## 8 really fun paper and pencil Math games

Games and Math go really well together, although a lot of people don't make that connection. Math really can be fun if some of its principles are taught through games. We see this in quite a number of free and commercial video games that teach math concepts, typically through solving arithmetic problems.

In this article I present 8 games of a different variety. They use paper and pencil, are free, are easy to learn, and teach logical thinking and strategy that involves looking ahead. They're great fun and they can usually be played by young and old alike. And, I've bet there are some games on my list that many of you have never heard of.

## Vedic multiplication using bases: an introduction

There are numerous introductions to Vedic mathematics on the web. I won't be doing a general introduction to Vedic Math now. In this article I want to explore one particular Vedic mathematics technique, using something called bases, to optimize certain multiplication problems.

This technique is extremely powerful and it takes getting used to. It's partially a cookie cutter technique but there's also some thinking involved in selecting proper bases for performing multiplication. Don't get frustrated if you can't understand this technique in one reading. It took me a fair amount of focused attention and practice to understand and appreciate the power of this approach. If there's enough interest I'll produce some videos explaining this Vedic technique.

## 24th Carnival of Mathematics

The 24th Carnival of Mathematics is available at Ars Mathematica.

There are 13 articles in this edition including submissions from bloggers who are new to me.

Check it out.

## Outstanding historical Math lectures

Professor Robin Wilson of Gresham College has delivered a number of outstanding lectures, mostly about historical mathematical subjects, that are available from the College's web-site. The lectures are viewable by Real Player and there are transcriptions in PDF format and lecture notes available. The lectures I've watched are a half hour long but I don't know if that's the case for all of them.

There are 30 lectures available from Professor Wilson. Topics include:

- Euclid
- Newton
- Euler
- Much ado about zero
- Prime-time mathematics
- How hard is a hard problem?
- Who invented algebra?
- Who invented the calculus? and other 17th century topics
- Wallpaper patterns and buckyballs

Two that I've particularly enjoyed are "Problems with schoolgirls" and "Who invented algebra?"

Enjoy the lectures and share a comment about the ones you like.

## Carnival of Homeschooling includes a couple of Math posts

Denise and I had Math-related articles published in the latest Carnival of Homeschooling:

Denise offers middle school and high school students some Puzzles for the New Year, posted at her popular and useful blog Let’s play math!.

Sol reviews a math resource written by a homeschooling parent (one that I think I will check out, given the popularity of geometry around here): Math Mammoth Geometry 1 Elementary Math Workbook posted at Wild About Math!.

If you blog about Math subjects that homeschool parents or kids would appreciate this is a nice carnival to be a part of.

## Review: Math Mammoth Geometry 1 Elementary Math Workbook

I know Maria Miller through her Homeschool Math Blog. As a fellow Math blogger I like to know what others in my community are up to so I follow her blog along with others. I'm also aware that Maria has a series of Math worktexts (workbook + textbook) and worksheets that she offers online through her Math Mammoth business.

I was curious about Maria's offerings and thought that others might be as well, especially homeschool parents, so I asked Maria for a review copy of one of her books. What follows is an unpaid review. I am not currently reselling Maria's books although I might in the future. Beyond a free copy of the book I am reviewing I have received no other form of payment.

I chose the Math Mammoth Geometry 1 Elementary Math Workbook to review. It's a 113 page book, filled with great explorations, clear explanations, and nice illustrations. And it sells for all of $5 as an electronically downloadable PDF file. This is a great value and the deal is even better for folks ordering a number of different books as a set to download or on CD.

## Review: MathNotations blog

Last November I proposed to exchange blog reviews with other Math bloggers as a way to get our blogs a wider audience. In that same post I threatened to review the blogs I like if I got no takers. Well, I've gotten no takers to date and I'm making good on my threat of reviewing blogs I like.

I really like Dave Marain's MathNotations blog. I've been following it for a few months and had the pleasure this morning of conversing with Dave over the phone. Dave shared with me that he's been involved in mathematics research and in Math education for many, many years. Dave loves Math tremendously and he's particularly interested in guiding students in mathematical investigations. Investigations are also a particular interest of mine as I'd rather guide a student to learning something neat and let him or her make the discovery than merely try to insert information into the student's brain.

