Archive for the ‘Mathematical’ Category

Mathematical Colors and Codes, Episode Two: Prime Factorization Codes

Thursday, July 2nd, 2020

Episode Two of my Mathematical Virtual Program Series is up!

In Episode Two, I talk more about prime factorization and ways to show it with colors. Then I show how you can use that idea to make a prime factorization code.

This video has a downloadable coloring page to help you make your own prime factorization code.

Here’s this week’s video:

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Code

Mathematical Colors and Codes

Monday, June 22nd, 2020

My Mathematical Virtual Program Series is up!

This program is a series of six videos with downloadable coloring pages. New videos will post on Mondays at 3 pm.

They will show kids how to use math to make colorful patterns and coded messages, learning about prime factorization and nondecimal bases along the way.

They’ll post on Fairfax County Public Library’s website, but I’ll post them here as well.

These will be best for kids who already understand multiplication.

And this week, Episode One is up! It covers Prime Factorization, with an explanation of my Prime Factorization Sweater. And it explains how you can color your own chart, using this downloadable coloring page.

I hope you enjoy it!

Here are links to the entire Mathematical Colors and Codes series:

Episode One, Prime Factorization
Episode Two, Prime Factorization Code

Review of One Fox: A Counting Book Thriller, by Kate Read

Wednesday, February 5th, 2020

One Fox

A Counting Book Thriller

by Kate Read

Peachtree, 2019. 32 pages.
Starred Review
Review written December 9, 2019, from a library book
2019 Sonderbooks Stand-out: #4 in Picture Books

I always enjoy counting books. Nothing helps a kid learn numbers better. But it’s nice when the book adds a little something to make it more interesting than just the numbers. This “Counting Book Thriller” actually tells an exciting story.

It’s all simple – and will give little ones so much to talk about to tell the adult reader about all the subtext. You can even think of this as a wordless picture book – with numbers, though there are a few words. But the story is in the pictures.

The first numbers are:

One famished fox

Two sly eyes

Three plump hens

Four padding paws

Five snug eggs

Oh, but the pictures! There’s nothing routine about them.

I’m going to save this book for a preschool storytime. You want the kids to be interested in the counting and also be able to infer what the famished fox wants with those plump hens.

There is a surprise ending, and a note at the book reassures us: “No hens or foxes were harmed in the making of this book.”

kateread.co.uk
peachtree-online.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.

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.

What did you think of this book?

Review of How Many? by Christopher Danielson

Wednesday, January 29th, 2020

How Many?

A Different Kind of Counting Book

by Christopher Danielson

2019, Charlesbridge. First published in 2018 by Stenhouse Publishers. 39 pages.
Starred Review
2019 Sonderbooks Stand-out: #2 in Children’s Nonfiction Picture Books

I already loved Christopher Danielson’s earlier book, Which One Doesn’t Belong? It came to my attention when it won a Mathical Book Prize. Now Charlesbridge has taken on his books to hopefully reach a wider audience.

Here’s how the book explains that it is different from other counting books:

This book doesn’t tell you what to count.

It doesn’t start with small numbers and end with big ones.

Instead you decide what to count on each page. You have many choices.

The longer you look, the more possibilities you notice.

And that’s what you get. The illustrations are photographs. The pictures show things like an apple being cored and two shoes in a shoebox. The text asks, “How many do you see?”

After that first picture, the narrator says:

If you thought, “how many what do I see?” then you get the idea.

It does give examples of things you can count: shoes, pairs of shoes, shoelaces, holes for the laces, yellow stitches. And it asks, “What other things can you count?”

The pictures get interesting in different ways. There’s a picture of an egg carton with one egg in it. There’s a picture of eggs frying, one of which has a double yolk. The eggshells are by the stove, and the eggs that were not used are still in the carton next to the stove.

In other pictures, some fruit gets cut in half. We’ve got pictures of pizza, and then pizza in slices. Pictures toward the end show kitchen scenes with many of the things we already looked at – including shoes on the floor.

Questions at the back give you ways to extend the ideas. I do love that there are no answers anywhere in this book.

This is a wonderful book for curious children! It builds sophisticated mathematical ideas into preschool and early elementary school children. Anyone who has learned to count will have something to think about with this book.

As the author says at the end, “When you count carefully and clearly state what you’re counting, you’re doing some great math!”

talkingmathwithkids.com
charlesbridge.com
Stenhouse.com

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Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/how_many.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 my own copy, purchased via Amazon.com.

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.

What did you think of this book?

Baby Martin’s Normal Distribution Blanket

Saturday, January 11th, 2020

I finished a Normal Distribution Blanket for my new little nephew, Martin!

