece of paper, but students need to use computers to access the online graph and article.

Graphing Review
Bitesize: Frequency diagrams.
Fun video/interactive review lesson. Frequency chart, circle graph, line graph and pictogram. Do the 10 question quiz to finish.

Graphing Review 2
Bitesize: Handling data
Line graphs, bar graphs, constructing circle graphs. 10 question quiz includes scatterplots and pictograms.
Interactive lesson.

Linear Equations – Online Activities

For the classroom

Graphing Point-Slope
IXL
Given a point and slope, graph the line. Simple, clean graphing program good for student work on the board.

Identifying Slope-Intercept
Recognizing Slope and Y-Intercept
Identify slope and y-intercept from an equation. All in slope-intercept form. Good for a mini checkpoint quiz.

Slope Investigations
Move the points around to see how the slope and graph of a line is affected. Mr. Kibbe’s Slope Demo

Slope and y-intercept Investigations
See how slope and y-intercept affect the graph of a line. Mr. Kibbe’s Slope and y-intercept demo.

Writing slope-intercept Equations
Kind of like Line Gems (for students), in that students write the equations that will go through the most points, but I like the cleaner look and feel of this one: Mr. Kibbe’s Slope Game.

For students

Writing slope-intercept equations
Line Gems
Write the equation of the line that will go through the most gems.

Writing slope-intercept equations
Algebra vs. the Cockroach
Write the equation of the line that will exterminate the roaches.

Probability and Statistics – Online Activities

For the classroom

Measures of Central Tendency
Bitesize: Mean, Median, Mode and Range.
A fun video/interactive review lesson. Finish with the 10 question quiz.

Transformations – Online Activities

For the classroom

Congruence, Translations, Reflections & Rotations
BBC – Bitesize: Introduction to Transformations Interactive lesson. Click on Activities for lesson. Do the 5 question “Test” when done.

The Transformation Game

I came across this Transformations board game. I haven’t used this in any of my classes, but I thought I’d go ahead and post it here so I would remember it later, and in case anyone else wanted to try it out.

If you use it, let me know how it went!

Linear Equations – Slope Project

I recently made a slope worksheet where I drew figures on a coordinate plane, and students had to state the slope of each of the sides of the figures. Then it occurred to me that this would make a really great slope project.

Students could create their own line design on a coordinate plane, and label the slopes of the lines they used. It doesn’t sound neat when stated like that, but here’s an example of what a final product might look like. (I only wrote the slope for six segments, but you get the idea).

Stained glass and linear equations (or inequalities) are fairly common, but I think keeping it just as slope might be better. Students don’t have to have lines running all across the coordinate plane since they only have state the slope for smaller line segments.

To ensure students don’t just draw a few squares, students should be given a list of criteria. For example, direct students that their design must include 6 negative sloped lines, 6 positive, 4 zero slope and 4 undefined slope lines. Or 5 pairs of parallel and 5 pairs of perpendicular lines, or some similar variation. That way students have to use different sloped lines in their designs, and it also gives them a finite number of segments they have to write the slope for. This way, they’re not penalized if they produce more complex designs.

Here’s the Sample Project word document in case you want to use it as an example or if you want to modify it. And here’s a Student Template.

Sumdog – Another Good Math Game Site

sumdogmain-11g18bk
From ordering decimals to the distributive property, this site has wonderful games that students will probably end up playing on their own time at home. I found this site on a lazy Sunday afternoon and was surprised to see a lot of students logged in and playing!

Sumdog

I played the games signed in as “guest,” but teachers can upload student lists and even get progress reports of student activity (this part requires a subscription). But the games are free, so even if you don’t plan on subscribing, I’d encourage you to introduce the students to the site.