One-minute cool math video

This is a cool 'n' short math video (HT Denise) from a math blog Love 4 Math. My kids laughed... good fun! Good job!

Factoring the time

I stumbled upon this comic that you might enjoy... factoring the time (from xkcd.com).

Kenken game for summer fun

As most of you are taking a break from math or school work, here's a little (addictive) math game to play online or as printed version: Kenken.

In it, you have to place the numbers in the grid kind of like in Sudoku so that no number appears twice in the same row or column, BUT there's an additional twist: it gives you "cages", and the numbers within a particular cage have to work to a given answer with a given math operation (either addition, subtraction, multiplication, or division).

KenKen practices logical thinking and is, I think, more fun than Sudoku.

It's easier to understand if you go see and try it yourself. The smaller sizes, such as 4x4 game, are great for kids, and the larger ones are good for us adults or older students.

• Kenken.com has nice Kenken puzzles online plus instructions, but only one for each size.

• MathDoku.com has an unlimited number of Kenken puzzles to play online in three sizes and several difficulty levels.

Math Jokes 4 Math Folks book

I recently received Math Jokes 4 Mathy Folks from the author, Patrick Vennebush. This is a very comprehensive collection of math-related jokes that all "mathy" people will definitely enjoy, and math teachers could use this book to enliven their lessons.

I have seen several of the jokes on the Internet, but never such a large collection.

The jokes are categories into chapters such as

• One-Liners, ("A hungry clock goes back four seconds.")

• Graphic Jokes, (For example, "Cube Roots" picture you see on the cover of the book.)

• Three Dudes, (An engineer, a mathematician, and a chemist are...)

• Conversion Chart, (10⁹ antics = 1 gigantic, or 454 graham crackers = 1 pound cake)

• Professions,("The secretary of defense informed the president, 'Yesterday, three Brazilian soldiers were killed. 'Oh, no!' the president exclaimed. ... 'How many is a brazillion, anyway?' ")

And so on.

In each section, the jokes that require the least math knowledge to understand are first, and then the material "advances". People who have studied math in college will get the most out of it, but there are joke for every level.

Please note the author has included a few bathroom jokes and a few slightly dirty ones - if you don't like those, they can easily be marked over.

Review of Algebra Unplugged

Algebra Unplugged by Kenn Amdahl and Jim Loats is not a textbook, nor does it have any exercises. Instead, it is filled with verbose, often humorous explanations of algebra 1 concepts for those who would rather hear or read math explained in many words, instead of in a few symbols.

Algebra Unplugged also often explains the reasons behind some peculiar mathematical notations or terminology, and in general, tells the students WHY things are done the way they are done in your "Real Algebra Book".

Note: the cover image doesn't directly have to do with the contents of the book... the book is not about music, nor graffitis. I think it's just conveying the idea that just like musicians might "jam" freely after the practice, with this book you'll get to experience algebra "freely" after the class.

Excerpt:

The Associative Principle

Organizing your singers into sections won't affect how many are in your choir. Grouping them is creating associations. The associate law recognizes the benefits of confining your tenors to one easy-to-patrol area. Fifteen tenors in a corner is no different from fifteen scattered throughout room. It's just safer.

If all you're doing to a series of numbers is adding them, you can add them one at a time, or you can put them in groups, then add the totals of each group.

I certainly enjoyed reading through the book, and feel it can be very helpful for algebra students who feel "lost" and want to understand more thoroughly how to navigate in the maze of rules, symbols, terminology, and unknowns.

Here's another fun little excerpt to get you a "taste":

Why They Make You Factor

Factoring is, on the surface, a foolish waste of time. You will read many books and factor many polynomials before you have a clue why you are doing it. The next sentence in this book will save you two months of confusion.

We factor to take advantage of some neat properties of zero.

In addition and subtraction problems, zero is powerless. You can add or subtract zero to a number for the rest of your life and you won't change the number at all. But zero become an all-powerful super-hero once you move into the domain of multiplication.

When you multiply any number by zero, you get zero. A million times zero equals zero.

When you divide zero by any number, you get zero. Zero divided by a million equals zero.

But you can't multiply any other two numbers together and get zero. And you can't divide any other number by anything and get zero. If the answer to a multiplication problem is zero, one of the numbers you multiplied must also be zero. And, if the answer to a division problem is zero, your original numerator was zero.

That's why we factor.

By all means, click to Amazon and "click to look inside" the book to read some more and see if you like the style. I did - but I never know if others do, or if teenagers do.