This is the same idea I used to make a blanket for my little niece Kara, but that one was in shades of pink.

Unfortunately, I didn’t get to try the blanket out on Martin in person, but I gave the blanket to my brother, his Daddy, to give to Martin.

Here’s the method. The blanket is simply a series of entrelac squares (diamonds). I knit one row of squares in one direction, then pick up stitches along an edge to make another row of squares in the other direction, and knit back and forth, with squares in between the squares of the previous row. The nice thing about it is that each square is knitted completely before you move on to the next square, so you don’t have to carry different yarns across the row.

I used Tahki’s Cotton Classic yarn because they have many, many shades, and I already had some spare yarn from previous projects — Cotton Classic is my go-to yarn for mathematical knitting projects. All those shades!

Choosing the shade of the yarn for each square is where the normal distribution math comes in.

I simply generated a list of random numbers from the normal distribution (using google to find a random number generator). The normal distribution is a bell-shaped curve, so I’ll get more numbers in the middle of the distribution.

I took five shades of purple and labeled them A through E. For numbers in the middle, I used lighter colors, and got gradually darker as the numbers went out from the middle. For numbers that were outliers, I added a sparkly silver yarn to color E — because it’s the outliers that make life beautiful. And aren’t we all outliers in some way?

Here’s the specific math for those who care or who want to reproduce the method:

I set the middle of the distribution as zero, with a standard deviation of one. For positive numbers, I did a garter stitch square, and for negative numbers I did a seed stitch square.

Here’s how I assigned the colors:
Color A: Absolute values between 0 and 0.5
Color B: Absolute values between 0.5 and 1.0
Color C: Absolute values between 1.0 and 1.5
Color D: Absolute values between 1.5 and 2.0
Color E (with sparkles!): Absolute values greater than 2.0

Now, I didn’t have a perfect progression from light to dark. Color D was the reddish purple. And it’s not obvious in the photo that E was definitely much darker than Color C. Making D the reddish purple seemed to get the weight of the colors to progress better. I should have done a close-up of the sparkles, but didn’t think of it this time.

One thing I like about visualizing a normal distribution this way is you get a more visceral feel for how the colors are distributed than just looking at the curve. There are almost as many B-colored squares as A squares — and there really are a lot of outliers. (It might be a better representation if I had gone out one more level and used six colors. But this worked.)

I’ve also done scarves this way (with stripes) and of course the pink blanket. And it always comes out pleasing to the eye. The normal distribution really is the way so much of nature is arranged.

You can find links to explanations of all my mathematical knitting at sonderbooks.com/sonderknitting!

Review of Prime Suspects, by Andrew Granville & Jennifer Granville, illustrated by Robert J. Lewis

Saturday, November 9th, 2019

Prime Suspects

The Anatomy of Integers and Permutations

by Andrew Granville & Jennifer Granville
illustrated by Robert J. Lewis

Princeton University Press, 2019. 230 pages.
Starred Review
Review written 9/19/19 from a library book

Okay, now I’ve seen everything! This is a graphic novel murder mystery about research mathematics!

The characters have names that play off of the names of distinguished mathematicians. The lead detective uses ideas from his namesake.

The most interesting part is that when the detective team goes to the autopsy of recent victim Arnie Int, lieutenant of the Integer Crime Family, they found everything inside his body has decomposed – except for prime numbers! The apprentice detective pulls a bloody number out of his body and says, “It’s a prime, sir!”

They find the body is similar to a previous victim, Daisy Permutation. I like the scene where the detectives discuss it while playing billiards:

“It’s not a similarity, but in both victims, the internal organs were completely decomposed.
Except that in Arnie Int there was a smattering of primes, and in Daisy permutation, a smattering of cycles.”

“But that’s only to be expected.
Cycles are the fundamental constituent parts of a permutation, just like primes are the fundamental constituent parts of an integer.”

And it’s all done in a dark style, with some clueless videographers to explain things to, and mathematical puns in the background.

The math itself – where they compare the set of integers to the set of permutations – went over my head, and I’ve got a Master’s in Math. I read the back matter where it’s explained, and it still went over my head – though I at least understood what basic concepts were at work. And I did, after reading, understand at least that cycles are the building blocks of permutations as primes are the building blocks of integers.

And I’m still tickled to death that someone made a graphic novel thriller about higher math.

There are fun ads on the inside cover, such as: “Are you looking to get away from it all? Why not come and stay at Hilbert’s fabulous “Infinite Hotel”? There is ALWAYS room for as many guests as want to stay.” And: “RIEMANN’S ROOTS: We’ll plant your organic roots in straight rows. Guaranteed to have at least 41.69% of the roots in a straight line!” And: “Fermat’s Dreams: Truly remarkable ideas for the future which this inside cover is too small to contain!”

