Review of Bedtime Math, by Laura Overdeck, illustrated by Jim Paillot

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

Bedtime Math
by Laura Overdeck

A Fun Excuse to Stay Up Late

illustrated by Jim Paillot

Feiwel and Friends, New York, 2013. 86 pages.
Starred Review
2013 Sonderbooks Stand-out: #6 Children’s Nonfiction

I already talked about Bedtime Math on my blog, when it only referred to a website. Then I used the book in my Every Child Ready to Read program, “Fun with Math for Parents and Preschoolers.”

I am tremendously excited about Bedtime Math, because I discovered how wonderful it is years ago, when my second son was about five years old. I’m not sure how it started, but he began asking for math problems at bedtime. (It might have been when I told him that when he turned six, his age plus his age would equal his brother’s age, and his age *times* his age would equal my age. His next question was, “What’s times?” One week later, his brother asked him “What’s 16 times 4?” and he figured out the answer in his head!)

Anyway, this started a stretch where I’d make up math problems for him at bedtime, after reading three books, when he was tucked in and cozy in bed. He learned the magic words I was NOT able to resist that would extend bedtime on and on: “Just one more math problem, Mommy, please!”

The problems in Bedtime Math are much better and more fun than the simply numerical problems I made up for my son. Each two-page spread has a fun scenario, followed by related math problems, one for “wee ones” (involving counting), one for “Little kids,” and one for “Big kids.” You can also get problems from their website or app.

The categories used are “Exploding Food,” “Wild Pets,” “Extreme Vehicles,” “Sports You Shouldn’t Try at Home,” and “Really Odd Jobs.”
For example, after telling us about squirt bottles for ketchup (“Squirting ketchup is also more fun than throwing a tomato: While a tomato smacking into something might explode and make a mess, ketchup already is a mess.”), here are the problems listed:

Wee ones: If you squirt 3 squirts of ketchup on a hot dog, and then 1 more squirt on your friend’s head, how many squirts did you fire off?

Little kids: If you line up some burgers and squirt ketchup on the 1st burger, then every 3rd burger after that, which burger in the lineup is the 4th burger to get squirted?

Big kids: If you squirt 2 cups of ketchup, and each cup used 14 tomatoes, how many tomatoes’ worth of ketchup did you just squirt?

I am excited about Bedtime Math! May the Math Madness spread! Laura Overdeck says in the Introduction:

Bedtime Math’s goal is simple: to make math a fun part of kids’ everyday lives, not just something found only in homework assignments. Math should be as beloved as the bedtime story….We never hear people say “Ewww, a book at bedtime?!” Likewise, there’s absolutely no reason to say that about math. Numbers are beautiful, and kids love attention. Bedtime Math just puts the two together. With that, let the games begin.

bedtimemath.org
mackids.com

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

Pascal’s Triangle Shawl to Row 10

Mathematical, Prime Factorization 1

Hooray! I’ve knitted my Pascal’s Triangle Shawl all the way to the 10th row!

Now, it’s not finished — I’m going up to 15 — but I can’t resist explaining it already. I think it is SO COOL! And even more patterns are going to pop out as I continue.

My mathematical knitting began with my Prime Factorization Sweater, done in intarsia, with Tahki’s Cotton Classic yarn. It shows the prime factorization of all the numbers from 2 to 100, using a different color for each prime, with 1, the background color, in white.

Later when the internet discovered my sweater, I made a Café Press Prime Factorization T-shirt so anyone can have the color-coded prime factorization of the numbers from 2 to 100.

Now, the trouble with intarsia, is you have to carry all the colors you use in any given row along the back of the sweater. And there are about a million ends to sew in at the end. But a couple years ago, I got a hankering to do something like this again, and it occurred to me that if I used stripes, I could deal with one color at a time. I made a reversible Prime Factorization Scarf, where the thickness of the stripes tells you how many times a factor occurs. It also uses a different color for each prime. This time 1 is black, and there is a black stripe between each successive number. Within each number, there is a two-row stripe for each factor. This is done in Plymouth Encore yarn.

Then my brother, even more mathematically minded than me (if you can believe that!) was going to become a father. His daughter needed a prime factorization blanket! And it occurred to me that it would be far easier to knit the design in Intrelac, using rows of diamonds. I went back to the nice soft Cotton Classic yarn, and white as 1, to be bright for the baby. I used garter rows to show how many factors of each color.

The Prime Factorization Blanket turned out fantastic! But the horrible part was giving it away.

I got to thinking. Intrelac naturally falls into a triangle shape. I instantly thought of something mathematical in the shape of a triangle — Pascal’s Triangle! And I have a special fondness for Pascal’s Triangle, having won a Chalk Talk competition on the Binomial Theorem at a Math Field Day when I was a junior in high school. The numbers in Pascal’s Triangle are the Binomial Coefficients from the Binomial Theorem.

