My musical friend Christi Gell sent K8 and me a delightful math picture book recently. One Grain of Rice, by Demi, is both visually and mathematically beautiful.
It’s exponentially better as you read it.
And that’s not a figure of speech! One Grain of Rice is the story of a girl that asks for a simple reward for a good deed. She asks for a single grain of rice on the first day and for 30 days, double the amount of rice given on the previous day.
I’ve heard this story told in a variety of ways, but the illustrations and scenario of this book make it appealing in ways that outshine all the rest.
The illustrations have a gold-leaf feel about them. And Demi shows the quantity of rice very literally, down to multi-page foldouts showing exactly how many animals it takes to carry that day’s amount of rice!
It starts small.
Here you see her getting “help” carrying the rice from various animals on the 9th, 12th and 13th days.
And on the 16th day, she really needs this help!
Soon the raja’s getting worried.
By the 24th day, she’s needing to borrow deer from the raja to carry it!
By the 30th day, she needs 256 elephants to carry it all. And all 256 of them are shown in a gorgeous 4-page foldout!
Don’t miss this math picture book!
One Grain of Rice is also the tale of a greedy raja that learns a lesson through the cleverness of a girl. The magnificient illustrations help kids (and grownups) see the magnitude of exponential growth, without even putting that label on it.
Head out now to get your own copy of the math picture book One Grain of Rice, by Demi. And send a copy to an artistic or mathematical friend too!
I rounded the corner at Barns & Noble one day and and this beautiful math picture book looked me in the eyes.
I just couldn’t resist buying Perfect Square by Michael Hall!
And what a treat it was!
It’s inspiration for math crafts, playing with color and patterns and talking about shapes – all in one neat little package!
A happy little perfect square gets cut, torn and shredded over the course of a week. But this optimistic shape uses the “abuse” to make itself into new and fun things each time.
Construction paper and scissors…
I made a bunch of squares from construction paper to start. With each page, I replicated the images.
One day the square gets cut into two triangles and crumpled up. So it makes itself into a mountain. This one was fairly easy.
Another day it was shattered, so it made itself into a bridge. The shattering resulted in 24 pieces – each a triangle or trapezoid. It was especially hard to do, so I’m sharing a picture of the bridge in this math picture book.
Another day, Perfect Square was cut into ribbons with crinkle shears and makes itself into a river. Long thin “mostly” rectangles were fun to do when I found my old scrapbooking scissors.
Are you ready to play?
I had a great time cutting each shape and seeing how I could replicate the images in the math picture book, Perfect Square. Some were easy, some were hard.
What can you do? What can your kids do? I’ll bet their creative minds go all over the place!
I love how Linda Gojak calls juicy, meaty problems “rich problems.” A good, fun thinkable is indeed a math word problem rich with problem solving challenges.
But getting started on a rich problem can leave you feeling rather poor. So Chapter 3 gives, and is called, “Getting Started Strategies.”
What’s that problem about anyway?
The first question you (or your child) should ask when given a problem is, “What’s it all about, anyway?” This is the strategy of “Restate the Problem in Your Own Words.”
Ask
What’s happening — what does it look like?
What bits of this problem are useless to me?
If a normal person were to ask the question, how would it be written?
Now what the heck does it really say?
Restating the question in your own words means understanding what’s being asked and what’s happening.
Is this a trick question?
Sometimes textbooks (and even life) give you problems without giving you all the required information. This is grownup-talk for what kids call a trick question.
If there’s missing information, call that bluff! What info do you need to calculate the final answer?
Is that information contained in the problem?
Can you find that information online or in a library?
Can you figure out that information using other stuff in the problem?
Is it just a flat-out trick question — there can’t be an answer because there’s no way to get the information needed?
Calculate the information, if you can.
Now it’s time to do a little pre-work. Gojak calls it “identifying a subgoal.”
If you’re missing some numbers in the problem but you can get these from others, then start calculating.
I walked 30 feet and then walked another 24 inches. How many feet did I walk?
The subgoal here — figure out how many feet I walked the second time.
Figure out how to show your work — or not?
