Review of Quack and Count, by Keith Baker

Animal Characters, Good for the Very Young, Mathematical, Picture Book Review, Readalouds 0

Quack and Count

by Keith Baker

Harcourt Brace & Company, 1999. 28 pages.

Here’s a simple picture book that’s fun and easy to read, and lays a nice foundation for counting and addition.

The story is simple. Lovely cut-paper artwork shows us seven ducklings. There are two rhyming lines on each set of pages, but the innovative part is that on each set of pages, we have different groupings.

On the page after we are initially introduced to the seven ducklings, it says,

“Slipping, sliding, having fun
7 ducklings, 6 plus 1.”

Six ducklings are grouped on the left-hand page, and one duckling has already slid down onto the right-hand page.

The next page is:

“7 ducklings, 5 plus 2
Playing games of peekaboo.”

Now you have five ducklings on the left and two on the right, all hiding in the long grass.

And so it continues.

This book is a beautiful way to give the idea of addition in a fun way, without overt teaching. They will see, without you even having to point it out, that 3 + 4 and 4 + 3 both equal seven. On each page, you can count the left, count the right, and count them all together, and your child will enjoy the experience even before he knows how to count himself.

This book gives an example of a beautiful and fun way to build a number sense into your little one. The short text means it would work well with very young children, and as they get older, you can let them count the ducklings themselves. The lovely artwork adds a level of enjoyment.

As a former math teacher, and a Mom who looked for excuses to teach my kids about numbers, and who has successfully reared two book-lovers and math-lovers, I simply had to highlight this delightful little book.

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Find this review on Sonderbooks at: www.sonderbooks.com/Picture_Books/quack_and_count.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library book from the Fairfax County Public Library.

Review of The Numbers Behind Numb3rs

Mathematical, Nonfiction Review, Starred Review 0

The Numbers Behind Numb3rs

Solving Crime with Mathematics

by Kevin Devlin and Gary Lorden

Plume (Penguin), 2007. 243 pages.
Starred Review

Okay, I admit that I’m a math geek. All I have to do to prove it is tell you about my prime factorization sweater.

So, it’s a no-brainer that I love the TV show Numb3rs. This book is written by Keith Devlin, “NPR’s ‘Math Guy,'” a consulting professor at Stanford, and Gary Lorden, “the Math Consultant on Numb3rs,” a math professor at Caltech (the school after which the fictional Calsci is modelled). They take the episodes of the first season of Numb3rs, explain the math concepts behind them, and talk about actual criminal cases where these concepts were used.

I think they do a great job of making the concepts understandable without getting bogged down with equations. I shouldn’t be surprised, since on the show Charlie always uses metaphors to explain what they can do with numbers.

A few of the things they talk about — with examples from actual cases — are DNA profiling, finding meaningful patterns in masses of information, using Bayesian Inference to detect the future, and making and breaking codes.

I don’t think I need to say much more about it. If you find this stuff fascinating, you know who you are! All I have to do is tell you this cool book exists.

If, on the other hand, this sounds mind-numbing and not the least bit cool to you, then no amount of my talking is likely to convince you, and I admit that you probably will not like the book.

But if you want to be dazzled by the power of numbers and get a handle on some of the powerful concepts that can be used to fight crime, you will thoroughly enjoy this book, as I did.

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Find this review on Sonderbooks at: www.sonderbooks.com/nonfiction/numbers_behind_numb3rs.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library book from the Fairfax County Public Library.

Review of Born on a Blue Day

Audiobooks, Biography, Mathematical, Nonfiction Review, True Stories 0

Born on a Blue Day

Inside the Extraordinary Mind of an Autistic Savant

by Daniel Tammet
read by Simon Vance

Tantor Media, 2007. 6 CDs, 6.5 hours.

Lately I’ve gotten hooked on listening to nonfiction. It’s a little bit easier to stop listening when I get to work (most of the time), and there’s something about driving that makes it a good time to access the part of my brain that stores facts. (That may not be a scientific description, but that’s how it feels.)

Born on a Blue Day tells the story of person with a brain that stores facts much differently than mine. Daniel Tammet is on the high-functioning end of the autistic spectrum, and he has amazing powers of memory. He has recited the digits of pi to more than 20,000 places, and can learn a new language in one week. He proved this in a televised experiment with Icelandic and after studying the language one week, appeared on several Icelandic television and radio shows, speaking in the native language.