And — here’s where I started getting excited — I knew that there are some fascinating patterns in Pascal’s Triangle. Why not show the prime factorization of each number in the triangle? That would show some of the patterns.

So I began my Pascal’s Triangle Shawl. The first thing I noticed when sketching it out is very cool. Even though the numbers in the middle of the triangle get hugely big quite quickly, they never have any prime factors bigger than the number on the end of the row. So if I take the shawl to row 15, I will only need colors for 1, 2, 3, 5, 7, 11, and 13. To show the prime factorization this way (the same as the blanket), I’ll use 12 x 12 squares, using garter stitch rows to show the factors, with smooth stockinette stitch between factors.

The numbers in Pascal’s Triangle can be calculated two ways. The first way, each number is just the sum of the two numbers above it. Starting with 1.

So the 0th row is 1.

The 1st row is 1 1.

The 2nd row is 1 2 1. We get the 2 by adding the 1 and 1 above it.

The 3rd row is 1 3 3 1.

The 4th row is 1 4 6 4 1.

The 5th row is 1 5 10 10 5 1

The 6th row is 1 6 15 20 15 6 1.

And so on. In the blanket, you can figure out what number each color represents by looking on the edges.

Here it is again:

You can see that I’ve used white for 1. 2 is blue. 3 is yellow. 5 is red. 7 is purple.

You can’t see the garter stitch rows too clearly in that picture, so here’s a close-up of a section:

If you look at the numbers on the bottom edge, 5 is the solid red diamond. Then 6 is next to it, 3 x 2, yellow and blue. Then comes 7, purple. Then 8, which is 2 x 2 x 2, so it’s three sections of blue. Then going out of the picture will be 9 = 3 x 3, so two sections of yellow.

In the center of the shawl, the cool thing is that every diamond represents the sum of the two diamonds that touch its lower edges. See the red and yellow diamond? That would be 5 x 3 = 15. It is the sum of the two diamonds touching its lower edges, which are 10 = 5 x 2 (red and blue) and 5 (red).

Here’s another detailed view, but this time I’ve written in the numbers:

In that picture, see how each number is the sum of the two diamonds below it?

And see how the factorization works? 70, for example, is 7 x 5 x 2, so the colors are purple, red, and blue. 126 = 7 x 3 x 3 x 2, so the colors are purple, two sets of yellow, and blue.

Okay, there are two very cool patterns that I’ve already noticed from looking at the shawl.

First, whenever you’re on a prime row (with a prime on both ends), ALL of the numbers in that row will have the prime as a factor. See how every number in the 3rd row has some yellow? And every number in the 5th row has some red? And every number in the 7th row has some purple?

The reason for that involves the second way you can build Pascal’s Triangle. The rth number in the nth row is the Combination nCr, the number of ways of forming subsets of size r from a set of size n.

Okay, if I’ve just lost everyone, I’ll use examples. The 3rd number in the 5th row can be calculated as 5x4x3/3x2x1 (= 60/6 = 10). The 2nd number in the 7th row is 7×6/2×1 = 42/2 = 21. The 4th number in the 10th row is 10x9x8x7/4x3x2x1 = 10x3x7 = 210. (You always have r factors in the denominator, starting from r and going down 1 each. We call that r! or r factorial. On top, you also have r factors, but they start with n.)

If n is a prime number, all the numbers in that row of Pascal’s Triangle will have n as a factor, and there’s no way it will cancel out with anything in the denominator (except on the very ends when you have 1).

But all that you will notice in the shawl is the color popping up, and you don’t even have to know why. In fact, I planned the shawl by figuring out the sums, and I’d forgotten about the combinations. So I was delighted when I saw that prime factors consistently show up in all prime rows. And then I remembered why.

The second beautiful pattern is related to the sums. The shawl nicely shows the distributive law. If two diamonds next to each other have a factor the same, the diamond above them which they both touch will have the same factor. That’s because ca + cb = c(a + b).

For example, 21 + 35 = 56
and 7×3 + 7×5 = 7(3 + 5) = 7×8

When you combine those two patterns, we’ve got some inverse triangles. Look at the big picture again:

Now focus on the diamonds with red in them. (Red is 5.)

On the row with 5 on the ends, 1 5 10 10 5 1, every number (except the 1s) has red in it. Well, by the distributive law, every number in the next row that touches two of these will have red in it. Those are the three middle numbers on the next row, 15 20 15. The next row will have red wherever it touches two of those, 35 and 35. And finally, we’ll have red in the diamond that touches those two, 70.

The same inverse triangle is going to happen with 7 and purple.

