Tag Archives: living math

Numberless Problems for Today – Free Download

In my last post, I linked to a really cool vintage resource called Problems Without Figures. As I pointed out, I decided to update it so I could use it with my kids more easily. I didn’t update the whole work because it was very long. I did the first 150 problems, which is a little less than half, but I thought I’d share my update here with you. It’s free to download. For more about the types of problems, the reasons to use a book like this, and how to use the book, have a look at my previous post. Below, I’m going to talk a little more about the changes I made to the book and why. I can’t promise that every problem in here is perfect. I’m pretty sure I thought through everything, but I didn’t have a professional editor. Feel free to send me any corrections and do tweak any problems to make them make more sense for your kids if needed. Note that the nature of these problems is to include superfluous information, have answers that are impossible to get without more information, have multiple potential solutions or paths to a solution, and to have “trick” problems where the answer is much simpler than the problem implies. None of those things are necessarily errors. Again, see my previous post for more about these problems.

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I changed the problems in a couple of ways. A large number I left the same or simply updated a word or two to be less old fashioned (such as “shall”), including some of the old fashioned problems about farms and orchards and the like, simply because it’s nice to have different perspectives occasionally. I updated the language in a few problems. For example,  instead of buying marbles and penny candy, kids are buying Legos and other contemporary items. For others, I changed the situation or the measuring units for a problem to be more up to date but tried to keep the spirit of the question. However, for several problems, I couldn’t come up with a modern equivalent so I completely rewrote the problem to be more contemporary.

Doing this was an interesting process for me. It let me think about how math has changed over time. Much of the original book was out of date because of the situations it portrayed. It assumed the readers were familiar with agriculture and farm animals. However, much of what has changed is the math. There were several measurement units that are simply not used anymore, such as the rod as a measurement of length. Other measurement units are in use today and students may have a general sense of what a bushel or an acre is, but they are less a part of everyday life. In general, while measurement math is still a key component of everyday math and we have the complexity in the US of having to go between customary and metric measurements, this book drove home for me how it was an even bigger share of the everyday math people used a century ago. For one thing, we tend to deal with standardized sizes of things much more often. Doors, windows, pieces of paper, tablecloths, picture frames, etc. are all standardized. If we want to know how much land we own, we look it up instead of measuring. If we build something, we tend to follow preset directions instead of making them up ourselves with all the accompanying measurement challenges.

On the other hand, there are types of math that were never or almost never covered in the original book. For example, there were only a couple of problems involving averages. There were no problems involving estimation. There were no problems involving statistics or ratios. Very few problems involved fractions or percents, which surprised me. There were no problems involving permutations or combinations.

Life today is more complex with more choices. We tend to need to know more about combinations and permutations just to order off a menu or decide how to buy something or what to wear. We have to evaluate more complex data and statistics to understand a news article or a scientific claim on the internet. We’re used to bigger numbers. None of the numbers in the original book were very big. These days we’re used to hearing about numbers in the millions and billions. Our tax code and economy are much more complex, meaning that percentages come into play a lot more often. When the original book was written, people lived with a cash economy and prices were more straightforward. It’s different now.

When I tossed out those few problems from the original, I tried to replace them with ones that asked kids about making the sort of decisions that we often have to make using math these days. So there are problems about how to make basketball matchups, how to choose which toilet paper to buy, how to know if a statistic is reasonable, and other more modern conundrums than how many acres in your fields or how many fence posts you need.

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!

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.