# Polyhedra in the Meantime

Here’s another post that languished without me getting around to posting it for a couple of weeks.  But hey, now it gets to have a pretty picture of some geometry adorning our Christmas tree, so it’s more festive now anyway.

BalletBoy has hit a bit of a math wall.  He’s been slowly trudging his way through Math Mammoth Blue.  He made it through nearly all of the parts of the various special topic books, like Clocks and Measurement, and through both the Place Value 3 and Multiplication 1 books, which are the heart of the third grade sequence, along with Division.

Then we hit a snag.  He knows his facts, but memorization has never been his strong suit.  He can run through the whole multiplication table with the flash cards in about six minutes.  But it’s not good enough to get him through division, which is so slow it’s at frustration level for him.  He’s only made it through half of the book and the second half will be even slower going.  Thus the the need for some breaks.

In the meantime, while we run drills and practiced things, we’ve had more of a chance to look at some of our other resources.  For one thing, we revisited geometry and make a little booklet of the polygons with cute smiley faces.  Then we did a shape scavenger hunt and made a little picture of them all outlined.  The tiles in the Metro are all hexagons, you know.  We also found areas and perimeters and played around with graph paper.  Some of the popular Sir Cumference books have been read recently here for this, though we’ve also been reading The Number Devil aloud as well, so math read alouds have abounded.

Also for geometry, we made the polyhedra models we’d skipped in Math Mammoth earlier.  I went to Worksheet Works to print out a bunch.  The kids made cubes, tetrahedrons and octahedons.  I made a truncated icosahedron, otherwise known as a buckyball.  When we colored them, they came out so pretty that the Husband said they should be Christmas ornaments, so we made some more for the tree.  That’s an icosahedron decorating the tree there.

We played around with measuring a little more and have especially enjoyed doing a few of the measuring dot to dot puzzles found at Math Pickle.

We’ve also finally started doing Ed Zaccaro’s Primary Challenge Math.  I saw Ed Zaccaro speak at a conference last year and just loved all the things he had to say about math and problem solving.  I had been concerned that some of the stuff in Primary Challenge Math might be too challenging, but it has turned out to be the opposite.  It’s perfect fun math for my kids.  As we’ve gone back to the Singapore Challenging Word Problems a little more, I’ve found that one of Zaccaro’s strategies, to plug in easier numbers for more challenging ones, has worked really well for BalletBoy.

# Math Split

Well, it’s happened.  Mushroom and BalletBoy have been on different levels with different things for awhile, even using different things occasionally.  However, biting the bullet to do two different paths with math feels like a big leap for us.  But we’ve done it.

BalletBoy’s Math

BalletBoy is continuing with Math Mammoth.  We use the blue series, which breaks the topics up into separate books.  He’s currently working on Place Value 2 and Addition and Subtraction 2b, with a little bit of Introduction to Fractions thrown in.  He’s also working on the Singapore Math Challenging Word Problems.

I’ve never done much of a post reviewing Math Mammoth here, but I just want to sing its praises for a moment.  I really love how Math Mammoth takes a topic and slowly teaches and circles around different ways to approach it.  The books are deceptively simple.  When I first began using it, I was concerned that they were too simple and that they were too structured.  I worried it wasn’t conceptual enough.  However, I have come to see that by giving kids really incremental steps, letting them have a crutch, such as an intermediary step in a simple problem, then gradually taking it away, is really useful for many kids.  I think that for really math-loving kids or kids who like solving problems or intuit steps, it would be tedious, but for BalletBoy it’s just right.

We’re also really enjoying the Challenging Word Problems.  He’s doing them a year behind, so he’s about halfway through the first grade problems.  I know they’re just first grade math, but occasionally the challenge problems make me pause and think for a minute before I’m sure I have the answer!  It scares me a bit for the future.  If this is first grade math, what will it look like in fifth?  Nonetheless, I’m really impressed with how these have taught BalletBoy how to break a problem down and show his work.  He doesn’t always get the challenging problems right, but he’s getting better at them.

