Mathematical – Page 6

Jul 7, 2018September 11, 2021

Review of Paths and Portals, by Gene Luen Yang and Mike Holmes

Children's Fiction Review, Graphic Novel, Mathematical, Science Fiction 0

Paths and Portals

Secret Coders, Book 2

by Gene Luen Yang & Mike Holmes

First Second, 2016. 92 pages.
Review written in 2016.

This is very much part two of a longer story – not really a stand-alone book at all. But I like what they’re doing here.

This graphic novel is a vehicle for teaching readers how to code using the LOGO programming language – but the story is fun and engaging.

There are puzzles along the way – coding challenges are presented and the reader’s given a chance to figure out the solution before each step is explained. In fact, like the first book, this one ends with a coding challenge. And this one begins with the solution to the problem posed at the end of book one.

The story will keep kids’ interest. There are even villains introduced in this book – a sinister principal and a whole rugby team doing his bidding to get new uniforms. So now their coding activities with the old janitor, Mr. Bee, who used to be a professor, are threatened. There are lots of secret rooms and something sinister going on.

With this second book, I’m impressed where the authors take things. They show how to generate random numbers and then make beautiful patterns with code. The progression is straightforward – but so interesting. The story makes it more than just a coding textbook, and the fact that it’s a graphic novel makes the instructions and examples much easier to understand.

secret-coders.com
firstsecondbooks.com

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

Disclaimer: I am a professional librarian, but I maintain my website and blogs on my own time. The views expressed are solely my own, and in no way represent the official views of my employer or of any committee or group of which I am part.

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Apr 23, 2018

Review of A Hundred Billion Trillion Stars, by Seth Fishman

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

A Hundred Billion Trillion Stars

by Seth Fishman
illustrated by Isabel Greenberg

Greenwillow Books, 2017. 36 pages.
Starred Review

Here’s a picture book for kids about the enormous numbers in our world.

For example, there are about seven billion five hundred million (7,500,000,000) people on earth – and they weigh about the same amount as the approximately ten quadrillion (10,000,000,000,000,000) ants on earth!

There are about three hundred seventy billion billion gallons of water on earth, and about three trillion trees. In the course of an average lifetime, you might eat up to 70 pounds of bugs.

That’s the kind of statistics this book is full of. There’s a nice touch that when a big number is given in numeral form, you’ll also see it written out in words. (Our minds glaze over all those zeros.)

One truly mind-boggling part is toward the back, where it says:

By the time you’re done reading this book, almost every single number in it will have changed, getting bigger or smaller right before your eyes.

Even the number of stars.

At the very back is an Author’s Note with a nice explanation of how we can figure out these numbers without trying to count to a hundred billion trillion, which is impossible. There’s a nice explanation of estimates:

These numbers are sort-of-definitely-ALMOST true. Let me explain. Some of these numbers change so quickly that to give you an exact number would be impossible. For instance, we don’t really know if the full weight of all the ants on earth equals the full weight of humans. But we can estimate that there are 3.5 million ants per acre in the Amazon rain forest. With some serious snooping, fact-checking, and extrapolating we can estimate a very large number of ants on earth, one that means the combined weight of all these ants should be near the combined weight of all humans, or maybe dogs, or mice. And yes, you might eat some of those ants. you might eat many different types of bugs – though of course I don’t know exactly how many, or whether you’ll do it on purpose. Maybe a fly will zip into your mouth as you bike, or you’ll swallow a spider while you snore at night. But it will be near 70 pounds’ worth over the course of your life (about the total weight of a golden retriever).

Estimates can help you imagine sizes and compare one big fact to another. That is why this book is called A Hundred Billion Trillion Stars, and not One Hundred Nineteen Sextillion Fifty-Seven Quintillion Seven Hundred Thirty-Seven Quadrillion One Hundred Eighty-Three Trillion Four Hundred Sixty-Two Billion Three Hundred Seven Million Four Hundred Ninety-One Thousand Six Hundred Nine Stars. We can get very near the correct number on many things, near enough for us to understand how big they are – especially in comparison to the world around us.

Here’s a lovely way to play with the concept of great big numbers all around us.

sethasfishman.com
isabelnecessary.com
harpercollinschildrens.com

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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 Fairfax County Public Library.