And today I started knitting the 11th row, using pink for 11. So fun! 🙂

Now, I must admit, I’m not particularly pleased with the overall look. The colors looked better in the blanket with rows of white between them. In the shawl, they’re all mashed together and it’s a little bit much with such bright colors. So when I finish this one, I’m planning to make a new one with more subtle differences. I found a wool yarn, Northampton from yarn.com, that has enough slightly different shades of purple. So I’ll be using these colors.

(I still have one more color on order, because the first one I ordered didn’t really go with these.)

The second shawl won’t be quite as good for explaining Pascal’s Triangle, but I think it will be much prettier! I will have to discipline myself to finish the first one before I start it. (I can solve that, I suppose, by using the same needles.)

So there you have it! Pascal’s Triangle knitted into a shawl! I will definitely post again when I finish it!

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

Review of Infinity and Me, by Kate Hosford and Gabi Swiatkowska

Contemporary, Mathematical, Picture Book Review 0

Infinity and Me

by Kate Hosford
illustrations by Gabi Swiatkowska

Carolrhoda Books, Minneapolis, 2012. 36 pages.

I wish I’d had this book when my son was young and obsessed with Infinity. He liked to make up numbers “bigger than infinity,” like “zappazudus” and “H-aloppus.”

This picture book follows a little girl who looks up at the stars in the sky and thinks about infinity. Then she asks all the people around her how they think of infinity, and gets a different answer with each person.

The pictures imaginatively express the abstract ideas. We’ve got numbers going on forever, driving on an infinity symbol forever, population expanding, things lasting forever, cutting things in half forever, and more and more.

The culmination? Love for her Grandma “as big as infinity.”

This is a lovely picture book perfect for setting minds spinning and starting cozy conversations.

khosford.com
chocolateforgabi.com
lernerbooks.com

Buy from Amazon.com

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

Fun with Math for Parents and Preschoolers

Library Links, Mathematical 0

This last Saturday I got to do an Every Child Ready to Read Workshop (sponsored by the Association for Library Service to Children and the Public Library Association), but I confess I made some changes.

The workshop, as prepared, was “Fun with Science and Math for Parents and Preschoolers.” The workshop I did? Well, I confess I left out the science and added lots of math activities.

Some friends on my Facebook page asked for details, and I thought it might be helpful for other librarians to know the adjustments I made. So I’ll just give the basic outline of the program. Imagine nice slides that came with the Every Child Ready to Read workshop.

As they came in, I gave every parent-child group a piece of paper and a box of crayons. I told them to write their child’s name in large letters so everyone could see. Some parents did this and some had their children do it. I let them keep the crayons and paper just in case the kids got restless during the talking-to-the-parents part.

We began with the welcome song, where we sing to each child. For example, if I were the child, it goes like this: “Sondy’s here today. Sondy’s here today. Everybody clap their hands. Sondy’s here today.” And we go all around the room. (I use this particular welcome song in all my programs because kids respond so well to their name. In this one, the addition of a writing activity with their parents and holding up the sign is perfect.)

What follows is a bit of an intro about Every Child Ready to Read. To warm up the audience, I mix it up by reading a book, and this time I chose Let’s Count Goats, with words by Mem Fox, and goats by Jan Thomas.

But the meat of ECRR2 is the five easy practices. These five easy practices, done often with your child, will help your child get ready to learn to read when they start school. What’s more, they’re fun. What’s more, they are also practices that will help your child learn math concepts. The beauty of them is that they use teachable moments and can be tailored to fit your child’s level.

The five easy practices are Talking, Singing, Reading, Writing, and Playing.

I have a lot of material on Talking about math as you go through your day.

Here are some examples of some questions you can talk about during the day:

How many toys are on the floor? (A great way to suggest cleaning up: see who can guess how many toys are on the floor.)

How many cars are going by? When riding in the car you can extend this by counting cars you pass and subtracting cars that pass you.

Look! Can you find a “3”? (Play “I spy” with numbers.)

How many spoons do we need? (Setting the table is a math activity.)

Can you find a matching sock? (So is sorting laundry.)

I spy something shaped like a circle! (Identifying shapes is a math activity as well as a predecessor to learning the alphabet.)

How many jelly beans do you want?

After that question, I talk about how when my boys were little, before they had much of a numerical concept, I’d ask them how many candies they wanted. They learn quickly that way! This is a great lead in to reading the book How Many Jelly Beans? By Andrea Menotti and Yancey Labat.

Also under Talking about math, I mention that counting, measuring, sorting, and comparing are all math activities. I pass out a handful of foam shapes to each family and tell them to decide how to sort them. They usually choose by either color or shape. They help the child sort them. Then they should count how many shapes in each group and write down the numbers. The families did great with this.