## Carnivals and Miscellany

There are a number of items I want to write about but each one is not a post's worth so I'll just list them out Vlorbik-style.

The Carnival of Homeschooling #105 - 2nd anniversary edition is out. Here are the comments on the Math-related posts from the editor of that Carnival - not my words.

- Maria has some thoughts upon an article that compared Russian and American word math problems at Homeschool Math Blog. You can guess that the former were far more advanced than the latter.
- Sol of Wild About Math! has some nice Sudoku sites that are kid-friendly. He found some Free Sudoku resources. Sudoku is a great game to build logic skills and an interest in Math.
- Denise of Let’s play math! in Word problems in Russia and America also writes about Andrei Toom extended version of a talk he gave a few years ago at the Swedish Mathematical Society.

Someone submitted a post of mine about the connection between good storytelling ability and math skills to the Carnival of Storytelling #8. Very cool!

My friend Birney published a post I wrote specifically for his blog, Energy Boomer. Birney's blog is all about how to be conscious of energy use and how to save energy. The post is Drive or Bike: Do the Math. It's not the kind of Math I typically write about so go check it out.

The upcoming Carnival of Mathematics will be hosted next week at Ars Mathematica.

The 360 blog had a post on 12/24 about someone who has a dodecahedral calendar generator. It's very slick and very convenient given that a dodecahedron has 12 sides and a year has 12 months! You enter the year and select a language and the program generates a PDF file with the right shape pieces that you can fold together into a dodecahedron. So, if you don't already have a dodecahedral calendar for 2008 here's your chance to make your own!

The outstanding Spirit of Mathematics blog has a reference to this outstanding 11 page article by Paul Dawkins: How to Study Mathematics.

## Impressive Math magic with 16 index cards

Here is one of my very favorite Math tricks that's sure to impress your friends (and yourself the first time you try it). I learned this trick over 30 years ago and amazingly enough I still remember it.

Take 16 index cards and prepare them as follows:

- Make a diagonal cut at the top left of each card as illustrated. This is to keep all the cards oriented the same way because they're going to get mixed up for this trick.
- Number each card using the numbers from 0 up to 15.
- Using a hole punch cut 4 holes in each card as shown in the card numbered 0 in the illustration. It's important that the holes line up from one card to the next. In other words, when you are holding all 16 cards in your hand you should see four holes that go through the whole set of cards.
- Using a pair of scissors cut notches in each of the cards, except for card 0, so that each card matches the corresponding illustration according to is number.

Now for the fun part!

- Have the person you're wanting to impress shuffle all the cards so that they're in a random order. Hold the cards face up, with the numbers showing. After shuffling check that the diagonal cut goes all the way through all 16 cards. That's how you know the cards are all oriented the same way.
- Take a thin dowel, knitting needle, small screwdriver or other object that can fit through the holes and notches.
- Hold the stack of cards in one hand. Put the needle through the rightmost hole (or notch) with your other hand and pull the dowel away from the stack of cards. Some of the cards will come with the dowel - those that have holes in that rightmost hole - and some won't.
- Take the cards that came up with the dowel and put them in the front (top) of the stack in the order they came in when the dowel pulled them away.
- Proceed to the second hole from the right. Using the dowel again, push it through the hole and pull the dowel away from the stack. Take the cards that came with the dowel (these will have holes in the second-to-right position) and put them on the top of the stack, in the order they came in when the dowel pulled them away.
- Repeat with the second-to-left hole and finally with the leftmost hole.

Now, look at the stack of cards. What do you see? They're in order!

Can you explain how this happened?

If you know about computer programming can you relate this trick to the binary number system and to how computers can sort things?

## A fun little counting puzzle to start 2008

To start out the new year I came up with this little puzzle, in two parts. This puzzle makes a nice little Math exploration.

What is the sum of the digits in all of the integers between 1 and 2008 inclusive?

The second part of the problem is harder than the first part or not, depending on how you solved the first part.

What is the sumof the squaresof the digits in all of the integers between 1 and 2008 inclusive?

Have fun and show your work.