As always, we read math books and play games.  BalletBoy kicked my butt in Corners the other day and he honed in to read about negative numbers with Mushroom on the sofa too.

Mushroom’s Math

Math Mammoth and Challenging Word Problems was not working for Mushroom.  Or rather, sometimes it was fine, but a lot of the time, it was a disaster.  He would get 20 problems right, then after finding out he got one wrong, he would get the next 20 all wrong, as if he was trying to prove to me that he was wrong all the time.  Basically his anxiety was kicking in, stopping him from finding any success.

So I decided to let him catch up with Miquon.  Because we were never using it as our primary program and only doing it occasionally, he’s only halfway through the second book, the Red Book.  I bought the next two, but it’s good that he’s only in the Red Book because he needs some confidence builders.  I also bought him another confidence builder, the Usborne Big Book of Sticker Math.  This is mostly first grade math.  It’s simple stuff, but he seems to like it.

I also bought him a math journal.  Here’s some of the things we’ve put in it so far:

• math using dollar and coin stickers
• a couple of brain teasers
• living math books based math – for example, we read Loreen Leedy’s 2×2=Boo at Halloween then he practiced easy times tables in the journal
• shopping math with the Lego catalog
• practice math for more practice so he can keep getting more fluent with math facts
• Miquon-like lab sheets

I want to do more with the math journal.  A thread on a certain forum pointed me to this page, where most of the stuff is a little too easy and not exactly my style, but gives a few starting point ideas for younger kids doing math journals.  Blog, She Wrote also has some good math journal related posts.

I want to keep up the Miquon, but one of my main things for Mushroom is the realization that while it’s more work for me, he really needs to be seeing lots of resources, doing things in a more spiral way.  It grates on me, really.  I believe in mastery.  But I also believe in teaching the kid you’ve got.  If Mushroom needs me to alternate between games, storybooks, worksheets, manipulatives and back around again, then I guess I’ll do it.  I’m looking at resources like Games for Math and Family Math for ideas.

To round things out, I’m upping the math games for Mushroom, especially games like the RightStart card game Corners and the game Knock Out, both of which encourage kids to be able to break numbers up and see their relationships more easily.  I also have ordered him addition and subtraction wrap-ups, which a friend showed me, but we don’t have them quite yet.  I’m letting him play more math games online.  He usually goes to Sheppherd Software, which has a whole lot of games and links to more.  I’m especially fond of this one, which allows kids to practice facts quickly.  Free Rice is another good quick resource for math practice, one with a nice social benefit (they donate rice to people in need).

In the end, I’d like him to end up in more or less the same place as his brother at the end of the year, so I’m looking at BalletBoy’s Math Mammoth table of contents as a guideline for skills I’d like him to achieve.

# 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.

# Mobius Strip Math Book

We read Zachary Zormer, Shape Transformer by Joanne Reisberg the other day and really liked it.  It’s from the same imprint that does the much better known Sir Cumference books.  This book dealt with mobius strips, as well as length, perimeter and area.  Zach keeps forgetting his show and tell math homework, only to turn scraps of papers and a small penlight into fabulous tricks for his classmates, upstaging his rival each time.

Of course, we immediately had to make our own paper tricks like the ones in the book.  This is one of the things I love about homeschooling.  I saw the book in the library and, being a lover of math picture books, I took it out.  We sat down to read it on the sofa for school and an impromptu lesson was born.  No prep work.  Just school fun.

Math picture books for kids are some of my favorite things.  I was glad to discover that Charlesbridge Publishing has so many more that I haven’t even read.  Of course, there are many other good “living” math books, such as MathStart books, Greg Tang’s books, Loreen Leedy’s math books, Mitsumasa Anno‘s math books and many more.  I’m also especially fond of the old Young Math Books, which go into a pretty high level of depth.  So here’s to real books instead of textbooks teaching about math.  Not that there’s anything wrong with textbooks, we like those too, just that I love these gentler approaches for kids who like to learn by curling up to hear a story on the sofa.