On the third slide for Talking, I have a link to www.bedtimemath.org, and this time I was able to bring their new book for checkout! We read an example problem from the website. I talked about how I did this with my own younger son. The magic words that my son learned could extend bedtime forever were “Just one more math problem, Mommy, please!” I could not resist that plea!

And bedtime, which is indeed a lovely time for reading to your child, is also a cozy time for talking with your child. The problems on bedtimemath.org and in their book are nice problems you can talk about a little bit and work out an answer together. They come at three different levels, so you don’t have to stop when your child is small.

The next of the five easy practices is Singing.

Singing slows down language, so it helps kids learn the sounds in words. It also helps them learn numbers by putting them to music. At this point, we sing “Ten Little Beasties” (same tune as Ten Little Indians), first clapping with each number, and then trying to hold up the number of fingers as we sing. Then we do “Five Little Monkeys Jumping on the Bed” with motions.

The centerpiece of the five easy practices, the most obvious one, is Reading.

Of course reading to your child will help them get ready to read! But did you know it will also help them get ready for math? I bring a cart full of books with mathematical concepts to the program. And at this point I read one of them. I like to use Quack and Count, by Keith Baker, because it also introduces the concept of addition, and it’s a fun story. The group this week spontaneously added a “Quack, Quack!” at the end of every page.

The fourth of the five easy practices is writing.

Here I talk about all the reasons to write numbers in life. Any time you write a list, you’re modeling this. Even if you don’t use numbers, if you write your grocery list in groups, that’s still a mathematical skill of sorting.
For a little activity here, I ask the parents to help the children count how many letters are in their name and write down the number on the paper next to their name.

The fifth of the five easy practices is playing.

For reading, dramatic play is so good. For math, I use this opportunity to put in a plug for board games. Candyland’s a great start, and you can’t beat Monopoly Jr for beginning addition and counting.

But playing is also at a much less formal level. Any measuring, counting, sorting, and comparing can be playing. At this point, we have all the families get in line in order of the number of letters in the children’s names from the front of the room to the back. This time, we went from BJ to Alexandra.

For another playing activity, we did a Venn diagram. I brought in a bucket of cars and trucks. I put two yarn circles on the floor. One circle was for red things. One circle was for cars. I put them on the ground so they overlapped. We figured out together where the different objects went. (“Is it red? Is it a car?”) I definitely should have used red yarn for the “red things” circle. But the kids had fun with it, anyway.

On another “Playing” slide, when it works, I show this clip from the Fred Rogers center.

This time, for some reason the link wouldn’t work. But it shows a family making beaded bracelets and necklaces using repeating patterns. Then we get the same idea reading the book Pattern Fish, by Trudy Harris.

Finally, we summarize the five easy practices. For a closing take-home activity, I pass out foam rectangles and half-sheets of paper. They can staple the paper inside the foam to make a counting book. They are welcome to decorate the outside with patterns using the foam sticky shapes. (We probably don’t have to have a craft at the end, since the program does go long, but I had the materials, and it’s a nice take-home reminder….)

So there you have it! Some simple ways to incorporate Talking, Singing, Reading, Writing, and Playing… about Math!

I’ve done this program twice, and we’ve had a lot of fun both times. The parents get lots of ideas, and we all have fun together. It does run long, a whole hour, but the kids stay engaged, so I must be doing something right.

Any ideas and tips you have from using the Every Child Ready to Read Workshops? Or just ideas for Talking, Singing, Reading, Writing, and Playing about Math with Preschoolers?

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.

More about Mathematical Knitting

Mathematical, Prime Factorization 0

On Wednesday, I finished knitting a Prime Factorization Blanket for my new little niece.

In my post about the blanket, I explained how the colors show the prime factorization of each number from 2 to 99. But I didn’t talk about the patterns, and I want to say a little bit about that here.

In fact, the only reason the Prime Factorization Blanket isn’t quite as good as the Prime Factorization Sweater is that I can’t have rows of 8 on the back and rows of 2 and 3 on the sleeves.

And the Prime Factorization Scarf is good for getting the flow of the numbers.

However, I do think the patterns in the 10 by 10 grid are a little easier to see with the larger diamonds on the blanket. Here’s the complete blanket laid out:

Let’s start by looking at the diagonals. 11 is 1 bigger than the base of 10. So the color for 11, red, goes in a diagonal across the blanket from the bottom left to the top right.

9 is 1 less than the base of 10. 9 = 3 x 3, so every number with a factor of 9 has two sections of yellow, the color for 3. You can see the yellows going diagonally up the blanket from the bottom right to the top left.

Oh, and I nearly forgot the more obvious ones. Since 2 and 5 are multiples of 10, they line up in columns. Every second column has turquoise for 2, and every fifth has green for 5.