Part of the trick to Daniel’s memory is that numbers have a specific shape, color and personality to him. Primes look different than other numbers, and when he multiplies two numbers, he can see the answer by the process their shapes use to combine. He learned all those digits of pi by simply learning the “landscape” — the view as the numbers passed by, which to his mind’s eye was exceptionally beautiful.

He also sees letters and words as having distinct shapes and colors. This helps him learn words in new languages, because he associates the word and its meaning with how the word looks to him.

This book is the story of Daniel Tammet’s life. His prodigious mental feats are a sideline of the story. The focus is on how he grew up and coped with being so different. He is proud to now be living independently with his partner, making a living, and even traveling all over the world and raising money for charities to help people with neurological disorders.

This book is both fascinating and inspiring. I’m not sure that many other autistic savants could articulate the way they see the world so clearly and beautifully.

I was also delighted to discover the reader was Simon Vance, who also narrates the Temeraire books. In this book, there were no characters to distinguish between, since it’s all told from Daniel Tammet’s perspective. But I’m getting quite a crush on Simon Vance’s voice. He’s a treat to listen to.

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Find this review on Sonderbooks at: www.sonderbooks.com/Nonfiction/born_on_a_blue_day.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

Source: This review is based on a library audiobook from the Fairfax County Public Library.

Review of If America Were a Village, by David J. Smith

Children's Nonfiction Review, History, Mathematical, Starred Review 0

If America Were a Village

A Book about the People of the United States

written by David J. Smith

illustrated by Shelagh Armstrong

Kids Can Press, 2009. 32 pages.
Starred Review.

I think this is a very cool book. It makes statistics accessible and understandable to children — and to adults.

The premise of the book is this: America now has more than 306 million people, and numbers that big are hard to understand. So we are going to imagine that all the people who live here are reduced down to a village of 100 people. The author proceeds to describe that village, and also what the village would have been like in earlier times of American history. Each person in the village represents more than 3 million Americans in the real world.

The author is presenting percentages, but by talking about actual people in a village, it’s far simpler to visualize and comprehend.

The author discusses many different aspects of the village. What languages do we speak? Where do we come from? Where do we live? What are our families like? (Did you know there are almost twice as many households in our village without children as with?) What religions do we practice? What do we do? How old are we? How wealthy are we? What do we own? What do we use? How healthy are we?

For example:
“If the America of today were a village of 100: 15 would be of German ancestry, 11 would be of Irish ancestry, 9 African, 9 English, 7 Mexican, 6 Italian, 3 Polish, 3 French, 3 Native American, 2 Scottish, 2 Dutch, 2 Norwegian, 1 Scotch-Irish and 1 Swedish. The rest have other backgrounds.”

I don’t know about you, but I would never have guessed that breakdown, and there were many other surprising facts in this book.

In many of the sections, the author compares the American village to the rest of the world, or to America’s past.

It’s funny how talking about America as a village makes a huge list of facts suddenly much more interesting, because now they are in a form you can visualize.

The authors have another book, which I also recommend, called If the World Were a Village. There are nice resources at the end, and ideas for using the book in the classroom.

I like the author’s ending statement in the notes at the back:
“It is my hope that this book will enrich and improve that sense of community — not just who we are, where we live and what we do and believe, but also where others live and what they do and what they believe — and that kids will then be inspired to find ways to make their country and their world a better place.”

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Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/if_america_were_a_village.html

Disclosure: I am an Amazon Affiliate, and will earn a small percentage if you order a book on Amazon after clicking through from my site.

My Prime Factorization Sweater

General, Mathematical, Prime Factorization 19

pfsweater

I wore my Prime Factorization Sweater to KidlitCon09, and it shows up in all my pictures, so I think it’s time for me to explain it.

This is the sweater that proves that I am a Certified Math Nut.

Okay, here’s how it works. You have to start in the bottom lefthand corner, because the mathematician in me couldn’t bear to start anywhere except where the origin would be on Cartesian coordinates. Naturally, the numbers go from left to right and from low to high.