One of the strategies in chapter 3 is “Select Appropriate Notation” — which means determine how you’ll show your work.
But first ask the question, “Do you want to show your work?”
Here’s the big place where classroom schoolers and homeschoolers will diverge. It isn’t really necessary to show your work. Ever. And in homeschool, children don’t have to.
If you want to show your work that’s great. If you want to share your work, you have to show your work. If you want to be a famous mathematician or even a run-of-the-mill engineer, you have to show your work.
It doesn’t hurt to learn to show your work. But it’s not required to be a great problem solver.
In fact, if your child struggles with notation, and you push this too hard, their developing problem-solving strategies could be stunted.
But should you show your work for other reasons?
Gojak writes:
“…you use notation to help you reach a solution.”
This is not necessarily true. Some people do. I don’t. The problem-solving strategy that works for me is doodling pictures and trial and error, strategies covered later in the book.
I rarely solve a problem using x and y — or even crude representations of x and y like question marks or blanks.
If you feel the need to verify that your child is thinking properly, ask them to explain it out loud. Or give them another rich problem. Don’t force them to show their work because you want to see it.
Read more about it…
Don’t forget to check out Math Coach’s Corner for some other thoughts on Chapter 3 of What’s Your Math Problem? Make sure to scroll to the bottom, because others are linking up their thoughts and opinions!
The first thing you see in this math picture book are the bright but simple images. Looking at them you feel like you’ve stepped into the surreal world of those old View-Master reels.
The rhymes are catchy and cute!
I’m all about iambic pentameter. Well, I really don’t know exactly what that is, but it sounds like it means bouncy poetry.
And that’s what this math picture book has!
While scallops on the beach look great, I’d rather see them on my plate.
Unfortunately it’s their loss, They swim their best in butter sauce.
Oh, but the counting’s even better!
Each page has objects (fruit, bugs, dice, etc.) spread out so that children can experiment with different ways to “see” how many there are. You can subitize, group, multiply, subtract – or do them all!
The answer key in the back helps you understand the intent of the authors.
But I recommend you try various ways yourself before turning to the back. Some of their methods were very different than what I came up with.
And you can try it at home!
There are 16 different pictures and riddles to practice on. But it doesn’t have to stop there.
You can do your own playing at home. Check out the grapes I did here:
I put this list together on Amazon when I was teaching at the Art Institute of Houston back in October 2002. I wanted the library to purchase a few – but they bought them all!
It was fun to go through the list and see what I’ve read and haven’t read. And what’s still around!
This post originally appeared on The HSBA Post on February 28, 2012.
When I opened Katy & The Big Snow by Virginia Lee Burton to find some math, I was shocked. I didn’t have to look far at all – it was everywhere!
Math is disguised in all sorts of fun places in this beautiful book!
Katy includes graphing!
The book starts off with the map of the city. Maps are graphing.
And when the city is shown on other pages, if the orientation is different, a compass is shown to indicate direction. The compass represents the x-axis (N/S) and y-axis (E/W). It also shows the 360º in a circle.
When Katy (the tractor) is introduced, you can see lots of symmetry – especially in her big snow plow. Symmetry is another important concept in graphing.
Factors and multiplication are in the book.
Katy’s features are outlined in the margins and include her horsepower. Instead of merely writing “55 horsepower,” Burton illustrates it with 55 horses, and they are counted in 5s.
Skip counting like this shows factoring as well as multiples (which are used in finding the GCF and LCM – remember those?).
And Burton doesn’t just stop at 5 and 10, she illustrates and counts all 55 horses.
(Note: I put the red circles on the images.)
So when you read Katy & The Big Snow with your children – you can support their math learning by seeing and saying the math in the pictures!
Share your thoughts and experiences in the comments!
This post originally appeared on The HSBA Post on December 29, 2011.
The Story of Ferdinand, by Munro Leaf, is a tale of mistaken identity: Ferdinand is a sweet bull who loves to smell flowers and has no interest in anything remotely violent. He is selected to be part of the Madrid Bullfights due to an unfortunate event with a bee.
I’ve enjoyed this book since I was very young. The nifty thing is the breadth of teaching opportunities Ferdinand gives us. There’s even math in it!