Once you’re used to focusing on one color, you can pick any color and watch how it distributes evenly around the blanket. Take 19 for example, dark pink. You can see it climb up the blanket from the bottom right to the top left on a steeper diagonal than the one for 9.

And if you look at the colors it’s paired with, first it matches with 2, then with 3, then with two sets of 2, then with 5.

Another fun pattern is that the columns are sets of numbers that are congruent mod 10. So if you add, subtract, multiply or divide any two numbers in the same columns, your result will be in the same column.

For example, 2 + 17 = 19. Well, 62 + 27 = 99. The numbers in the second equation are from the same columns as the numbers in the first equation.

And that’s only the beginning of the patterns you can find.

Now that I’ve mailed off the blanket, I’m consoling myself by getting excited about the Pascal’s Triangle Shawl I’m going to make.

Pascal’s Triangle is formed by starting with 1, then adding a row of numbers where each number below is the sum of the two numbers above it.

Here’s how it works:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 11 55 165 330 462 462 330 165 55 11 1
1 12 66 220 495 792 924 792 495 220 66 12 1
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1

The cool thing? Even though you’ve got really big numbers, when you factor them, the only prime factors are ones that have already appeared in the triangle. So I only need colors for the prime factors 2, 3, 5, 7, 11, and 13.

I’m stopping at row 15, because on row 16, we’ve got numbers with more than 6 prime factors, and that’s the most I’m prepared to accommodate unless I make my diamonds bigger. But up to 15 is going to be lovely.

I chose colors yesterday and tried to order the same colors. I’m not sure the ones I have aren’t discontinued colors by now, but when my order arrives, I can get going. (In fact, I’ve already started with the colors I have, hoping I won’t have to take out too much.) Here’s the color scheme I chose, using Cotton Classic yarn by Tahki.

2 is on the bottom left, and then it goes around counterclockwise. So 2 will be pale pink, 3 will be rose, 5 will be red, 7 will be purple, 11 will be yellow, and 13 will be turquoise. And they are going to repeat in beautiful ways, just you wait!

I’ve already begun, though if it turns out that the pink I’ve ordered is a different shade from what I have, I’ll have to take out the square for 2 that I’ve begun. But I can’t stand waiting for the order!

You can see there the initial diamond for the first row: 1.

Second row has two diamonds for the second row: 1 1

Third row, I’ve knitted the first diamond for 1, and I’ve begun the next diamond, for 2.

When I get to the row with 4, I will start showing the prime factorization, so 4 will be listed as 2 x 2, with two sections of pink.

The way I’ll show the prime factorization will be exactly like the blanket, but the patterns will be very different, always with the diamond representing the sum of the two numbers on its lower edges.

And it will get cool on the top edge with numbers like 6435 = 3 x 3 x 5 x 11 x 13

I can’t wait to show pictures of the final result. I think it will be beautiful!

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

Review of Flight 1-2-3, by Maria van Lieshout

Contemporary, Mathematical, Picture Book Review, Starred Review, Travel 0

Flight 1-2-3

by Maria van Lieshout

Chronicle Books, San Francisco, 2013. 36 pages.
Starred Review

As a counting book, and as the ideal book to familiarize a small child with plane flight, this book is wonderful.

A note at the back reads, “Typeset in Frutiger by Swiss designer Adrian Frutiger. Since this distinctive and legible typeface was commissioned in 1968 by Charles de Gaulle International Airport in France, it has been in use on airport signage all over the world.”

The book begins, “When taking a flight, what do you see?” We’ve got 1 Airport, 2 Luggage carts, 3 Check-in desks. Most of the people are the iconic figures you see on airport signage, except the family we’re following. The boy has a yellow cap and backpack, and his parents distinctively come along on the journey through the airport and security to the gates and the airplane.

The numbers are fun, too. After getting to “10 Gates,” it skips to “100 Fastened seat belts,” then “2,000 Miles. 3,200 Kilometers.” And “33,000 Feet. 10,000 Meters. A million places to explore.”

The final page celebrates “One happy meeting.”

This is just a lovely book to look at. The simple font and iconic pictures are perfect for small children to easily see what’s going on. And they will be able to find the things from the book in the airport, whatever airport they may happen to visit.

I so wish this book had existed when my children were small and we were flying around Europe! As it is, I think this will spark a “Things That Go” theme for my next Mother Goose storytime. I want to let all the parents know about this wonderful book!

chroniclekids.com

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Picture_Books/flight_123.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.

The Prime Factorization Blanket!

Mathematical, Prime Factorization 2

Yes! My Masterpiece is finished!

What is this, you ask? This is a Prime Factorization Blanket!

With colors, it shows the prime factorization of all the integers from 1 to 99.

