Math Lately

Mushroom plays a symmetry game in Beast Academy.

We have bounced around with math so much more than I anticipated this year.  I thought I’d post about all the various things we’ve ended up using and where we landed.  Math continues to be one of my favorite subjects to teach.  I was never a “math person” as a kid.  It was always boring because it was too easy in elementary school and then boring because it was too hard later on.  But since then I’ve learned to appreciate math, especially when I unexpectedly ended up teaching it when I was still a school teacher.  I really want my kids to be challenged by it and to know it’s more about solving puzzles and asking questions than about doing sums, though you can’t solve the problems and answer the questions without first learning how to do all those sums and procedures.

BalletBoy’s Math

The boys have done separate maths since first grade, when BalletBoy happily plugged on and Mushroom became completely disenchanted with the whole idea of math.  For BalletBoy, Math Mammoth has been his spine for what seems like eons and he began the year by wrapping up the last bits of 4a.  Math Mammoth is not exactly exciting math.  The pages can be crowded and the pace can go slow, but for a child who just wanted to plug away at math and get it done, it was a perfect program.  However at the end of 4a, when I went to print packets from 4b, he had a sudden desire to do something completely different.  Meanwhile, the Singapore Challenging Word Problems, which had been his supplement for almost two years, also became…  not too hard exactly, but too confusing.  I often found the wording on the problems confounding such that I didn’t even know what they wanted.  What had always been slightly annoying became too much to interpret when coupled with harder math.

So it was time to change things up.  We tried to switch back to MEP, which we have used for brief periods since first grade, but it wasn’t right for him either.  I knew the Key to Math books would be a breeze for him, so I had him do the first and second books of several series, including Fractions, Measurement, and Decimals.  If you don’t know this program, it has short, gentle workbooks about specific topics.  The look of the texts is nicely pared down and I like how they have an incremental approach that isn’t as overwhelming as Math Mammoth’s.  However, the biggest topic in fourth grade math, long division, was still missing from his education.  We had to find something else.

After a lot of consideration, we landed on Math in Focus.  He had already covered most of the topics in the second half of their fourth grade syllabus, so he’s working on completing most of 4a right now, including .  He says he likes it so much that he’d like to do the fifth grade program next.  In case you’re not familiar with it, Math in Focus is “the other” Singapore math.  When I looked at it ages ago, I liked it a lot less than Singapore Primary Math, but I think I didn’t give it a fair enough shake.  It has the look of a more American style program, but the math is much more similar to Primary Math.  I really appreciate, coming from using Math Mammoth, how pared down the amount of problems is to the ones that really matter.  We also found Fan Math’s Process Skills in Problem Solving, which we like so much better than the Singapore Challenging Word Problems.  The problems are much more clear and there is much better modeling of solutions and information on how the solutions are arrived at in the back.

Mushroom’s Math

Mushroom is my real math lover.  At the start of the year, I had him working on Beast Academy and the Key to Math books on Fractions and Decimals.  He’s now in Beast Academy 4a and I’ve been dragging things out in the hope that 4b will be out (it was supposed be by late February or early March, but I’m still waiting!!!).  I cannot sing Beast Academy’s praises enough.  The program didn’t work for BalletBoy when he tried it when it was newer, but it has been a boon for Mushroom.  The story in the comic book style text is always funny and very well done.  We especially like the recurring elements such as the little beasts rivalry with the bots, the way Grogg finds bizarre solutions to problems, and the multiple personalities (and alliteration) of Professor Grok.  The tricky, thought-provoking problems in the text are also great for encouraging kids to really delve in and think.  They’ve been good for teaching Mushroom patience with his math.

After he finished some of the Key to books, I felt that with Beast’s slow release pace, he needed to do some really basic fourth grade math review, so I bought him a Spectrum math practice book.  It’s not a real curriculum, but he just needed to practice traditional algorithms.  It’s been a mixed bag.  I think it’s good for him to do this and it has been mostly very easy, but there have been a few things, including the long division algorithm, that he really needed to learn and other things, such as stacked multi-digit multiplication, unit conversion, and names of shapes (memorization of lists is just not his strong suit so “hexagon” is like new information every single time), that he really needed to review.  Some days it’s good for when he needs to escape the frustration of an especially tricky Beast problem, but other days, he has been known to scream, “This is not math!  This is just adding numbers and stuff!”  Well, at least I know he gets that math is more than this.  If I could go back, I might buy the fifth grade book instead of the fourth, since it presumably would have a slightly trickier range of numbers for him to practice.

Extra Stuff

As is the case every year, we use a lot of extras for math.  This year, probably the two most used extras have been the Murderous Maths books and Hands on Equations.  Murderous Maths is a great resource that presents math that’s both easy and difficult (or, as the books would probably say…  diabolical!) with a sense of humor.  The explanations are often really clear and clever and they touch on ways to see numbers and math that most elementary math texts don’t bother with.

We did the first level of Hands on Equations last year, but I put it away for awhile and pulled it out again to finish the second and third levels.  It’s not a difficult program by any means, but I didn’t want to run through it all in a couple of weeks, so we’ve been doing a lesson once a week or less to draw it out.  The system they present is really very ingenious and some of the tricks they employ have really grown on me over time.  At first I felt like it might be too simplistic, but I now see how they are slowly introducing the basics of algebra one skill at a time.  There’s not much too the program other than a laminated scale and some dice and game pieces, but I think it’s probably worth the cost of the homeschool kit to see how they’ve laid out these lessons.  Between Hands on Equations and Dragonbox, I feel like the kids are going to go into algebra in a couple of years with a really firm grasp of basic concepts to give them a head start.

