Librarians Help – With Math!

Mathematical, Prime Factorization 2

Today I had my Colors and Codes program that I mentioned last week.

Now, I spent ten years of my life teaching college math, but doing math programs at the library is so much more fun!

Why? Well, the biggie is I don’t have to grade them, so it makes the whole thing much more light-hearted. I’m showing them things about math that I think are really cool, and they get to think about ways to do it themselves. And it’s all just for fun. At the library, we teach people things they want to know! If they don’t want to know them, they don’t need to come. It’s that simple!

Here’s what I did. I showed the kids my prime factorization sweater (wore it of course), and we worked out how it works. (That was fun!) I told them if colors can represent numbers, they can also represent letters. Just use 1 to 26 for A to Z. So you can write messages this way. I showed them a prime factorization code, then showed them other bases and how you can make codes with them. We wrapped it up by getting out sticky foam shapes and they could put a coded message or just a pretty pattern around a picture frame or on a bookmark or a door hanger.

The highlight for me, I think, was when a girl was working on coloring in the prime factorization chart on the hand-out. She was stuck on 24. I asked her what it equaled, and she said 12 x 2. So we looked at 12, and then the light went on and we talked about how you could do figure it out different ways, but you always got three 2s and one 3.

Now, I’m going to write some notes to myself while the program’s fresh in my mind. It went well; the kids had fun. But I want to do it again this summer, and hope it will go even better.

1. I’ll set the age level higher. I do think I lost a few kids this time. I think I’ll set it at 10 or 11 years old rather than 8. You want the kids to be fully comfortable with multiplying. Now that I think about it, when I did this program a few years ago at Herndon Fortnightly Library, I think the age limit was 10.

2. We’ll do some coloring on the prime factorization chart before I move on. This group did work out with me how it works. I didn’t want to get bogged down, but I think some coloring would help them understand it better.

3. I’ll have them figure out the numbers for their name in every code I go over. For example, my name, Sondy, in a base 10 code is 1915140425. (S is the 19th letter, O is the 15th, and so on.) In a prime factorization code, it’s 19 1 3 5 1 2 7 1 2 2 1 5 5 1. (19 x 1, 3 x 5 x 1, 2 x 7 x 1, 2 x 2 x 1, 5 x 5 x 1) In a Base 6 code, it’s 3123220441. In a Base 5 code, it’s 34 30 24 4 100. In Binary, it’s 10011 1111 1110 100 11001. Taking the time to do that would mean they’d get what I was having them do when they went to use the foam sticky pieces.

4. We’d do some coloring on the other charts before we moved to the foam shapes. Then I’d have them do their name with the colors they picked.

5. I’d show them exactly how I did my name on the bookmarks, one using colors and one using shapes.

Did I mention everyone did have a good time? But I think I’ll do a little more hands-on, using their names, before I move to the craft next time.

But it was a great trial run!

And don’t forget! Librarians help! We get to show kids how much FUN Math is! And we don’t even have to test them on it!

Colors and Codes

Mathematical, Prime Factorization 0

I just got a tweet that made me prouder than I’ve EVER been of my Prime Factorization Sweater, and that’s saying a lot.

The tweet was from @milesmac, Miles MacFarlane, a teacher, with the words, “#LeilaN students deciphered @Sonderbooks Prime Factorization Sweater – Now making own code #7Oaks”

Here’s the picture that accompanied it. Even by the backs of their heads, you can tell those are engaged kids!

Yes! That’s what it’s about! Mr. MacFarlane, you made my day!

And the timing is lovely. Next week, at my own City of Fairfax Regional Library, I’m doing a program I’m calling “Colors and Codes” where we’re going to do exactly that. I’ll wear the sweater (or maybe my prime factorization t-shirt and bring the sweater. And the scarf). I’ll show them how we can assign each letter of the alphabet a number from 1 to 26. We’ll start with a factorization code, but move on to things like Base 6 or Binary. And I’m going to have foam shapes for them to make crafts with codes in colors or shapes.

Yay! See, we don’t have to make Math fun! Math is fun!

Prime Factorization Progress – To 39

Mathematical, Prime Factorization 0

I’ve already posted several times about my Prime Factorization Knitting, and I can’t resist posting pictures every time I get another row of numbers done on my new niece’s Prime Factorization Blanket.

You can get more detail of how it works in the earlier posts, but basically each prime number gets a color, and each number gets a square divided into the colors for the factors of that number. I’ve finished up to 39. (I’m not putting an exclamation mark after that statement, since I haven’t gotten to 39 factorial.) Here’s how the blanket looks so far:

And here’s a close-up on each side, with the numbers written in. You’ll have to figure out the factors. And I can assure you that it’s a lot easier to tell when there are two or three (or four or five) of the same factors in one number when you can see and feel the blanket. I divided it with garter ridges, and the photo couldn’t really catch that.