Here is the entire blanket, laid out flat:

Here’s how it works: Every prime number gets a color. The numbers start in the lower left corner.
I left a space for 0.
1 is the background color, white.
Then the next color is 2, a prime, so it gets its own color, blue.
3 is prime, and gets its own color, yellow.
4 is 2 x 2, so that square is two sections of blue. (You can tell on the blanket that there are two sections.)
5 is prime, and gets a new color, green.
6 = 2 x 3, so that square is part blue and part yellow. And so on.

I’ve got 0 through 9 on the first row, 10 through 19 in the next row, then 20 through 29, and so on through the top row, which is 90 through 99.

To show it more clearly, let’s look at each quadrant. Here’s the bottom left quadrant:

I put in the factors for each color. (After a few colors, I stopped putting in the “x” symbol for times.) I put a reference number on the left side so you can easily see which row. This set has 1 through 4, 10 through 14, 20 through 24, 30 through 34, and 40 through 44.

Now let’s look at the bottom right quadrant:

This picture shows 5 through 9, 15 through 19, 25 through 29, 35 through 39, and 45 through 49. For example, see if you can spot 48, which has a prime factorization of 2 x 2 x 2 x 2 x 3. Or look at 38, right below it, which equals 2 x 19.

By the way, this blanket is for my little niece, the daughter of my brother, who is, if it’s possible, even more of a math geek than me. On the 17th of December, my sister-in-law had an ultrasound, and we learned that the baby would be a girl, so I chose shades of pink for the next primes that came up, 17 and 19!

Now here’s the upper left quadrant:

This picture shows 50-54, 60-64, 70-74, 80-84, and 90-94. Can you find 62 = 2 x 31? Or 94 = 2 x 47? (I have to note that the colors are more distinct in person, and you can tell by the garter ridges how many sections there are of each color.)

And finally, the upper right quadrant:

And this, of course, covers 55-59, 65-69, 75-79, 85-89, and 95-99.

I’m so happy to finish it! The yarn is the same as what I used for my Prime Factorization Sweater, Cotton Classic. This yarn has enough colors (most important qualification), and it’s wonderfully soft — perfect for a baby blanket. I used a lot of leftover colors from the sweater, in fact.

The only really hard part? Giving it away! But I got the *idea* because my brother’s wife was having a baby, so this seems only fair to send it to the baby, as promised. Unfortunately, she lives on the other side of the country — so the one stipulation is they must take *lots* of pictures of her with it!

In fact, I thought of a way to console myself for giving away the blanket. My next project will be a Pascal’s Triangle Shawl!

I tested out, and the shape will work great!

I loved doing the entrelac squares for the blanket — it was much much easier than the intarsia I used on the Prime Factorization Sweater. And it will be easy-peasy to make a triangle instead of a square. I’ll use factors and do Pascal’s Triangle…. More on this to come, you can be sure!

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

Oh, and don’t forget! If you want your own prime factorization t-shirt or tote bag, you can find them at my Cafepress shop.

Review of The Boy Who Loved Math, by Deborah Heiligman and LeUyen Pham

Biography, Children's Nonfiction Review, Mathematical, Picture Book Review, Starred Review 0

The Boy Who Loved Math

The Improbable Life of Paul Erdös

by Deborah Heiligman
pictures by LeUyen Pham

Roaring Brook Press, New York, 2013. 38 pages.
Starred Review

I’ve been looking forward eagerly to this book ever since Betsy Bird reviewed it. My hold came in today, and I am absolutely delighted! I need my own personal copy!

Now, I have a Master’s in Math. Having studied mathematics at UCLA, I’d like to think that my Erdös Number (explained in the book) is at least 4, maybe even 3. So I’m simply saying that I’m predisposed to like it.

But there’s so much here for anyone to like! Even without looking deeper (more on that later), the pictures are full of life and interest, fitting the lively descriptions of a little boy in love with numbers.

Here’s an example from page 6:

So Paul kept counting . . .
And thinking about numbers. One day, when he was 4, Paul asked a visitor when her birthday was. She told him.

What year were you born? he asked.
She told him.

What time?
She told him.

Paul thought for a moment.
Then he told her how many seconds she had been alive.

[The picture shows 1,009,152,358 in a speech bubble coming from the little boy. He’s with his Fräulein and a woman who could indeed reasonably be 32 — even the details are right!]

Paul liked that trick. He did it often.

She goes on to show Paul growing, full of movement, learning more, always thinking about numbers. I love the detail that the illustrator included at the end: “As a young boy, Paul was known to flap his arms when something particularly excited him. This behavior continued through his teen years, when his friends would often have to explain to passersby that there was nothing wrong with Paul — he was just thinking hard.” The illustrations reflect this, full of life and movement.