I’ll post a picture of the front of the sweater:

pfsweater_front

Okay, look at the bottom row. It looks like there is a blank space on the left. That represents 1, because 1 is the background color, because 1 is a factor of every number.

Next is a blue square, which represents 2.

Next is a red square, for 3.

Then comes 4. 4 = 2 x 2. So 4 is represented by two blue rectangles.

Then comes 5. 5 is prime, so 5 gets a new color, yellow.

Next is 6. 6 = 2 x 3. So 6 is represented by a blue rectangle and a red rectangle.

7 gets a new color, purple.

8 comes next. 8 = 2 x 2 x 2. So 8 is in a square with three blue rectangles.

Then comes 9. 9 = 3 x 3. Two red rectangles.

Last on the bottom row is 10. 10 = 2 x 5, so we have blue and yellow.

The second row starts with 11, which is given the color pink.

12 has three factors, since 12 = 2 x 2 x 3, so two blues and a red.

Get the idea? This sweater presents a chart giving the color-coded prime factorization of every number from 2 to 100.

The patterns are wonderful and fascinating. You’ll quickly notice that the yellows and the blues line up, because 5 and 2 are factors of 10. You also might notice that all perfect squares are symmetrical. Multiples of 11 go in a lovely pink diagonal across the sweater. There are hundreds more patterns. It would be a lovely visual aid for teaching number theory. Fun to quietly wear to Math competitions, too!

What’s more, you can use this as a quick conversion table to convert to Octal (Base 8), because on the back I did the same thing with rows of 8:

pfsweater_back

The fun thing about rows of 8 is that the patterns are all different! Notice how the last column is full of blue squares because every number there is a multiple of 8 and has at least three factors of 2. And now 9 (two reds) acts like 11, going diagonally up the sweater, as does 7 (purple) in the opposite direction.

On the sleeves, I did rows of 2 and rows of 3. The rows of 3 is the only one where the blues do not line up, because 2 and 3 are relatively prime.

Isn’t it just the coolest thing in the world?!!!

Okay, I warned you: This is the item that proves I am a Certified Math Nut. I can get hugely excited and animated talking about this sweater.

I have already done a library program called “Puzzles and Patterns” showing kids how they can make simple codes using the ideas from this sweater. There’s definitely a children’s book in there, but I haven’t gotten around to writing it yet. I definitely plan to some day!

One of the cool things about this sweater is that it works in any language and on any planet!!! You see, even if an alien race had only four fingers on each hand, they could look at the back of the sweater and all their numbers would work. For that matter, a number system with a base of 7 or some other strange base would still work, even though it might not be in neat rows for that base. The chart is entirely independent of the symbols used to represent a number, and based only on color.

So we had a family joke that if an alien ever came to our door, we’d run and get the sweater to prove that we are intelligent life.

I only hope the aliens are not color blind!

Of course I also like to tell the story that when I was knitting this sweater, I brought it along to visit my family and friends one Christmas. Most of my family are Math Geeks, too, so they were impressed. But one friend had a young son who listened to my explanation and responded, “That’s just weird!”

What can I say? He does have a point. Call me weird, but I still think it’s one of the coolest things in the world!

Edited to add: Here’s a link to my CafePress store, where you can order t-shirts using this idea, showing the color-coded prime factorization of the numbers from 2 to 100, with the number also printed below the color-coded square.

Also, here are all my entries about other prime factorization projects.

My posts on Mathematical Knitting and related topics are now gathered at Sonderknitting.

Review of Greater Estimations, by Bruce Goldstone

Children's Nonfiction Review, Mathematical, Stand-outs, Starred Review 0

greater_estimations.jpg

Greater Estimations

by Bruce Goldstone

Henry Holt and Company, New York, 2008.  32 pages.

Starred review.

2009 Sonderbooks Stand-out: #3 Children’s Nonfiction

This book is fascinating.  I brought it to a staff meeting, and my co-workers couldn’t resist looking through the pictures.  I’d enjoy doing a program around this book.

Greater Estimations presents photographs of large quantities of things — rubber duckies, popcorn, parachuters, honeybees, plastic animals, and many other things — and shows the reader strategies for estimating how many there are.  The author also talks about estimating length, height (of buildings), weight (of dogs), area, and volume.