The authors have definitely succeeded in keeping the conversation on a lighthearted level. They make light of mathematicians and mathematics and tenors (of course, some might not like that). The book often uses apples, bananas, rats, kangaroos, catbox, jabberwocky, etc. as variables, instead of always resorting to x, y, and z. The authors let Little Weenie Numbers show us the way when things get complicated (these are 1, 2, 3, 4, 5, 6 and other small, easy-to-handle numbers).

The only complaint I have is that the book could have given a bit more attention to graphing with more graphs and actual visual illustrations. The author Kenn Amdah confesses he is not a visual person, so that is why.

Check also for used copies. The book is listed at both Amazon and Barnes & Noble

The same authors have also written Calculus for Cats, a clear and entertaining introduction to the mysteries of calculus. It is written with similar goals in mind. It doesn't contain exercises. For some reason, the analogies to the world of cats didn't quite "jibe" with me as well as the writing in the algebra book. This doesn't mean that that book is not useful; it can be tremendously useful for people who feel intimidated or even dismayed by calculus. It just didn't feel quite as fun to read as the algebra book to me.

This book is also listed at Amazon and Barnes & Noble.

Sticker Math Fun (K-2)

When I was a kid, my mom sometimes bought my brother and me activity books to fill up our summer time. Well, if you're into activity books, here's a Sticker Math Fun by Usborne that I can recommend for summer math learning and practice (grades K-2) (or for later in the school year as well, for that matter).

It has different mathematically-sound activities for addition, subtraction, beginning multiplication, fractions and clock, mostly on about 1st grade level but some for kindergarten and some for 2nd.

It is filled with quite variable and creative activities, and not just dull simple adding and subtracting. The activities include missing addends or subtrahends, number patterns, finding numbers that add up to a certain number, and so on.

It is in full color with kid-friendly imagery.

We bought this book several months ago, and I can say my kindergartner-1st grader has really enjoyed the book! And the third grader has wanted to do several pages as well.

The normal price is $15, but this morning when I checked, you can get copies from Amazon marketplace sellers for less than $5 (with shipping)! Go check it out!

Paper models for polyhedra

Have you ever wanted to fold a pyramid or some of the other interesting polyhedron out of paper?

At least, take a look at the pictures! www.korthalsaltes.com provides hundreds of free printable paper models for various solids, including platonic solids, pyramids, and lots of polyhedra. Some are available as colored versions also.

Folding and gluing one or two is a great summer math project also, and will keep kids busy for a while.

April fun

Just wanted to highlight two April-related posts from Denise:

April Math Calendar - something fun! You can download your own copy for printing.

And:

April Fool's Day: Fun with Math Fallacies

Use that brain

You know the old saying, "Use it or lose it." It definitely applies to our brain, as well, and not just our muscles (it's been proven). Using the brain can even help prevent dementia in seniors!

So, if you feel that your brain isn't getting the exercise it needs amidst all the routine housework, kids schoolwork, holiday preparations, and just life, bookmark the following link list.

Then, every day go to one of the sites on the list, and do one puzzle, riddle, or whatever it might be. There are plenty of sites on the list to keep you busy for a while. It says "50 games" but some of the links go to sites full of games:

50 Fun, Free Web Games to Make Your Brain Smarter, Faster, Sharper

For example, promise yourself to have some brain gym time just before or after you finish reading your favorite blogs or news sites or check email in the morning. It should work!

Origami

Origami is the ancient art of paper folding.

Yesterday I was asked by my daughter to make a paper boat (after reading a Curious George book where he made them). Well, that was easy for me because I learned that when I was a child.

Then she asked me to make a paper bird that she saw in the Adventures of Penrose book. I've never even attempted to make one before. The book had "instructions" but those images just looked quite cryptic. So I turned to the Internet. I found several sites that had picture instructions, but they all made me just puzzled; there would always be one step that I couldn't see how they did it.

Then, I found this site: www.origami.org.uk. They had ANIMATED instructions on how to fold a flapping bird! Finally I was able to make one!



Just thought I'd pass this one, in case some of you are interested in the paper folding stuff. It can be pretty fun for the kids.

Coffee Shop

I couldn't resist playing this fun game and you and your kids might not resist it either.

Basically you first buy some inventory to make coffee, adjust your coffee recipe (more or less milk, more or less sugar, etc.), define a price, and go selling. These funny animated folks pass by your coffee stand and voice their opinions, whether it's needing more milk or is too pricey or good quality for the price, etc.



At the end of each day you'll see a graph of your earnings and of your reputation. Then you go shopping for more inventory and adjusting your recipe and price. The play continues for 14 days. And the weather changes, too.