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Apr 5, 2018April 5, 2018

Review of Which One Doesn’t Belong, by Christopher Danielson

Children's Nonfiction Review, Mathematical, Starred Review 0

Which One Doesn’t Belong?

A Shapes Book

by Christopher Danielson

Stenhouse Publishers, 2016. 36 pages.
Starred Review
Mathical Award Winner

I’m reading and reviewing this book during my Newbery year even though it was written in 2016 and isn’t eligible – because it makes my mathematical heart sing!

The idea comes from the old Sesame Street song – “One of these things is not like the other” – except on these pages, all four shapes can be the correct answer!

The book starts with an example and explains why you might have chosen any of the four shapes. (There’s also an emphasis that there’s not just one reason to choose any given shape.)

Here’s the explanation that follows the first example:

On every page of this book, you can choose any shape and say that it doesn’t belong.

The important thing is to have a reason why.

How is your shape different from the others?

What if you had picked a different shape?

While the question is the same on every page, some pages are more challenging than others.

You may need to put the book down to think and come back later.

So when you’re ready, turn the page and decide which one doesn’t belong.

It’s interesting to me that no answers are given – not even on the website. I didn’t figure out a good answer for every shape – I guess I need to keep thinking!

At the back of the book, the author says this:

I made this book to spark conversations, thinking, and wonder.

I hope you will see similarities and differences in unexpected places.

I hope this is a book you will leave open, think about, and return to. I hope you will share it with others.

I hope you will send me your own sets of shapes to challenge me to say which one doesn’t belong.

Find me at talkingmathwithyourkids.com

Sparking conversations! Encouraging critical thinking! Wow!

As a former math teacher, one of my favorite things about this book is the way it teaches there is not only one right answer. And that there might be different reasons for any given answer.

As far as I’m concerned, the Mathical Book Prize was well-deserved. I’m not sure when I’ve been more excited about a math book for kids.

On the website, a parent talks about discussing the book with a four-year-old – and yet the puzzles aren’t boring for an adult with a master’s in math. How often can you say that about a book?

talkingmathwithyourkids.com
stenhouse.com

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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 Fairfax County Public Library.

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Oct 22, 2017October 22, 2017

Outliers Blanket!

Mathematical 1

I did some more mathematical knitting for my new niece Kara!

For this blanket, I used the entrelac squares format I’d used in the prime factorization blankets, but the concept I’d used in the outliers scarves.

I took numbers from a normal distribution, using the generator at random.org.

Then I chose five colors in shades of pink, since we already knew Kara would be a girl.

For numbers in the middle of the curve (part of the bell), I used lighter colors. (z-scores of -0.5 to 0.5) For every half a z-score, I used a darker color. For the true outliers, numbers with a z-score bigger than 2 (or less than -2), I used the darkest color – but I added a sparkly silver thread.

This is to show that the outliers are what make life beautiful.

And aren’t we all outliers in some way or other?

I also distinguished between negative and positive numbers by using garter stitch for positive numbers and seed stitch for negative numbers.

It was a huge treat to try out the blanket with Kara. It wasn’t as big as I originally intended, but with random numbers I was able to stop when I decided it was done.

Kara’s big sister Zoe really enjoyed the blanket, too!

Mar 18, 2017September 11, 2021

Review of How Much Does a Ladybug Weigh? by Alison Limentani

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

How Much Does a Ladybug Weigh?

by Alison Limentani

Boxer Books, 2016. 28 pages.
Starred Review

The more I look at this book, the more I like it. Right now, I’m planning to use it for my next Toddler and Preschool Storytimes, and even bring it to Kindergarten and first grade classes for booktalking. The idea is simple, but it’s got so much depth.

Here is the text of the first several pages:

10 ants weigh the same as 1 ladybug.

9 ladybugs weigh the same as 1 grasshopper.

8 grasshoppers weigh the same as 1 stickleback fish.

7 stickleback fish weigh the same as 1 garden snail.

You get the idea! The book progresses, counting down, through starlings, gray squirrels, rabbits, and fox cubs to 1 swan. Then, of course, to finish off, we learn:

1 swan weighs the same as 362,880 ladybugs.

The illustrations are simple and clear. This whole book could almost be thought of as an infographic, except that the animals are not icons, but detailed illustrations.