Here’s the left half:

And the right half:

Don’t forget that you can get your very own Prime Factorization T-shirt at my Cafe Press shop for a lot less effort than this blanket is taking (but okay, you won’t have as much fun as I’m having). I took it to a Youth Services Librarian meeting today, and only the unwary asked what it was going to be. I must admit, it’s a lot better for knitting during meetings when I’m on one of the white rows.

Will I finish before Baby’s arrival in May? I hope I will at least be close….

Prime Factorization Blanket – to 29

Mathematical, Prime Factorization 0

I got done another row of numbers on the Prime Factorization Blanket for my arriving niece!

It’s hard to see the ridges in the solid colors, so here are close-ups of the left half, then right half:

The bottom row in the picture is 1 (white), 2 (blue), 3 (yellow), 4 = 2 x 2, 5 (green).

The second row is 10 = 2 x 5, 11 (red), 12 = 2 x 2 x 3, 13 (tan), 14 = 2 x 7, 15 = 3 x 5.

The top row is 20 = 2 x 2 x 5, 21 = 3 x 7, 22 = 2 x 11, 23 (baby blue), 24 = 2 x 2 x 2 x 3, 25 = 5 x 5.

Now the right half:

Here we have the bottom row of 5 (green), 6 = 2 x 3, 7 (dark purple), 8 = 2 x 2 x 2, 9 = 3 x 3

The second row is 15 = 3 x 5, 16 = 2 x 2 x 2 x 2, 17 (pink), 18 = 2 x 3 x 3, 19 (dark pink).

The third row is 25 = 5 x 5, 26 = 2 x 13, 27 = 3 x 3 x 3, 28 = 2 x 2 x 7, 29 (periwinkle)

I really like the way it’s turning out!

You can read more about my prime factorization knitting in previous blog posts or via my Pinterest board. And don’t forget to look in my cafe press shop for prime factorization t-shirts.

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

Review of Anno’s Mysterious Multiplying Jar, by Masaichiro and Mitsumasa Anno

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

Anno’s Mysterious Multiplying Jar

by Masaichiro and Mitsumasa Anno

Philomel Books, New York, 1983. 44 pages.
Starred Review
2012 Sonderbooks Standout: #7 Children’s Nonfiction

How did I not know about this book?! How did I not know there is a picture book that explains factorials?! It was written before my boys were born — and I didn’t know to buy it for them! This is a crime!

I was at the library, refilling our display of children’s nonfiction books. I find that if I put out children’s math books, they get snapped up. I make sure to put out fun children’s math books, like anything by Greg Tang, or A Million Dots, by Andrew Clements, or Piece = Part = Portion, by Scott Gifford. But while I was looking through the 510s for good fun math books, I found Anno’s Mysterious Multiplying Jar.

The idea is simple. Mitsumasa Anno and his son show us a jar that contains a sea and an island. Each island has 2 countries. Each country has 3 mountains. Each mountain has 4 walled kingdoms. In each kingdom are 5 villages. In each village are 6 houses. In each house are 7 rooms. In each room are 8 cupboards. In each cupboard are 9 boxes. And within each box, there are 10 jars.

How many jars are there all together? There are 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800. The second half of the book shows this even more clearly, using dots. And there’s an afterword as well, that explains some of the further uses of factorials.

It’s so simple. So beautiful. And it explains factorials! To children! Yes!

Buy from Amazon.com

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

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

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

Disclaimer: I am a professional librarian, but I write the posts for my website and blogs entirely 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.

This review is posted today in honor of Nonfiction Monday. You’ll find the round-up at The LibrariYAn.

Prime Factorization Blanket – Second Row

Mathematical, Prime Factorization 1

I’ve finished the second row of numbers (third row of rectangles) in my Prime Factorization Blanket!

The fun part was that my brother and his wife found out on the 17th of December that their baby is a girl. So, since I was coming up on the prime number 17, I chose to use pastel pink to represent 17. For good measure, I used a pretty rose pink to represent 19.

I only hope that having all that turquoise blue won’t make people think it’s a blanket for a boy, but I’m hoping it’s multicolored enough, it won’t give that idea.

I couldn’t manage to write in all the numbers on the picture, like I did after the first row, but in real life I assure you, you can tell when there are two factors of the same prime.

So here’s how you read the blanket:

The bottom row starts with a blank space for 0.

1 is the same as the background color, since 1 is a factor of every number.