Hoodamath.com/games/coffeeshop.php

My daughter wanted to keep the coffee price way too low, like $1.65 or $2.00 and in no time was almost running out of money... : ) My hubby played it for hours.

The game practices decision making and analyzing several variables - critical thinking in other words.

Icosahedron from picnic supplies

This was such a fun video to watch! This guy makes an icosahedron from plastic plates, and then from plastic cups - and one more from just plastic and duct tape.

It can serve as a fun summer math project for kids who love explorations, cutting, gluing, building, and that sort of stuff!

He is hilarious! See the video:


Video from Makezine.com

Read the instructions for the icosahedrons

Find out what is an icosahedron

I will derive!

Just a fun little song (parody of "I will survive") for all of us who've taken calculus.

Humorous short history of mathematics

Enjoy:

A Very Short History of Mathematics

This is how it starts:

MATHEMATICS is very much older than History, which begins* in +1066, as is well known; for the first mathematician of any note was a Greek named Zeno, who was born in -494, just 1,559 years earlier. Zeno is memorable for proving three theorems: (i) that motion is impossible; (ii) that Achilles can never catch the tortoise (he failed to notice that this follows from his first theorem); and (iii) that half the time may be equal to double the time. This was not considered a very good start by the other Greeks, so they turned their attention to Geometry.

continue here...

Hat Tip to Let's Play Math.

Geometry fun with GeoMag

While on vacation, a friend of mine gave my older daughter a set of Geomag. You might already know about it, but it was new for us.

This has proved to be a fantastic learning toy! She's thoroughly enjoying building various shapes.

For example, she made a cube with sides 2 bars long and was proudly explaining to me how to do it: "First do a square, then put legs up from each corner, and then another square."

I made a tetrahedron that also had 2 bars on each side, according to the model. She thought it was neat and built that one several times herself last night.

I can see how the toy can help build geometric insight and beautifully demonstrate the common three-dimensional figures.

We've already ordered another set to accompany the small 42-piece set she got. You can find Geomag kits of various sizes and colors at Amazon.

Performing well below grade level

I am leading a training next week on how to introduce grade level concepts/standards when the students are performing well below grade level, and I am sure that math is going to be an issue. Any suggestions?

These are my 2 cents on teaching under-performing students.

Let's imagine we have an 8th grader performing on 3rd grade perhaps.

I would dismiss for starters geometry and measuring topics, and concentrate on this train of topics, in THIS ORDER:

addition
subtraction
multiplication
division
fractions
decimals.

... the goal being to cover the basic arithmetic up to pre-algebra.

Think of mathematics as a building. You need to have the foundation building blocks before you can go forward.

Maybe the child stopped understanding the math on 2nd grade or 3rd. We need to find the exact point after which he has not understood everything.

You can gauge this by the way by asking the child simple questions such as,

• I give you an addition 8 + 2 = 10, you give me a subtraction sentence (1st grade knowledge).


• How much do you need to add to 600 to make a thousand? (2nd grade place value)


• Draw a picture of 4 x 3 (3rd grade knowledge)


• There are 293 flowers and 145 are red. How many are not red - how do you find that? (using subtraction in finding parts)


• Draw a picture of 20 : 4. (division concept, 3rd grade)

etc.

So for such imaginary 8th grader, I'd make up a separate curriculum that goes through addition, subtraction, multiplication, division, fractions and decimals, in this order.

A teenager can go through those topics in 1 year, and understand it all, if he wants to. Obviously you'd want to show the student the train of topics too so they know what's coming next. You'd want to motivate them that hey, in one year I can learn all this basic math. You'd want to show them how the basic topics lead to the next ones.

Addition: you'd start at adding single-digit numbers, then memorizing addition facts, then 2-digit addition, then multi-digit addition.

If the student does NOT know addition facts, then spend a week practicing them! But not in random order. Like I do in my books (Addition 1 and Subtraction 1) you need to put those facts into contexts, study them in systematic, logical fashion such as sums of 5, sums of 6, etc. (using fact families). Or, adding to 9, adding to 8, etc.

Not knowing the addition facts makes the student SLOOOOOWWWW in doing simple addition problems, and makes it hard to get into subtraction or multiplication. So it is important, even if he's on 8th grade, and it is 1st grade stuff.

On to subtraction. Cover the three situations where subtraction is used, even if it is 1st grade stuff. Cover multi-digit subtraction. Shouldn't take many weeks.

Then multiplication concept. Times tables. Multi-digit. Absolutely remember to show what principles 23 x 38 is based on (multiplying in parts). Spend several weeks here.

And so on.