This book can capture your attention for a long time, and if it gets you curious about quantity, the author will have achieved his goal.  He also teaches you ways to satisfy that curiosity on your own.

I find myself wishing that Bruce Goldstone had placed some answers in the back of the book.  I do appreciate his point that estimation is NOT about getting exact answers.  But I do wish he’d given feedback on a few more pages to have some idea if my ability to estimate was improving as a result of his hints.

Anyway, in life you don’t get answers given to you.  This book gives you tools to help you figure out an approximate answer to numerical questions all by yourself.

Buy from Amazon.com

Find this review on the main site at:

www.sonderbooks.com/Childrens_Nonfiction/greater_estimations.html

Review of The Cat in Numberland, by Ivar Ekeland

Children's Nonfiction Review, Mathematical 0

cat_in_numberland.jpg 

The Cat in Numberland

by Ivar Ekeland

illustrated by John O’Brien

Cricket Books, Chicago, 2006.  60 pages.

I love this book!  It takes the concept of “countability” which I learned about in upper division math classes and graduate school, and makes those concepts accessible and understandable for elementary school children!

It starts with a hotel in Numberland, run by Mr. and Mrs. Hilbert.  The Numbers all live in this hotel, the Hotel Infinity.  Number One lives in Room 1.  Number Two lives in Room 2, and so on.  “For instance, Number One Million Two Hundred Thirty-Four Thousand Five Hundred Sixty-Six lives in Room 1,234,566.”

The numbers have certain games they like to play together, and there are certain quirks to the owners.

Some more fun begins when Zero comes to visit and wants to stay, but the hotel is full.  How could they possibly fit him in?

They come up with an ingenious solution:

“Everyone moves up one room:

Number One moves to Room 2,

Number Two moves to Room 3,

Number One Million Two Hundred Thirty-Four Thousand Five Hundred Sixty-Six moves to Room 1,234,567, where he finds a bigger bed and is more comfortable.

Room 1 is now empty, and Zero moves in and goes to sleep.

All the other Numbers go back to sleep in their new rooms, and Mr. and Mrs. Hilbert go back to sleep in their old room.

Only the cat by the fireplace does not go back to sleep, because she is trying to figure it out.

The hotel was full, she thinks.  There was one guest in each room.  Now it is full again, and there is still one guest in each room, but there is one more guest in the hotel!  Zero was outside.  Now he has moved in, and yet nothing has changed!  How is that possible?”

This is only the beginning of the perplexities facing the cat at this amazing hotel, based on the work of great mathematicians Georg Cantor and David Hilbert.

I find this book absolutely delightful!  I wish it had been around when I was taking Real Analysis.  Or, better yet, when my little boy was obsessed with infinity, and kept inventing “numbers” that were “bigger than infinity.”  I think he would have enjoyed this story.

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Find this review on the main site at:

www.sonderbooks.com/Childrens_Nonfiction/cat_in_numberland.html

Review of The Oxford Murders, by Guillermo Martinez

Fiction Review, Mathematical, Mystery 0
oxford_murders1.jpg 
The Oxford Murders
by Guillermo Martinez
translated by Sonia Soto

Reviewed September 17, 2007.
MacAdam/Cage, San Francisco, 2005. 197 pages.

This delightfully philosophical murder mystery was written by a man from Buenos Aires with a PhD in Mathematics. Of course I liked it!

The character telling the story is a PhD student from Argentina studying at Oxford. He’s staying in an apartment owned by the widow of a great mathematician. One day, soon after he arrived at Oxford, he encounters an eminent logician and together they discover the old woman dead, murdered.

The murderer has left a note, apparently a challenge to Dr. Seldom, the logician. The note refers to the murder as the first of a series, and includes a symbol, a circle. Sure enough, there’s a second murder, along with the symbol of a fish, drawn from two curved lines.

Part of the fun is this book is the mathematical aspects of the case. Dr. Seldom explains that they still don’t have enough information to determine the next symbol in the series. In fact, they can never be absolutely sure they have found what the murderer is thinking of. But perhaps if they can figure out the next item in the series, they can solve the crime.

I thoroughly enjoyed this story, a good mysterious puzzle, as well as some interesting things to think about.

This review is on the main site at:

www.sonderbooks.com/Fiction/oxford_murders.html