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.

Graph-o-mania

Midway through the year, we switched to Math Mammoth’s Blue Series and as of a couple of weeks ago, we finished up what constitutes their “first grade” books, which are Addition, Subtraction, Place Value 1.  I didn’t love all the methods in the place value book.  We switched pretty quickly to using our abacuses, which the notes in the book vaguely suggest you can do.  We also sped ahead somewhat and added much bigger numbers than they suggested, in part because the Math Mammoth drawing out the number method really limits how big your numbers can be while the abacus does not.

We could move on to what Math Mammoth deems the second grade material, which is mainly addition and subtraction with larger numbers.  However, I’d rather play around with some other topics and let the really basic numbers keep sinking in for Mushroom and BalletBoy by playing games and letting them do real world math as it arises.  We covered enough measurement to last us for years, but we could stand to do a little more with geometry and money, so I’ll take us on a little detour with those in the coming weeks.  Plus, they have specifically asked to do more logic, having flown through Lollipop Logic very quickly.

The last couple pages of the Math Mammoth place value book introduce the idea of reading and making simple bar graphs.  So we made that our first detour.  I took a few books about graphs out of the library for the kids, but the best, by far, was The Great Graph Contest by Loreen Leedy.  The more we use her books, the more I adore them.  This one is a lot like Measuring Penny in that it takes a concept and explores it in a bunch of different ways.  The kids (well, animals, really) in the story get into a contest of making ever more elaborate graphs.

We started with the Math Mammoth basic bar graphs and I asked the kids to come up with something to record.  They both decided to record how many servings of each food group they ate in a day.  I’m posting a picture even though I feel like it doesn’t make me look like I provided the most healthy food day, honestly.

We then took that idea further and the kids dreamed up a survey to ask and record an even bigger bar graph about.  They had a good time polling.

But drawing from the Loreen Leedy book, we also ran around the house making graphs out of real objects, like the characters in the book do.  We made a stacked graph of all the board games (Lego games, card games, puzzles, solo games and other games).  Then we made a Venn diagram of them (games with cards, games with cards and other pieces, games with just other pieces).  Then the kids ran around the house making graphs of other items.  Here’s the one BalletBoy made of books he’s reading currently (there are five of them) and books Mushroom is reading currently (also five!).

And here’s the bar graph of all the shoes in the house and who they belong to (yes, it was made on my bed, which just made me scratch my head, but whatever).  That long bar in the middle is mine (and he didn’t even go into my closet to find my lesser used shoes!).  After this, we rearranged them into a different graph of sandals, shoes and boots.

Overall, this was a fun topic for us.  I’m hoping geometry is similarly enjoyable yet mathy.  We already broke out the geoboards we made with the kids’ grandfather at the end of last summer.

Measurement Books

One of our co-ops is starting a new theme on measurement.  We often do very little to go along with our co-op themes.  We might check out a few books from the library and we talk about what we’re learning about in the co-op, but otherwise, I haven’t been connecting it with other aspects of our schooling.  However, this time around, I thought it might be a good chance to take a break (mostly) from our math curriculum and do a unit on measurement at home too.  I bought the Math Mammoth blue series book on measurement.  Here are the kids measuring their new books with paperclips and crayons.  BalletBoy insisted that they all needed to be green crayons for some reason.  Some of the content is a little too sophisticated for my first graders, but much of it will be a good little text for us to do as we explore the topic.

We also checked out an absurd pile of books on measurement from the library.  Here are some highlights.

Measuring Penny by Loreen Leedy
As always, Loreen Leedy’s clever book leads the pack for measurement.  This is a classic one.  A girl measures her dog in every way she can imagine for a school project.  It’s an inspiring sort of book in that it’s easy to use it as a jumping off point for measuring more things.

Room for Ripley and Super Sand Castle Saturday by Stuart J. Murphy
We found these two titles from Stuart J. Murphy’s MathStart series.  They’re both good.  In the first, volume is explored in simple terms as a boy fills up a bowl for a new fish.  In the second, many kinds of measurements are explored as kids build sand castles.

How Tall How Short How Far Away by David A. Adler
This cheerfully drawn book gives a quick introduction to the history of measuring length, showing little pictures of Egyptians measuring with their arms to make cubits.  After talking about what measurements we use today for length, it invites the reader to think about which ones are right for which tasks.

If Dogs Were Dinosaurs by David Schwartz
This book, along with its companion, If You Hopped Like a Frog, use excellent illustrations to show a comparison of sizes and lengths.  This is a creative little book that’s short enough to be enjoyed by younger kids, but interesting enough to be enjoyed by adults.  There’s no story, but each page is a thought provoking little summary.

How Fast Is It? by Ben Hillman
This book, with glossy photoshopped images, was full of fun facts comparing the speeds of different things.  Each page had a different topic.  It highlighted not only some of the fastest things, but also just compared some unexpected things like the speeds of swimming birds and flying fish.

Science Factory: Units and Measurements by Jon Richards
We checked out several measurement activity books, but all of them quickly went back to the library except this one.  Almost all the projects in this book involve making your own measuring devices, such as an hourglass with two bottles and a balance out of a coat hanger.  I want the kids to make a measuring wheel and measure the distance around our block.