I love that the animals chosen are not your typical animal-book animals. But most of them (except maybe the stickleback fish) are ones a child is quite likely to see in their own yard or neighborhood.

The back end papers list average weights of all the animals (in a colorful diagram) with the note, “Different animals of the same species can vary in weight, just as different people do. All the weights in this book are based on animals within the average healthy weight range.”

I love the way this is a counting book, a math book (about relative weight and even multiplication), a beginning reader, and a science book (about these different species).

It’s also a beautiful picture book. The note at the front says, “The illustrations were prepared using lino cuts and litho printing with digital color.” They are set against lovely solid color backgrounds, so the animals show up nice and clear.

I have a feeling that reading this book frequently with a child will get that child noticing small animals and insects in the neighborhood and thinking about weights and differences and good things like that.

A truly brilliant choice for early math and science thinking.

boxerbooks.com

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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 Fairfax County Public Library.

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Mar 11, 2017March 11, 2017

Another Coded Blessing Blanket!

Mathematical 0

I finished another Mathematical Knitting Project!

This is another Coded Blessing Blanket.

This time, though, it’s for my 22-year-old son.

I’d finished knitting for babies in the family. (Though now it’s time to knit again.) So I asked my son if there were anything he’d like me to knit for him. He said, “Blue Blankie could use a stunt double.”

Blue Blankie is the blanket I knitted him when I was expecting his birth and I was on bed rest. After he was born, I gave him the blanket every time I fed him. I was happy when he took Blue Blankie with him to college, but yes, sadly, Blue Blankie is falling apart.

However, Tim said he’d like a purple blanket this time. And I’d already used the same pattern to knit a blanket for my niece Alyssa with a blessing coded in the stitches. So I decided to do the same for Tim.

Here’s how it works. The stitches make a sort of plaid pattern with knits and purls. The pattern has a sequence of 12 rows that make one large pattern-row. Each pattern-row has seven smooth panels on the front side of the blanket. And each smooth panel is split into two parts. So I used those panels to code words of seven letters or less.

The code I used was base 5. So A = 01, B = 02, C = 03, D = 04, E = 10, F = 11, and so on. So I only need 5 stitch patterns, using three stitches.

I used some simple patterns. 0 is knit each stitch. This matches the background.

1 is purl each stitch, making a bumpy row.

2 is a cable made by holding 2 stitches to the back.

3 is a cable made by holding 1 stitch to the front. (Making the cable go the opposite direction from 2.)

4 is a yarnover and knit 2 together — making a hole.

Here’s a closer look at how the stitches turned out.

And an even closer look.

The first four rows are my son’s name, Timothy Ronald John Eklund. So the first row, for example, is 40 14 23 30 40 13 100. (To knit Y, I began one stitch ahead of the 7-stitch panel, using 9 stitches for 100.)

I’m not going to tell what the rest of the blanket says, except to say it’s a blessing. Can Tim read the code?

Now, this is exactly the same way I made Alyssa’s Blessing Blanket, but it turned out that hers had an error. I had almost finished Tim’s at Christmas time, but finally proofread it — and found an error, took out about 50 rows, and reknitted them. But now it’s done, and it’s error-free!

And it was a wonderful thing to knit a blanket full of love for my 22-year-old son who had just moved to the other side of the country.

May you thrive, Tim!

Jan 10, 2017January 10, 2017

Review of How to Bake Pi, by Eugenia Cheng

Mathematical, Nonfiction Review, Stand-outs, Starred Review 0

How to Bake ?

An Edible Exploration of the Mathematics of Mathematics

by Eugenia Cheng

Basic Books, 2015. 288 pages.
Starred Review
2016 Sonderbooks Stand-out: #5 Nonfiction

I have a Master’s in Math, so I love math books for a general audience. Besides, my math degree is very old by now, so a book like this taught me about a whole field of mathematics I hadn’t known about before. And it’s written by a woman!

She had me from the Prologue, where she debunks some math myths and begins with a recipe. Here are some parts I especially liked:

Cooking is about ways of putting ingredients together to make delicious food. Sometimes it’s more about the method than the ingredients, just as in the recipe for clotted cream, which only has one ingredient — the entire recipe is just a method. Math is about ways of putting ideas together to make exciting new ideas. And sometimes it’s more about the method than the “ingredients.”

