Do More Math Projects

I think when we think of projects, history, science, nature studies, electives, and so forth are the first things that come to mind. However, I’ve been making a concerted effort to do more math projects lately and I really want to advocate for engaging with math in that way. It’s fun and adds another dimension to math. It helps show how math is relevant to other subjects and everyday life. It shows how math can be artistic and useful.

So far, we’ve been enjoying a few different resources for math projects and I thought I’d highlight them here.

Time Travel Math
This is a great book from Prufrock Press, intended to be used for gifted fourth and fifth graders. There is a loose story about a pair of twins, Harriet and Thomas, who find a secret way to travel in time, but only if they’re wondering about math. The story is cheesy, but it’s not at all poorly written, which helps it work. They travel in time three times, first to learn about ratio with a young Leonardo da Vinci, next to learn about geometry and tessellations with a young M.C. Escher, and finally to learn about area in ancient Egypt with Imhotep. Each section has questions for students to think about as the text tells the story and reveals the math. Those are followed by either short math labs or activities about the topic and then finally by a much longer project. For ratio, students make a giant object. For tessellations, students make a quilt out of tessellations. For area, students make a mobile to balance shapes. I highly recommend this book. We’ve finished the first two sections and are looking forward to the third. I think the recommended ages on the book is probably a little too narrow. The projects and math could be right for kids any time from third grade to before formal algebra, at which point the concepts would be too simple.

Math Projects Series
This series is out of print, but most of the titles can be found inexpensively. There are titles about making math games, making kites, designing playgrounds, and designing houses. We have tried out two of them – one about designing playgrounds and one about designing houses. I especially liked the way that the playground book led the kids forward with different activities, considering how playgrounds are used and playing around with simple shapes for design. This is the piece of doing a math project that I think I didn’t initially understand. Doing questions beforehand and practicing the concepts isn’t busywork or wasted time. It’s time kids need to understand the math and get the most out of the project. Unfortunately, when we went to use the houses book, we were very disappointed by the vagueness of the instructions and ended up ditching it. Still, I would like to see the math behind the kites and bridges books because I like the goal of the series.

GEMS Guides
These are math and science guides for elementary and middle school with hands on projects for kids. There are ten math guides in all with different age ranges and topics, including combinations, probability, algebra, and polyhedra. We used Math on the Menu, which is about combinations and have a couple more on tap and are looking forward to them. Again, the key thing provided is support for how to think about the math as you do the project. The projects for the ones I have are much more process oriented with less of a final product at the end. For example, in the combinations one we did, there was a story and a number of problems revolving around it, but no product at the end to show off. These books require more tweaking for the homeschool classroom since part of the GEMS philosophy is having kids all share their methods and approaches in finding different answers. Two of the GEMS Guides, about cooperative logic problems, are probably not really adaptable.

Amazing Math Projects You Can Build Yourself
This book is filled with many different ideas for math projects, such as making your own abacus or playing around with polyherdra models. Unlike the other books mentioned, there’s less building up of specific skills by slowly structuring the project to have more meaning. Instead, there are just many different ideas for every sort of math all thrown together. This is more like a book of ideas than a guide. It’s written to the student with text about the projects that explains the math or the connections with history, art, or other subjects. Some of the “projects” are extremely fast and simple while others are more involved. If you’re looking for something to get the juices flowing for doing more hands on math and mini-projects, then this is probably a very good starter book.

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Weird Math

We’ve been doing “fun” math word problems here lately.  I think nearly everyone in homeschooling already knows about Ed Zaccaro’s great series of books, including Primary Challenge Math, but in case you don’t, his books are wonderful.  I have been looking forward to using Primary Challenge Math for awhile.  It explains a type of problem, then gives three different levels of problems about it.  It’s hard to say exactly what makes it so appealing.  The math isn’t so different from what’s in many quality word problem sets.  However, the way Zaccaro lays it out is fun and engaging and not overwhelming at all.  The boys have enjoyed this.

Second, we have done a few problems from the bizarre book The Book of Perfectly Perilous Math.  The problems in this book all involve monsters and impending doom.  If you can solve the problem, you’ll survive and if not, then you’re done for.  Each problem also includes a math lab to explore, which is fun.  We got this at the start of the year and have only done a few, but it’s been a neat thing to have on hand.  Some of the problems, such as about probability and statistics, will be better suited to fourth grade anyway.