And the author makes a smooth transition from childhood antics to a stellar adult career:

By the time Paul was 20, he was already famous around the world for his math. People called him The Magician from Budapest.

But he still did not know how to . . .

do his laundry

or cook his food

or butter his bread.

That was not a problem.
He still lived at home and
Mama still did everything for him.

She goes on to explain his unusual, collaborative manner of living. He’d fly to different countries, staying with other mathematicians, and then he had a way of bringing out brilliance in others as well.

Now, like I said, I have a huge soft spot for mathematicians, and my heart simply warms at the picture of the big group of actual mathematicians (women included, yes indeed) discussing together number theory, combinatorics, the probabilistic method, and set theory.

So the first run through of the story is wonderful enough. A story showing a brilliant mathematician with an unconventional life who produced great mathematics and brought out brilliance in others. How many picture book biographies are there celebrating mathematicians? It simply makes me happy.

But look a little deeper. The illustrator’s note shows the incredible level of detail she worked into the illustrations. Early on, the numbers you see are amicable numbers, and worked into the buildings we have dihedral primes, good primes, Leyland primes, Mersenne primes, prime triplets, unique primes, palindromic primes, Ramanujan primes, and two-sided primes. Paul Erdös worked in graph theory, and there are diagrams in the illustrations including the famous Konigsburg Bridge problem and other famous graphs. She includes actual buildings from Budapest and actual distinguished mathematicians as well.

And this book achieved something picture book biographers aspire to — I am absolutely going to read more about Paul Erdös. But even better, this is a book that celebrates young number lovers and will encourage them that their passion is part of something grand.

I’m posting this tonight in honor of Nonfiction Monday, hosted today at

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

Review of That’s a Possibility! by Bruce Goldstone

Children's Nonfiction Review, Mathematical, Starred Review 0

That’s a Possibility

A Book About What Might Happen

By Bruce Goldstone

Henry Holt and Company, New York, 2013. 32 pages.
Starred Review

A book about probability for kids! Hooray! What’s more, I find it tremendously impressive, because Bruce Goldstone keeps things far, far simpler than I could possibly have done if I were trying to write such a book.

Back in my college-math-teaching days, I often taught Introduction to Statistics. That’s probably why it never would have occurred to me that it’s possible to write a book explaining probability without even using fractions. In fact, the only place where he comes close at all is in the explanation about flipping a coin: “So the odds that the coin will land heads up is 1 out of 2 possibilites. (You can also say 50%, because 50 out of 100 is the same as 1 out of 2.)”

He manages to explain every fundamental concept with pictures. The pictures are vibrant, colorful, and interesting – and they so beautifully get across the concepts.

He begins by talking about possibilities. For example, there’s a picture of a kid holding 7 animal-shaped helium balloons. He asks, “If one of these balloons POPS, will it be the monkey? That’s a possibility!”

Then he goes on to talk about when things are impossible. And then what it means to be certain. Then the concepts of “likely,” “probable,” and “improbable.” Those are easily showed with pictures. He uses colorful pictures of flowers, parrots, and gumball machines.

And he goes on beyond the concept of “equally likely outcomes” (which he doesn’t mention, but didn’t I tell you I don’t know how to keep it as simple as he does.) There’s even a page that says, “Your imagination can help you think of possibilities, too.” It shows a girl jumping into a swimming pool, and asks, “What will probably happen when this jumper hits the water?”

Then it goes on to odds and flipping a coin. He explains “independent outcomes” without using those words – the idea that no matter what has already happened, your odds of getting tails on the next toss will always be 1 out of 2.

Then he looks at colorful spinners and a simple game that uses them. Then he looks at the classics of probability theory: playing cards and dice. Instead of listing all the possibilities of a 2-dice roll, he puts pictures of all the possible rolls in a chart, using one white and one black die. Kids can see at a glance that it’s more likely to roll a 7 than any other number.

Then he takes on Combinations and Permutations, again keeping it beautifully simple. Squidgy the Bear has 10 shirts and 10 pairs of pants. We see a picture of all 100 combinations before the author asks us what are the chances he’ll wear one particular outfit.

And the culmination (about permutations), before the notes at the end, is especially fun. Rabbit, Ribbit (a frog), and Robot run in a race. What are the possible results? They’re all pictured for you. I especially like the final questions:

Can you say all the possibilities together without getting your tongue twisted? That’s a possibility, but is it probable?

The notes at the end explain some activities kids can do at home, and then define some terms (like permutations) he didn’t use earlier. This is only very slightly more complex than what went before.