Here’s about the myth that you have to be really clever to be a mathematician:

Much as I like the idea that I am very clever, the popular myth shows that people think math is hard. The little-understood truth is that the aim of math is to make things easier. Herein lies the problem — if you need to make things easier, it gives the impression that they were hard in the first place. Math is hard, but it makes hard things easier. In fact, since math is a hard thing, math also makes math easier.

Here’s talking about what it’s like to do research in math:

It’s true, you can’t just discover a new number. So what can we discover that’s new in math? In order to explain what this “new math” could possibly be about, I need to clear up some misunderstandings about what math is in the first place. Indeed, not only is math not just about numbers, but the branch of math I’m going to describe is actually not about numbers at all. It’s called Category Theory, and it can be thought of as the “mathematics of mathematics.” It’s about relationships, contexts, processes, principles, structures, cakes, custard.

Yes, even custard. Because mathematics is about drawing analogies, and I’m going to be drawing analogies with all sorts of things to explain how math works, including custard, cake, pie, pastry, donuts, bagels, mayonnaise, yogurt, lasagna, sushi.

True to her promise, she begins each chapter of her book with a recipe, and uses the recipe to illustrate the math about the recipe on the conceptual level.

Abstract Algebra was always one of my favorite fields of math, and Category Theory is a level of abstraction higher. What could be cooler than that?

But if the idea of extreme abstraction doesn’t get you as excited as it does me, think of it as math concepts explained through recipes. That conveys better how friendly this book makes the concepts.

She has analogies for almost everything. Here’s where she explains what abstraction is:

Abstraction is like preparing to cook something and putting away the equipment and ingredients that you don’t need for this recipe, so that your kitchen is less cluttered. It is the process of putting away the ideas you don’t need for the present purposes, so that your brain is less cluttered.

Here’s her explanation of proof by contradiction:

Imagine trying to “prove” that you really need to boil water to make tea. You would probably just try to make tea without boiling the water. You discover that it tastes disgusting (or has no taste at all) and conclude that yes, you do need to boil water to make tea. Or you might try to “prove” that you need gas to make your car go. You try running it on an empty tank and discover it doesn’t go anywhere. So yes, you do need gas to make your car go.

In math, this is called proof by contradiction — you do the opposite of what you’re trying to prove, and show that something would go horribly wrong in that case, so you conclude that you were right all along.

I think this book is truly beautiful. And I suspect it might provide glimmers to people who have never before seen beauty in math at all. If that’s not enough to appeal to potential readers, well, it has recipes.

basicbooks.com

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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 Fairfax County Public Library.

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Sep 9, 2016

Review of What in the World? Numbers in Nature, by Nancy Raines Day and Kurt Cyrus

Children's Nonfiction Review, Mathematical, Science 0

What in the World?

Numbers in Nature

by Nancy Raines Day
illustrated by Kurt Cyrus

Beach Lane Books, New York, 2015. 32 pages.

This is a simple picture book introducing a little bit of counting and a little bit of science to young readers.

Each number is introduced by a question, “What in the world comes . . .” and gentle pictures by the seaside illustrate each set.

Here’s an example from the middle:

What in the world comes four by four?

Petals of poppies, hooves – and more.

What in the world comes five by five?

The arms of sea stars, all alive.

There are only two lines per double-page spread, and plenty of open space in each painting, so this is for young readers who can handle the gentle pace. It would make a nice bedtime book, since the book finishes up with “sets too big to count.” The final two spreads show us a darkening sky with the words

Stars in the sky –

a vast amount!

You can hear from these examples that the rhyming isn’t stellar, but it’s doesn’t quite cross the line into bad. One other quibble I have is that on the sets of ten page with “Fingers and toes that wiggle and bend,” the picture of the boy does show his fingers and toes (in the water), but his arms are crossed with one thumb hidden – so you can’t use the picture to count ten fingers and ten toes.

However the simple idea – a counting book based on nature – is a lovely one. This is a gentle book that naturally leads into counting with children things in the world around them. A great way to practice counting and a great way to open their eyes to nature.

NancyRainesDay.com
KurtCyrus.com
KIDS.SimonandSchuster.com

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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 Fairfax County Public Library.