The back matter takes up 50 large pages, so it takes as long to read as the 180 pages of the graphic novel part. Yes, it includes the math, but also you’ve got notes on the mathematicians referred to, notes about the references in the art, and an explanation of how the book came to be – beginning as a screenplay (which has been performed in live readings).

Here’s the beginning of that section:

Integers and permutations are fundamental mathematical objects that inhabit quite distinct worlds though, under more sophisticated examination, one cannot help but be struck by the extraordinary similarities between their anatomies. This comic book stemmed from an experiment to present these similarities to a wider audience in the form of a dramatic narrative. In these after-pages, we will clarify some of the mathematical ideas alluded to in the comic book, giving the details of Gauss’s lectures and Langer’s presentation at the police precinct. We will also break down the content of some of the background artwork, explaining how some of it refers to breakthroughs in this area of mathematics, some of it to other vaguely relevant mathematics, while some content is simply our attempt at mathematical humor.

Our goal in Prime Suspects has been not only to popularize the fascinating and extraordinary similarities between the fine details of the structure of integers and of permutations, but also to draw attention to several key cultural issues in mathematics:

— How research is done, particularly the roles of student and adviser;
— The role of women in mathematics today; and
— The influence and conflict of deep and rigid abstraction.

I’m not sure everyone will love this book, but I sure do! Sure to be all the rage in graduate wings of math departments across the nation!

press.princeton.edu

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Find this review on Sonderbooks at: www.sonderbooks.com/Fiction/prime_suspects.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.

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.

What did you think of this book?

Review of Monkey Time, by Michael Hall

Wednesday, March 13th, 2019

Monkey Time

by Michael Hall

Greenwillow Books (HarperCollins), 2019. 48 pages.
Starred Review
Review written March 9, 2019, from a library book

Here’s what I like about this picture book: You can use it in multiple ways.

On the highest level, you can use it to teach children to tell time. There are “minutes” lined up around the tree like a clock. Diagrams in the back show what it looks like for all the multiples of 10 minutes up to 60. Twelve branches on the tree are positioned like the numbers on an analog clock.

There are also some rain forest animals pictured. They are named at the back.

You can also use this book to practice counting – all the way to 60. Or to count by tens.

But I’ve got a Mother Goose Storytime for babies on Pi Day this year – and I think I’m going to use this book on the very simplest level – as words that are fun to say. It will introduce them to the idea of a clock while I’m at it.

Here’s how the book begins (over several pages):

Psst! Wake up, Monkey!
It’s time to play.

Wheee! I bet you can’t
catch a minute, Monkey.

Chase me over.
Chase me down.
Chase me all the way around.
Faster, Monkey, faster.

Hop! Pop!
Ha-ha. You missed me.

Little round “minutes” keep running around the tree, and Monkey keeps trying to catch them. The tree fills up when sixty minutes have come out. (Don’t worry, the text doesn’t closely follow all sixty minutes.)

This clever little picture book reminds me of Chicka Chicka Boom Boom by personifying a concept and making a story with them that’s fun to say.

A simple and fun way to introduce the concept of telling time.

michaelhallstudio.com
harpercollinschildrens.com

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

What did you think of this book?

Review of The Cookie Fiasco, by Dan Santat

Tuesday, December 4th, 2018

The Cookie Fiasco

by Dan Santat

Hyperion Books for Children, 2016. 60 pages.
Starred Review

First, let me talk about the new series this book introduces: Mo Willems’ Elephant & Piggie Like Reading. There are four pages at the front and four pages at the back where our beloved Gerald and Piggie talk about reading the book. The title page has a picture of Gerald holding the very book, ready to open it up and read it.

Now I’m not crazy about this frame – Just a little bit of Elephant and Piggie is not enough! Fortunately, they did choose excellent authors for the books-within-a-book, so this wasn’t a way to pass off any old thing and sell it with the Mo Willems brand. The Pigeon is even hiding on the back end papers, just as he does in the regular Elephant and Piggie books.

But what I love about The Cookie Fiasco are the mathematical implications! This book reminds me of the classic The Doorbell Rang, by Pat Hutchens. Like that book, it’s a simple story that small children can enjoy – but you can pull it out later when they’re learning about fractions and make multiple applications and elucidations.

The story is simple: Hippo, Croc, and two Squirrels have three cookies. Four animals, three cookies.

They discuss how to share the cookies, but nothing seems fair. While they are discussing the options, Hippo nervously starts breaking the cookies in half.

