Showing posts from July, 2013

Different sizes of infinities

I know the following piece is a bit long, but I REALLY hope you will take the time to read and try to understand the thoughts (if you don't know them already). This is one of the areas where YOU can show your students something about mathematics that is FASCINATING, AMAZING, awesome, mind-boggling!!! ... show them that mathematics is NOT just mundane, mind-numbing manipulation of numbers in calculations. This topic is not extra-curricular; it IS taught in pre-algebra / algebra 1 (real numbers), BUT you can explain some parts of it even to 4-6th graders.
This sounds really strange. How could there be different kinds or sizes of infinities?

I first encountered this idea in my university studies, and I thought it was absolutely FASCINATING!

The video below goes through the basics and explains them well, though really fast. I recommend you pause the video at those points where it goes too fast for you, and "rewind" or rewatch those parts. I will explain some of the poi…

Worksheets for counting coins & bills

I have had these money worksheet generators for a while on my site, but recently I went through them and fixed some errors they had (SORRY!). For example, one problem I fixed could have caused the worksheet to take a long time to generate. They should work better now.

Please let me know if you have ideas for improvements - if they are easy to implement, I will do so.

You can make worksheets for counting coins and bills in 6 different currencies. You could even let your kids/students explore other currencies just for fun! Some of these countries, such as Australia, have really colorful and pretty coins/bills.

US money worksheets
Canadian money worksheets
Australian money worksheets
British money worksheets
European money worksheets
South African money worksheets

European and US money are also available as Spanish versions:

Dinero estadounidense
Dinero europeo

Math Teachers at Play #64

Math Teachers at Play #64 carnival is up and going at

I haven't yet had a chance to explore the posts; but I will! Please take a look! There are always many interesting and good ideas in these carnivals!

Free worksheets for linear equations (pre-algebra, algebra 1)

There is a new worksheet generator at

Free equation worksheets

You can make customizable worksheets for linear equations (first-degree equations) for pre-algebra and algebra 1 courses (grades 6-9).

You can choose from SEVEN basic types of equations, including one-step equations, variable on both sides, or having to use the distributive property.

Please use the quick links below to generate some common types of equation worksheets.

One-step equations, whole numbers, with no negative numbers involved
One-step equations, whole numbers, the root may be a negative number
One-step equations; involves negative integers

Two-step equations
Variable on both sides and includes parenthesis

Challenges; includes rational expressions, such as (x - 5)/6, within the equations

I don't claim it is perfect... though I hope I got it working right. Let me know if you see something you'd like changed, and I can try work it in if it is not too big of a change.

Free worksheets for evaluating simple expressions - for prealgebra and algebra

I have just finished making another worksheet generator, this time for evaluating simple expressions (finding the value of an expression) when the value(s) for the variable(s) are given.

This is a skill practiced in grades 6-8, and specifically in pre-algebra and algebra 1 courses.

The worksheets look kind of like this:

Here are some quick links. Refresh the worksheet page to get another of the same kind, until you are happy with the problems & layout.
Level 1: usually one operation, no negative numbers in the expressions
Level 1: usually one operation, variable may be negative/positive integer
Level 1: usually one operation, variables and the constant may be negative/positive integers

Levels 1 & 2: variables have positive integer values
Levels 1 & 2: variables and constants are negative or positive integers
Levels 1 & 2: variables and constant are positive and may have one decimal digit

Levels 2 & 3: variables and constants are positive integers
Levels 2 & 3: some v…