In a school year's time, it absolutely is possible to cover the basic arithmetic if the student is a teenager. I just would cover it all, including 1st grade topics, to make sure to catch those points where the student "dropped" off.

Any comments anyone?

Maria Miller

Developing positive attitude

What are the incentives needed in order to develop a positive attitude in children and other students towards mathematics?

I don't think special incentives is the main factor in developing a positive attitude towards mathematics.

I feel it is sufficient to get a few of the basics right, and then that alone will take care of most of it, and then students will like math just fine.

Disliking math is not something that is inherent in us or in our kids. Little kids don't dislike math or numbers. They're just fine with them! This "I hate math" or "I don't like math" attitude seems to develop during school years.

Now, I also don't think that children are disliking reasoning, because they're happy to do puzzles and play games where you have to think.

And, students' negative attitude towards math also is NOT due to (school) math being difficult. The math we learn in school is not difficult. You don't have to be a math whiz to understand it.

If you can learn to read and to use computer software, surely you can learn basic math. It's not that complex.

So... here are the two main factors that I feel contribute most to what attitude children develop towards math:

1) The teacher's attitude.

If you love math and are enthusiastic about it, it is seen in your teaching, and your attitude will be somewhat contagious.

It's true the other way around as well: if you don't like math, yet you teach it, students will sense your attitude. (I've written about the teacher's attitude in this article.)


2) How the math is being taught.

Children can end up not liking math when it is taught in such a way that they don't understand it. And, when they don't understand math, then they don't like studying it.

When they don't understand it, then they don't like studying more of it.

The teacher obviously can influence A LOT how the math is taught, but curriculum or the book also plays a role.

So, if we as teachers can get these two basic things straightened out, our students should learn to like math... or at least not hate it.

---

See also:
Four habits of highly effective math teaching

Is your math curriculum coherent?

How to motivate and prevent math anxiety

Math and Fun

I strongly believe math can be quite fun in some aspects of it; yet I also believe that not all of it has to be all fun.

It's good for students to learn to work through problems that are just that: work and no fun. That's what real life and real jobs will involve too.

Of course most of us try to get an occupation that we are interested in and can enjoy for the most part, but even then, we probably won't like all parts of our "dream job".

So in math, as in all education, we need to let our students learn to work, struggle, prowl through it.

But we can also let our students have some fun every once in a while. This can make them enjoy math, like math, appreciate it, like learning, and so on. I'm sure it's easy to agree with that.

In lower grades you might have more play than work, and then later on it's more work than play. For example, maybe you're studying coins and their values. Your child can play with real coins, do paper-and-pencil problems, and maybe play an online game about money or coins.

When studying algebra, it is going to be more on the work side, since algebra is similar to learning the "alphabet" and "basic grammar" of a new language. The "fun" topics tend to come after you've learned your basic language and can go off exploring (such as in calculus).

So I feel there is a balance between these two.

---

Along these lines, I've recently turned my attention to a math website Called Googol Learning whose founder Susan Jarema is making math to be googols of fun (googol is the number 10¹⁰⁰, or 1 followed by 100 zeros).

For example, she encourages you to, and gives ideas and resources for starting your own math club! This could be a family math night, or a monthly gathering of a few kids and adults together.

Susan uses a lot of music to make things more fun. She's produced audio CDs that combine math, music, and story telling for better learning.

Susan also gives interactive workshops in schools and homes.

One of these workshops is also now recorded on a CD (Crazy 4 Math), and for another one there is a family and teacher's kit (Discovery Multiplication Math Program).

The site also features a list of virtual field trips about volcanoes, tsunamis, earthquakes, or how many everyday things are made.

And what would be math fun without games? On her site you'll also find a list of best online math games.

Some humor

They say laughter is the best medicine - and it has been proven in scientific studies that laughing does help our health. Keeps stress at bay!

So here's a joke for the computer oriented...

and for those frustrated by exams... I especially liked the last picture! You get so deep into your calculations that you feel you get lost or so...

And there's lots more in the internet, some good some bad, some worse etc. Here are two more for you quoted from a certain page (see link at the bottom):

A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one.

An chemist, a physicist, and a mathematician are stranded on an island when a can of food rolls ashore. The chemist and the physicist comes up with many ingenious ways to open the can. Then suddenly the mathematician gets a bright idea: "Assume we have a can opener ..."

Click here to read more of these physicist, mathematician, engineer jokes.

Ma and Pa Kettle math

A little fun video clip where Pa and Ma Kettle prove themselves good 'mathematicians'! He "proves" by long division that 25 ÷ 5 = 14, and she "proves" by multiplication algorithm that 5 × 14 = 25.