Then they have six cookie pieces, but still four friends. It’s still not fair. While they continue to discuss, Hippo continues to break the pieces. After a while they have twelve pieces, and realize that each one can have three pieces. Problem solved! Equal cookies for all!

There is a grand page of munching cookies – and then a cow shows up with three glasses of milk. Uh-oh!

The only thing wrong with this book is the one Gerald points out in the frame at the end – It may make you hungry for cookies.

It’s a simple, silly story. You don’t need to talk about the math behind it at all. But someday, when a child is learning to divide three by four, you can use this as a lovely illustration. And similar fractions. There’s even room for talking about common denominators. I’d love for this book to get a mention in the next set of Mathical Awards, I liked it so much.

dantat.com
pigeonpresents.com
www.hyperionbooksforchildren.com

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

What did you think of this book?

Review of Goodnight, Numbers, by Danica McKellar

Wednesday, November 28th, 2018

Goodnight, Numbers

by Danica McKellar
illustrated by Alicia Padrón

Crown Books for Young Readers, 2017. 28 pages.
Starred Review

Yes! This is the very best sort of counting book – with multiple things to count on each page.

For example, on the page for Four, the text says,

4
FOUR
Goodnight, four paws.
Goodnight, kitty cat.
Goodnight, four froggies
on the bathroom mat.

In the picture we do see four paws on the kitty cat, but also four stripes on its tail. We see four froggies on the bathroom mat, and we also see four rubber duckies in the room.

There are four shampoo bottles on the side of the tub, four toy turtles, four rolled-up towels, four stripes on the towel the dad is holding, four dots on the stool, and four bubbles in a framed picture (with framed spaces for ten things – this is consistent on each page).

Mind you, the rhyming text is simply nice, not stellar. But it’s not glaringly bad, either, which is an accomplishment with rhyming text!

The pictures are soft and sweet – and so many things to count! Another example on the Five page is the Mom has a necklace with five daisies, and each daisy has five petals.

The back of the book has a note to the parent/grandparent/caregiver reading the book. It points out the educational value, in case they missed it, and gives more ideas for bringing numbers into children’s lives.

This book would pair well with the bedtimemath.org website and app. They recommend doing math problems with your child at bedtime, as well as bedtime stories. This book is both!

This is a great way to talk about numbers and counting in a cozy and friendly way. It’s never too early to show your children that math is all around them.

McKellarMath.com
randomhousekids.com

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

What did you think of this book?

Review of Sam Sorts, by Marthe Jocelyn

Wednesday, October 10th, 2018

Sam Sorts

(One Hundred Favorite Things)

by Marthe Jocelyn

Tundra Books, 2017. 32 pages.
Starred Review

Here’s a wonderful picture book full of early math concepts that can be used in many different ways. It’s also good as a story (Well, a little bit – a story about a boy tidying up), and for those children who enjoy super-detailed illustrations (like I Spy and Where’s Waldo).

Mainly, it’s about Sam’s quirky collection of one hundred favorite things and the many different ways they can be sorted and counted.

After a page declaring that his things are in a heap and need to be tidied up, Sam starts in:

First he finds Obo the robot, one of a kind. Then two snarling dinosaurs, three little boxes, and four fake foods. How many things is that?

Sam gathers many things in various groupings. I like the page that shows a Venn diagram with three circles made of string.

Spider Rock joins the other rocks. Sam’s favorite rock is the round one. He looks for more round things. Two of the buttons are exactly the same. What else comes in twos?

The Venn diagram shows rocks in the first set, then round things, then things that come in twos. There are things in both intersections. There are things that don’t fit any of those categories on the outsides.

Things continue to be sorted in various ways.

Another way Sam makes a pair is by finding a rhyme.

Some things match because they have stripes. A few have dots or holes. Only one has checks. The snake is striped AND green . . .

On another page, the things are sorted onto a rainbow by color. Then many other categories are shown. (“Soft,” “Noisy,” “Pointy,” . . .)

Sam gets overly exuberant after putting out all his “guys.” “Look out, guys . . . The animals are coming!”

Once things are in a heap again, Sam decides to tidy up again. The next page has all the things laid out, separated by a striped background. The text asks, “How many categories? How many things?” There are ten categories with ten things each, so here is a great exercise in counting to one hundred. (One little problem with that page is that for at least a couple categories, it’s hard to figure out what the category might be.)

But if nothing else, this introduces the concept of sorting and sets and looking at things in different ways. This is a wonderful early math activity, and I love the playful approach.

www.penguinrandomhouse.ca

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

What did you think of this book?