So, what makes me rave about this book? He keeps it so simple! The design is magnificent, and the pictures are beautiful and colorful – and helpful at the same time. But having taught probability to college students, let me tell you, his ability to explain the concepts at an elementary-school level is nothing short of genius. Magnificent!

brucegoldstone.com
mackids.com

This review is posted today in honor of Nonfiction Monday, hosted this week at Sally’s Bookshelf.

Buy from Amazon.com

Find this review on Sonderbooks at: www.sonderbooks.com/Childrens_Nonfiction/that’s_a_possibility.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.

Show Me the Awesome: Math at the Library

Mathematical 0

This month I’m excited about Show Me the Awesome: 30 Days of Self-Promotion, hosted by Liz Burns, Kelly Jensen, and Sophie Brookover. The Awesome artwork is by John LeMasney.

The idea is wonderful: Librarians talking about the awesome things they are doing.

Now, I’ve long believed that Librarians, as a whole, are tremendously undervalued. I have a sporadic series on my blog I call Librarians Help, trying to spread the word about the good we do. Read all the 30 Days of Awesome posts! If you’re a librarian yourself, you’ll get some great ideas. If you’re not, you’ll learn about some truly awesome things librarians are doing.

Mind you, I signed up to post in this series before I moved to a new home. Surely, a full month after moving, I’d be all settled in my new place, right? (Cue hysterical laughter here.)

I also signed up before booktalking season began. Today, for the first time in four years, I went to a local elementary school and talked with all seven grade levels about our Summer Reading Program and whet their appetites for some of my favorite books. I remembered how exhausting it is, but I had forgotten just how awesome it is to see all their faces listening to you tell about the books, and getting feedback that they are now determined to read some of the books you shared. I took a nap when I got home tonight, but I’m in a great mood. Getting kids excited about reading is such a mood booster!

But for my Awesome post, I already had in mind something I wanted to talk about: Math in the Library.

Before I got my MLS, my first Master’s degree was in Math. I taught college-level math for 10 years. And though I love math, the teaching job never felt like a calling, the way librarianship does. Part of what I love about the library? We don’t have to test anyone! No, at the library, we’re all about learning, and we assist learning for people who want to learn.

What’s more, I’ve always believed there’s no need whatsoever to “make” Math fun. Math *IS* fun! And we get to show that to kids!

So, what are some awesome ways recently I’ve gotten to show people how much fun Math is at the library?

Fresh in my mind, this morning I booktalked You Can Count on Monsters, by Richard Evan Schwartz, Great Estimations, by Bruce Goldstone, and Just a Second, by Steve Jenkins. But let me tell you about some programs.

First, I took Every Child Ready to Read‘s program, “Fun with Science and Math for Parents and Children,” and I changed it to “Fun with Math for Parents and Children.”

We did have fun! We emphasized the practices parents can use to build a foundation for reading in their children: Talking, Singing, Reading, Writing, and Playing. And we talked about how you can apply those things to Math as well. I outlined some things I did in an earlier post. I am hoping that some of these parents are all the more eager to count with their children as they go about their days, to talk about math, and to play games with their kids. I made sure to introduce them to bedtimemath.org, and I hope some of the parents are starting a bedtime tradition of math problems at bedtime.

See how we can take a totally different focus than a teacher has to in the classroom? I can give the parents ideas of ways to have fun, and they can choose the ones they go with. (For example, when picking up toys, ask your kids how many toys they think are on the floor? Count as you pick them up, and it will go faster!) Did you know that setting the table or matching socks are early math activities?

My other Awesome Math program that I’m excited about is called Colors and Codes. In this program, I show the kids my crazy Prime Factorization knitting projects and Prime Factorization t-shirt, to give them the idea that you can use colors to represent numbers. Then, if you use numbers 1 to 26 for the letters A to Z, you can use colors to represent letters. Which means that colors can be used to write messages.

I start with showing them prime factorization color codes and move on to other bases. Base 6 and Base 5 work well for the 26 letters, but I also show them Binary (Base 2). I show them they can also use shapes. With binary, they can use practically anything: sounds, lights, dots & dashes…. Then I have lots of foam shapes available, and let them make craft projects. They can devise their own codes using these ideas and decide what they want to say.

The program uses very sophisticated mathematical concepts — and it’s totally fun! If they don’t quite get it, well, they can make a pretty picture, and I bet later some of the ideas will come together for them. (I did give them all a hand-out to color themselves.)

Oh, and one more low-key but totally fun program I do at our branch is “Brain Games at the Library.” Playing games builds logic skills and mathematical thinking. But see how there’s no pressure, no testing, and only fun? For the Brain Games program, we give them gently used books as prizes. It’s fun to watch the kids thinking they’re getting away with something when they take a pile of books home from their wins!

All this is to say that I’m so happy I still get to teach Math! Only now I get to show people how much fun it is!

Librarians Help! Showing how Awesome Math is!