To integrate math in this wonderful tale, try using some of these questions when you read the story:
Distance
Where is Spain? Where do we live? How far away is Spain from us?
Height
Look at the page where it shows how tall Ferdinand is. How many marks are there on the tree stump? How long was the time between each of the measurements? Is that equal? Would there be a better amount of time between each mark?
Suppose the marks for Ferdinand’s height were at 6 months, 1 year, 1.5 years and 2 years. Approximately where on the stump would those be?
Amount
Five men came to to pick the “biggest, fastest, roughest bull.” Why do you think there were five?
How many Banderilleros are there? How many Picadores?
Page Numbers
Most books have page numbers. Ferdinand doesn’t. Why do you think that is? How many pages is Ferdinand? Could the book be written in fewer pages? How would that be done?
What’s next?
You can use the book Ferdinand and these math stimulators in your Five in a Row math day or integrate it into any other math curriculum. Or do it just for fun! Also try doing math with other picture books you have.
Oh – and don’t forget to share how it went in the comments!
Last minute shopping? Me too! How about some of these math gifts for your favorite folks…
For Kids
Numb ‘n’ Number by Peter Weatherall – A collection of fun math songs.
Worms! What kid doesn’t like worms? And these are measuring worms!
For Grownups
Math T-Shirts by ExBoyfriend Collection – Sad? Funny? These are cute for even the “non-math” people.
Want something a little more fancy? How about math jewelry like this Fibonacci necklace!
For Families
Math games are great for full family fun – and games like Uno… well, that’s math too!
For Math Geeks
Old math books! Husband found a College Algebra book from 1947 for me – gave it to me as a “just because” gift. Here’s a Trig book by the same guy. You probably can get an old math book for your favorite geek at any second hand book store!
Math Music! The Klein Four Group’s instant download Musical Fruitcake CD (I just downloaded it, myself!) To give you a sample of how cool these guys were (they are now professors all over the world), here’s a fun Christmas song from them:
How about it – what are you up to for last minute shopping? Are you done?
This post originally appeared on The HSBA Post on November 22, 2011.
How to Make an Apple Pie and See the World by Marjorie Priceman is an “instructional” picture book that takes children on a journey through the world to pick up ingredients to make an apple pie.
Lots of great shapes!
An apple pie recipe is included in the back which has obvious math. But you can use the rest of the book for some math lessons as well!
Here’s a set of math stimulators to share with your kids. Don’t forget that math is a discovery process; if your children are compelled to answer a question or not answer a question, that’s okay.
Here are the questions and some hints and coaching tips for you, the parent.
Find the shapes in the pictures.
See if you can find circles, trapezoids, ovals and rectangles. Also identify the irregular shapes. Have your children trace them and see if they’re made up of regular shapes.
How far is it from your house to Europe?
Also ask: How fast will the ship have to go in order to get to Europe from your house in six days?
How many Italian words do you think you would need to learn each day in order to speak Italian?
How many words are there in an average Italian’s vocabulary? How many words do you need to be considered fluent in Italian?
What time does your train leave Italy?
Notice the time on the clock.
This one encourages children to look at the pictures as well as the text. Also ask, “How far is it to France from Italy?” And to take it farther, “What time would you arrive in France?”
How far is Sri Lanka from France?
Pull out an atlas or globe to get some geography lessons. Also ask, “Which route do you think is the fastest to get there? Which would be the most fun?”
If you were to make two apple pies, how many apples should you pick from the apple tree?
This is what many students would call a trick question. In the book, she picks 8 apples so that she and her friends can enjoy 3 and use 5 to make the pie.
It takes some thought for a child to realize you only need 5 apples for the pie, so you’re not doubling the amount you pick. You have to double the amount for the pie (2 x 5) then add the 3 apples for the friends to enjoy.
Looking at the recipe, how much of each ingredient would you need if you made two pies?
This question allows them to double everything on the recipe. You can also triple or quadruple or get into fractions by asking, “What if you made one regular sized pie and one mini pie – how much of each ingredient would you need then?”