Finally, I have finally taken out an old favorite of mine, Louis Sachar’s Sideways Arithmetic from Wayside School.  I adore this book and used it for fun when I was teaching sixth grade math.  I haven’t seen people mention using it as a resource, which makes me sad.  More people should know about it!  The opening chapters give math problems where each letter stands for a digit 0-9 and you have to figure out what each is by looking at the whole problem.  For example, four + eight = twelve and elf + elf = fool.  It’s good mathy fun.  The rest of the book gives amusing logic problems.  It is already a big hit here.

I Love Math Books

I heard about the I Love Math series through the Living Math website awhile back, but I didn’t immediately bite and buy them.  Despite their praise-filled reviews, I couldn’t quite get a handle on what these looked like and what they might contain.  Because they were sold as Time Life book sets about twenty years ago, I suspect you’re unlikely to find them in many libraries (they weren’t in ours).  However, I finally bought a couple of them – Look Both Ways and Do Octopi Eat Pizza Pie? and was glad I did.

Each book has a lot of different things all around a central theme.  The theme in Look Both Ways is cities.  There are mathy poems and stories that take place in cities, math puzzles and problems, and math games.  Different parts of the book are done by different illustrators and writers in somewhat different styles.  One page is photos of buildings encouraging readers to find different shapes and look at symmetry.  Another page is cartoon animals in a story about directions through the city.  The table of contents as well as small notes at the bottom of some of the pages explain what math is being covered by various activities, such as odd and even numbers, addition and subtraction, geometrical shapes, money and so forth.  In some ways, we’re already past these, which is too bad.  I think they’re mostly K-3rd grade math and some of the things in them will be too simple for Mushroom and BalletBoy.  However, they’re appealing to kids and have a sit down and browse feel.  They introduce some solid concepts so I may get more, especially for Mushroom.  You know, as if we didn’t have enough living math books already!

Mushroom’s Math

I posted before about how Mushroom has split off for math.  We’re doing a whole spiraly, roundabouty, wibbly wobbly timey wimey curriculum.  And while I usually adore things that are wibbly wobbly timey wimey, I would much prefer to do something more straight up Asian mastery style.  But, hey, you take the kid you’ve got, right?

We’re doing a hodgepodge of things.  He keeps a math journal, in which I put quick drills, a few “challenge” problems, some money math, some catalog math, and a whole bunch of other things.  He’s continuing through Miquon and is almost done with all of the Red book and moving into the proper second grade Blue book.  He’s also playing games a lot more and doing well at them.  We have the Right Start Games, and while I knew the Right Start Curriculum wasn’t for me as a teacher, we’re enjoying the games a lot.

Below you can see a selection of the sort of math journal pages we’ve done so far, in case you’re curious.

 

But here is the lovely thing.  He seems to be less afraid to do math and put out an answer.  I have discovered he actually likes having a math “drill.”  He understands that it’s practice of ideas he already learned and seems to get that if he makes a mistake, then it’s just a mistake, not a total failure of concepts.  What an amazing thing!

And he occasionally makes some great leaps.  We read The Greatest Guessing Game, which is a Young Math Book (I know I’ve said it before, but I’ll say it again: I adore the Young Math Books!) about division and Mushroom began dividing things left and right.

He has been doing more real life math more comfortably.  The other day, after doing arrays in Miquon, he arrayed the Christmas cookies.  He added up the money he had spent for Christmas so far as well.

But here is the best bit.  I apparently checked out a book quite a long time ago from the library and then lost it (it seemed to have fallen into a funny corner of the car during transport).  It was an early 80’s title with slightly psychedelic monster illustrations called Crazy Creature Number Puzzles.  It’s possible for me to not known when it came from because our public library does not assess any fines on juvenile materials.  I know, you’re jealous, right?  Anyway, I discovered it from who knows when and instead of returning it (I’ve probably accidentally renewed it too, anyway), I made Mushroom do some of the problems in it.  They’re easy enough for K-2nd grade math, though they’re tricky enough that it might take you a minute or two to figure them out (well, not most of them, but a few of them took me a minute or two).  But he did them!  And then he said to me when I assigned some more, “I really like those Crazy Creature Number Puzzles.”  Yes, that is a direct quote that I have not made up.  Really, this was his biggest hurdle, being able to be patient enough to sit and think through a problem and try different solutions until he got the right answer.

So I’m feeling pleased with the less curriculum approach right now.

PS – Sorry if the image sizes are a little wonky.  There’s some sort of image sizing bug on my blog!