2 is turquoise blue.

3 is yellow.

4 = 2 x 2, so two sections of turquoise.

5 is green.

6 = 2 x 3, so a section of turquoise and a section of yellow.

7 is purple.

8 = 2 x 2 x 2, so three sections of turquoise.

9 = 3 x 3, so two sections of yellow.

Then I did a row of white rectangles (diamonds). Second row of color:

11 is red.

12 = 2 x 2 x 3, so two sections of turquoise and one of yellow.

13 is brown.

14 = 2 x 7, so a section of turquoise and a section of purple.

15 = 3 x 5, so a section of yellow and a section of green.

16 = 2 x 2 x 2 x 2, so four sections of turquoise.

17 is Pink!

18 = 2 x 3 x 3, so a section of turquoise and two sections of yellow.

19 is rose pink.

Next I’ll do a row of white rectangles, then start the next row with 20. The primes in that row will be 23 and 29, so I’ll have to bring in two new colors.

The color sections will show up better after I’ve knitted the white rectangles, but I was impatient to show what I’ve done!

I’m very pleased with how this is turning out. I may have to make myself a Pascal’s Triangle Shawl when I’m done….

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

Bedtime Math!

Mathematical, Prime Factorization 0

I’m so excited! Today, thanks to a note in the ALSC (Association for Library Service to Children) newsletter, I found out about Bedtime Math.

Why do I think Bedtime Math is so awesome? Because that’s totally what I did with my younger son.

My first Master’s degree was in Math, and I was a college math instructor for ten years. College students in general ed math classes are generally not excited about math. So when we started doing math problems with my excited son at bedtime — I’m not sure how it started — my son quickly learned those magic words I absolutely COULD NOT resist — “Just one more math problem, Mommy, please!” He could extend bedtime forever with those magic words.

I don’t remember how it got started, but I do know that we were in the thick of this when he was 5 years old. His brother turned 12 years old in March. I turned 36 in June. Sometime in there, I told him that when he turned 6, then his age plus his age would equal his brother’s age. But, even better, his age TIMES his age would equal my age. His next question was pretty natural, “What’s TIMES?”

One week later, his brother asked him a problem I never would have tried: “What’s 16 times 4?” Timmy (the 5-year-old) figured it out *in his head.* Without knowing times tables. So that was the context of “One more math problem, Mommy, please.” I’d give him progressively harder addition problems — and then it got to be progressively harder multiplication problems. All done in his head, at bedtime. For fun.

Of course, it all starts with counting. I remember with my older son, just counting as high as he could go in the car while running errands. It’s fun when they really realize how it works and that they could go on and on forever. He was also the one who kept making up words for “numbers bigger than infinity.” I couldn’t quite convince him that didn’t work.

(Now my younger son, a Freshman at the College of William & Mary, recently spent his free time devising an algorithm to choose a completely random book from all the volumes in the campus library. That’s my boy!)

In my current job as a librarian, I was thinking about all the counting and math we did when my kids were small. And then thinking about the Every Child Ready to Read workshops, where we encourage parents to read, talk, write, sing, and play with their kids. I’m going to do the workshop “Fun With Science and Math for Parents and Children” — only I think I’m going to take out the Science and just focus on Math.

See, the thing is, I don’t believe for a second you have to “make” Math fun. I think math *IS* fun, and children naturally think so, too. Can I communicate that to parents?

I’m also planning to do a program with older kids about using math to make coded messages with colors or shapes. It uses ideas from my Prime Factorization Sweater and my Coded Blessing Blanket. I did the program a few years ago, a little afraid I’d lose the kids, and they totally loved it.

All this is to say: Bedtime Math! YES! I can present this as an idea for parents who need help thinking of problems to talk about with their kids, who might not think them up as easily as I did. (I also taught my kids the chain rule in calculus because I wanted to teach it to someone who would get it right. But I don’t think I’ll recommend that to parents.)

I still say, as a librarian, part of my job is the FUN side of learning. At libraries, we help people find information to teach themselves. But in the children’s department, a huge part of our job is helping parents make learning a natural and fun part of their family life. We don’t have to test them! We don’t have to follow the book or the curriculum! We can show them ways to think about the concepts that are just plain fun!

I’m going to be looking for more articles about early learning of mathematics. I think it can fit in nicely with Early Literacy Skills that we emphasize so much. But mostly I’m jazzed. Other Moms are going to hear those magic words: “Just one more math problem, Mommy, please!”

Prime Factorization Blanket – First Row

Mathematical, Prime Factorization 1

So, Tuesday I posted my plan for making a Prime Factorization Blanket for my new niece or nephew. I then learned that my brother and his wife may know the baby’s gender by December 17th. Did I want to wait that long to choose the colors and start?