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Aug 12, 2016January 11, 2020

Normal Distribution Scarf

Mathematical, Prime Factorization 1

Today I finished a second Normal Distribution Scarf.

The first one I made was designed to highlight outliers to show that outliers are what makes the world beautiful.

For this one, I only wanted to show the Normal Distribution. I decided to knit it the long way so this time I wouldn’t have to sew any ends in.

I took colors from light to dark, in shades of pink. Colors B and C were a little closer than I wanted them to be, but it still gave the idea.

I generated numbers from a normal distribution and made a big list. For positive values, I purled the row, and for negative values, I knitted — so those values should be about even, making random ridges.

For the color, I used the absolute value, from light to dark. Since the normal distribution is a bell curve, there should be many more values in the lighter colors.

For 0 to 0.5, I used White.
0.5 to 1.0 was Victorian Pink.
1.0 to 1.5 was Blooming Fuchsia (only a little darker than Victorian Pink).
1.5 to 2.0 was Lotus Pink — a bright, hot pink.
Above 2.0 was Fuchsia — a dark burgundy.

Naturally, I used a lot more of the lighter colors. So for my next project after my current one, I think I’m going to do another normal distribution scarf, but this time reversing the values. So the new scarf would be mainly dark colors with light highlights.

In fact, if I weren’t using pink (maybe purple or blue), it would be fun to make scarves for a couple this way. Use dark, staid, sedate colors for the man, with light highlights. Use pastel shades for the woman — with dark highlights. [Hmmm. If I knit a scarf for a boyfriend before he exists, would the boyfriend jinx not apply?]

In this version, the lighter colors were more prominent.

Here’s a view of the scarf draped over my couch, showing both sides.

The different look has to do with where the knits and purls were placed and which side has a ridge and which is smooth.

Here’s a closer look:

I like the way the color combinations turned out so pleasing.

The only real problem is that the scarf is made out of wool, and it was almost 100 degrees outside today. So for now, I’m going to have to enjoy it draped over my couch rather than wearing it. I’ll look forward to this winter!

Update: I made an opposite scarf to this one, also generating random numbers and using the same exact yarn, but going from dark to light. Together, they make a matched set, so I gave them to my daughter and her wife-to-be!

Jul 31, 2016August 16, 2021

Fibonacci Blanket – Finished!

Mathematical 0

I finished my Fibonacci Blanket to give to my little niece Meredith!

The blanket is a Golden Rectangle, with a Golden Spiral, based on the Fibonacci numbers.

Here’s how the Fibonacci sequence works. You start with 1, then each number in the sequence is the sum of the two previous numbers.

So the sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …. To get the next number, just add up the two previous numbers.

To make a Golden Rectangle, start with a square with sides of length 1. On the side of that square, make a square that touches it and has sides of length 1. For the next square, use the sides of the two previous squares next to each other. So that square will have sides of length 1 + 1 = 2.

Spiral the squares around so that the sides of the new squares are always the sum of the two previous squares. This Golden Rectangle that results (all these squares together) is a pleasing proportion to human eyes. If you extend the Fibonacci series out and take the average of each number divided by the previous entry, it gets closer and closer to ?, phi, the Golden Mean.

You can also make a Fibonacci Spiral inside the Golden Rectangle by inscribing a semicircle inside each square. My semicircles aren’t perfect in this blanket (I eyeballed them.), but I think it gives the idea.

To make the blanket I chose shades of pink once I found out the baby would be a girl. I began with one color in the square for 1. The next square used stripes of that color and a new, slightly lighter color. The next square used the colors for each of the two previous squares and added a new color. I just alternated rows with each of the three colors.

That was the pattern I used for the rest of the blanket. Mirroring the Fibonacci Sequence, I used a color from each of the two previous squares and added a new color representing the new square.

Then I crocheted a chain-stitch Golden Spiral on the finished blanket.

I did the blanket in garter stitch, since that stitch is the best for squares. If the number of ridges and number of stitches are equal, you’ll get a square.

My unit square had six ridges (twelve rows), so one unit was six ridges. I went up to 21, so my final square was 21 x 6 = 126 stitches wide and 126 ridges high.

Best of all, the colors turned out very pretty for my lovely niece Meredith!