Happy August!

In this newsletter, my MAIN item is the post about

Then there are

~Maria

1. Math Mammoth news (SALES!)

2. Different sizes of infinities (grades 4-12)

3. Worksheets for counting coins & bills (grades 1-3)

4. Worksheets for order of operations (grades 2-9)

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

- Homeschool Buyers Co-op has a
**GROUP BUY**for the large Math Mammoth and Make It Real Learning bundle products! The discount will be 20% - 50% depending on the number of participants. The sale runs till August 31, 2013. **Math Mammoth August sale is here NOW as well!**ALL downloads & CDs are 25% off! Use coupon code AUG2013 at Kagi store.**The sale runs till Monday, August 19, 2013.**You can go to MathMammoth.com first, then find the links to Kagi's order pages there. Or, you can use these direct links to the order pages:

- We are working on finishing the
**revised version of grade 6-A**so that those of you who'd like to use it for this school year can do so. The 6-A will be released as a "beta" version, download only, near beginning of September.

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 points FROM the video below.

Did you know... that in ONE sense, there are

I know... in one sense, there aren't... but in another, there are. That is because to

...itISpossible to make a one-to-one match between the set of even numbers and the set of all counting numbers:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... | |||||||||

↕ | ↕ | ↕ | ↕ | ↕ | ↕ | ↕ | ↕ | ↕ | ||||||||||

2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | ... |

This one-to-one correspondence (bijection) SHOWS or proves that the set of counting numbers and the set of positive even numbers are the "

Could you easily come up with a way to

Think about that... if you can make such a list, then you can put counting numbers and fractions into ONE-TO-ONE correspondence! (Because just by the fact it is

The image below shows how to make the list. We put all fractions into a two-dimensional GRID, and then start going diagonally through the grid, starting with 1/1, which is 1. (Follow the arrows.) You will encounter equivalent fractions, which will be skipped over.

Again, think about this: ALL possible fractions

The set of all real numbers (the set of all decimals, both rational and irrational numbers) IS such a set!

The PROOF is on the video, starting at 2:58. Again, it goes fast, BUT I feel it is well explained, so just pause the video and run the explanation several times till you get it.

We call the set of all real numbers

I had not heard of the analogy of the night sky before (as in the video)... that rational numbers (fractions) are like the visible stars, and the irrational numbers are the rest, the blackness. That is kind of the way I've thought about it, though... that rationals are like individual dots on the number line, and irrationals are the "fill ins" that totally cover the number line.

Even the concept of

(Near the end, the video shows a little "crack" in the word "MATH". Well... I am not sure. I think that it's NOT mathematics itself that would have a deficit or a crack, but that there is some kind of a limitation somewhere... maybe in our HUMAN thinking.)

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

US money worksheets

Canadian money worksheets

Australian money worksheets

British money worksheets

European money worksheets

South African money worksheets

Dinero estadounidense y dinero europeo son disponibles en español también:

Dinero estadounidense

Dinero europeo

There are actually

- The first generator (grades 2-5) lets you choose from
**five different operations**to include (the four basic operations plus exponents), choose to include**parentheses or not**, and choose the basic**number ranges**used in the different operations. You can use decimals or whole numbers.

Unfortunately, it does not work correctly if you include both exponents and parenthesis. It also does not display negative numbers in the best way. Sorry about that! However, I feel the generator is STILL very useful for lower grades to make problems including the four operations, or problems with exponents without parenthesis, so I am including it here. - The second generator (grades 6-9)
includes by default all four operations and parenthesis. You can choose
to include
**exponents or not**. This one uses fraction line for division, and thus__involves fractions__. It uses a raised dot for multiplication (as is customary in algebra). Again, you can include decimals or not, control the number of problems, workspace below the problems, font size, and whether there is a border around the problems.

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.

Feel free to forward this issue to a friend/colleague! Subscribe here.

Till next time,

Maria Miller

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