Short answer: No. I got to thinking: It’s not like this won’t be a very multi-colored blanket. I had thought about using shades of blue or shades of pink at the beginning, but I don’t think that’s a good plan. Since the colors represent numbers, and since a baby’s going to see this, better to have distinct colors with distinct names as the prime factors that show up most often.

On top of that, I happen to have a full skein and more of a turquoise blue left over from another project. Turquoise worked out very well as the color for 2 in my prime factorization scarf. It doesn’t cry out “boy,” but neither is it a bad color for a girl. And best of all, it goes well with pretty much every other color. (And 2 has to do that.) I decided to go with bright, rich colors for the primes that will be most predominant.

Thanks to a fairly long management meeting and a day off today where I needed to read, I’ve already finished the first row. I’m very happy with the colors! Now, the first row consists of just knitting 9 squares. The next row of white will convert them into diamonds. I’m also proud to say that I sewed in the starting ends of all the yarn. And that’s my plan to go on with: At the end of each row, I’ll sew in all the ends that were loose at the start of that row. (I don’t want to sew in the ends right next to a live stitch.) That way, it won’t be a daunting task at the end of the blanket.

So here’s the first row, the numbers 1 through 9 (0 is a blank space.), with the numbers the colors represent written on the picture:

I admit it’s getting where I’m going to have a hard time giving this away! Good thing I’ve publicly said it’s for my new niece or nephew!

And that does remind me. If you’d like your own Prime Factorization T-shirt or Tote Bag, or if you have a friend or loved one who really needs one for Christmas, be sure to check my Cafe Press Prime Factorization Store! 🙂

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

Mathematical Knitting — Blessing Blanket

Mathematical, Prime Factorization 3

Alyssa Karise is here! And her blanket is ready to send! Here’s the finished blanket. It’s actually a rectangle, but I wanted the message to be in the picture, reading from the top to bottom, left to right, so the perspective warps it a little.

I used Base 5 math to code a message into the blanket, which I explained when I started. But now I can show you how it worked out.

You can see in the picture above that the blanket makes a sort of grid. The “smooth” squares in the blanket were knitted on the back side with the stitches P3, K1, P3 (purl 3, knit 1, purl 3). There are six of these squares in each row of the grid. I knitted my code on the back side so that the words would go from left to right. I coded letters into each square this way: P1, next two stitches are first digit of letter, K1, next two stitches are second digit of letter, P1.

I used two stitches for each digit of the letter, using a Base 5 code. I used P2 for 0 (since I was on the purl side); K2 for 1; yarn over, knit 2 together (ykt) for 2; ssk, yarn over (sky) for 3; and purl cable one stitch, holding to the back (cb) for 4. Here’s how the letters were made:

A: 01: p2 k2;
B: 02: p2 ykt;
C: 03: p2 sky;
D: 04: p2 cb;
E: 10: k2 p2;
F: 11: k2 k2;
G: 12: k2 ykt;
H: 13: k2 sky;
I: 14: k2 cb;
J: 20: ykt p2;
K: 21: ykt k2;
L: 22: ykt ykt;
M: 23: ykt sky;
N: 24: ykt cb;
O: 30: sky p2;
P: 31: sky k2;
Q: 32: sky ykt;
R: 33: sky sky;
S: 34: sky cb;
T: 40: cb p2;
U: 41: cb k2;
V: 42 – cb ykt;
W: 43: ykt cb;
X: 44: cb cb;
Y: 100: k2 p2 p2; (I knitted this as k2p1 (k1) p3, leaving the garter stitch in the middle.)
Z: 101: k2 p2 k2.

Here’s what I planned to have the blanket say (I added Alyssa’s name at the end when it was clear what that would be. Fortunately, I was knitting from bottom to top.):

Alyssa Karise,
Grace and Peace.
Grace and peace to you from God our Father and the Lord Jesus Christ.
Grace and Peace.

When I had the blanket all finished, ends sewn in, and I laid it out to take pictures — I discovered I’d left out a word! Urgh! But it’s still a Blessing Blanket. And I still thought about and prayed for Alyssa as I knitted. And it’s still warm and soft. I’m not going to say what word I left out, because I want to see if the baby’s parents can “read” it well enough to figure out! (I’m bad!) Astute readers of this blog who possess really really good eyesight might be able to tell as well.