More Living Math Books

Yes, I’m obsessed.  But honestly, it’s a case where the way my kids learn and the way I want to teach happily coincide.  They always want to hear “living” math books.  I always want to read them.  They retain the information reasonably well and, best of all, they’re completely open to hearing about new math concepts through math story books.  Here’s a few that we’ve been reading recently:

 

You Can Count on Monsters by Richard Evan Schwartz
This is such a unique and unusual little book.  I was a bit blown away by it when I first saw it.  The style is bold and colorful with really weird monsters.  It was clearly created on a computer with a graphics program.  The first dozen or so pages introduce the idea of prime and composite numbers and give kids some basic ways to think about them.  Then, each number from 1 all the way up to 100 gets a two page spread.  If the number is prime, then it gets its own monster, with some characteristic that indicates the number (you have to hunt to find it for some of them).  If the number is composite, it gets a factor tree, dots arranged to depict it and the prime monsters from its factor tree playing together in the picture.  Or, as in the image above for fourteen, you get a funny configuration of the monsters together (that’s seven eating two).  There’s no text after that first introduction so it’s not really a story, just a fun little book.  Mushroom and BalletBoy really liked going through it and I think it’s one we can do again when they’re doing more multiplication and division than they are now.

  

Animal Babies Math series by Ann Whitehead Nagda
We haven’t done all of these books, but we have done several of them now.  Each title features an animal baby in a zoo (a panda, a tiger, a polar bear…) and a math topic (subtraction, division, time…).  The format is very interesting.  On the left page, it tells the story of the animal’s growth in math terms.  On the right page, there’s a narrative account of the animal’s growth.  I really like that the books have that extended narrative since it makes them good for reading aloud.  I also appreciate that the books give different ways of thinking about topics.  For example, in Panda Math: Learning About Subtraction from Hua Mei and Mei Sheng, the book introduces several different algorithms for subtracting different types of numbers as well as different graphic representations.  The numbers presented in the book gradually get harder to deal with as well.  The focus is obviously on applied math in these books.  They aren’t my favorite fun math books, but they’re good and Mushroom is especially fond of them.

Youth Math Books brought to you by the 1970’s
I’ve mentioned these books a few times.  You can find a good list of them at this site, which is apparently mostly defunct but still maintains some good book recommendations. We discovered a new cache of them at the library (our library rotates much of its children’s collection because it’s so large) and have been reading a few more of them.  These books introduce all kinds of math concepts, including a few that are typically thought of as more complex, for elementary age children.  They’re are sadly out of print, but you can find many of them through your favorite used book sources.  This time around, we especially enjoyed reading Less Than Nothing is Really Something by Robert Froman, which was about negative numbers.  I also really like Base Five by David Adler.  To me, these books, along with Miquon and a pile of Cuisenaire rods, represents the best that (old) new math had to offer.

Math Picture Books

We’ve gotten back to math picture books in the last week or so.  Last year, we didn’t do a formal math curriculum for kindergarten, so games and picture books were a cornerstone of what we did.  This year, we’ve moved away from using them, but I picked out a few things at the library and pulled some stuff off the shelves and I was reminded of how much fun math picture books can be.  There are many, many math picture books, but here’s a few of our favorites.

Uno’s Garden by Graeme Base
This little tale is part environmental parable, part seek and find book and part math.  The numbers of all the different elements in the story ascend and descend in different ways – counting, doubling, prime numbers, multiplication.  It’s a fascinating little book that can be read again and again for different elements.

One Grain of Rice by Demi
Demi is such a great illustrator.  I like her detailed art with its Asian influences.  The kids like her use of shiny gold.  She’s also a good storyteller.  This book tells an old folktale with a mathematical lesson.  As a reward, the emperor agrees to give a woman a single grain of rice on the first day and double it every day for a month.  Obviously, emperors should be made to study more math.

Anno’s Counting Book by Mitsumisa Anno
Any of the Anno books could have made my list.  We own two of the Anno’s Math Games books and I also think Anno’s Counting House is an excellent book for learning what combinations of numbers add up to ten.  However, we’ve been enjoying simple numbers this week, looking for patterns and counting things out.

Math-terpieces by Greg Tang
This is one of the kids’ all time favorites.  Each page shows a famous work of art and an element next to it you need to group into certain numbers in different ways.  Such as finding four ways to group Monet’s water lilies so they make eight.  Greg Tang has other math picture books, but this is by far the best, especially for younger kids.  I can’t sing this book’s praises enough.

More, Fewer, Less by Tana Hoban
We use this book much the same way we use Anno’s Counting Book, by looking at patterns and counting out numbers.  The book contains only photographs without text.  The reader is invited to compare sets of things in the photos – such as different colors of shoes or sandals to boots.  I also ask the kids to find certain numbers of things.