To see how the coding actually looks, I took pictures of the top three rows. Here is AL – KA – GR:

Since the stitches are done on the purl side, k2 gives you straight bumps. So A = p2 k2 gives you a smooth panel, then bumps. L = ykt ykt gives you a hole from the yarnover, then two stitches together, in both sides. On the second row, K = ykt k2 combines both of those. Then we have A, which looks just like the first A. The third row has the same combination reversed in G = k2 ykt. Then R = sky sky. With sky, the stitches are knitted together before the yarn over, so the hole is on the right of the combined stitches.

The next section shows YS – RI – AC, and a fourth row, ND:

Y = k2 p2 p2, so I started on that first stitch I usually leave a purl stitch. So it looks the same as A, only shifted over one stitch to the left. S = sky cb shows us our final “digit”. The cable in back comes out as one stitch going over another with no hole. The second row is easier to see. R = sky sky, so you can see both sides have the hole on the right. Then I = k2 cb, and you can more easily see the cabled stitch crossing over. On the third row, we have A = p2 k2 and C = p2 sky. The fourth row, the end of the word AND, gives you a nice look at the cables again, with N = ykt cb and D = p2 cb.

I’ll give you the end of the top three rows, but I’ll leave it to the reader to work out that at least I didn’t make a mistake on the top of the blanket:

Making this was so much fun! In fact, I’ve been dragging my feet about sending it on. But tonight I noticed that the yarn label happens to have a pattern for a one-skein scarf, and I happen to have one skein left. So perhaps making myself a scarf out of this wonderful 85% cotton 15% angora yarn (Serenade) will remind me to send thoughts and prayers and blessings to my sweet little niece, Alyssa Karise.

And, meanwhile, my brother announced that his wife is expecting a baby. His baby needs a prime factorization blanket! I am swatching to figure out how best to accomplish this, and will definitely be letting my readers know!

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

Review of How Many Jelly Beans? by Andrea Menotti, illustrated by Yancey Labat

Children's Nonfiction Review, Mathematical, Starred Review 1

How Many Jelly Beans?

A Giant Book of Giant Numbers

by Andrea Menotti
illustrated by Yancey Labat

Chronicle Books, San Francisco, 2012. 26 pages.
Starred Review

Hooray! A book that really shows how completely huge the number one million is!

The story is simple. Emma and Aiden (with thoughts expressed by their dog) are asked how many jelly beans they’d like. Emma starts with ten, and we see a close-up of her hand with ten jelly beans.

Aiden, however, wants twenty, and the picture shows that, with ten in each hand.

Emma’s response seems quite realistic for a kid. “He can have twenty? I’ll have TWENTY-FIVE!” The responses escalate: fifty, seventy-five, one hundred. All of those amounts are shown on a tabletop. Since the tabletop in the pictures is the same every time, just with greater or fewer jelly beans distributed across them, this doesn’t really show the quantities viscerally. However, that will change by book’s end.

I like it when they get to details. Emma tells Aiden he can’t eat five hundred jelly beans, and he tells her that in a year he could eat a thousand jelly beans.

On the next big double-page spread, we see jelly beans distributed on pages of a calendar. Emma says, “Wait a second. That’s only two or three jelly beans a day.”

She comes to the logical conclusion: “I could eat FIVE THOUSAND jelly beans in a year.” Now the view pans out to Emma happily jumping on a bed covered with five thousand jelly beans. (Never mind that they would scatter all over the place if she really tried that.)

They go on. Ten thousand jelly beans. A hundred thousand jelly beans. Now the children are shown as quite small, with a hundred thousand tiny jelly beans spread out around them. I like it when Aiden tells us how he’d distribute the flavors if he had a hundred thousand jelly beans. Only one would be lemon.

But the truly marvelous part of this book, the tour de force, is the foldout section showing ONE MILLION jelly beans. In fact, when you first pull it out, the kids are saying, “Wow! A million jelly beans is a lot!” But then they say, “This is only HALF a million jelly beans! Look up there!” When you unfold the page further, then, at last, you see a million tiny jelly beans.

So here, at last, is a book that allows you to see one million things at one glance. The only way to truly give you the feel of this book was to take a picture:

Here’s the book closed, already an extra-large format:

And here’s the book opened up, showing a million jelly beans. I can hardly hold it up:

Now, I’ll be the first to admit that this book is not going to hold up well to library usage. It was not easy even for me to hold up the book with the page open without tearing the pages. And if you tear the page along the folds, it’s not going to be at all easy to mend.

But you know what? I don’t care! I love that someone did this, that Andrea Menotti and Yancey Labat made a book that truly shows kids just how enormous a million really is. And maybe, just maybe, a million jelly beans would be too many.

chroniclekids.com

Buy from Amazon.com

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

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

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

Disclaimer: I am a professional librarian, but I write the posts for my website and blogs entirely 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.