Tag Archives: math games

Probably Probability

We had never covered probability, so I felt like it was time to dive in with a little bit of a focus. Now that we’ve done a good bit of it, I feel like we would have been fun and totally possible to have done it a few years ago as well and then returned to it with a stronger focus before moving into pre-algebra. It’s one of those topics that’s not really covered in books for younger kids, yet kids are constantly encountering probability in their lives, in part because of games. I think it makes a huge amount of sense to cover it earlier.

game sticks
Throwing game sticks in an activity from the GEMS Guide.

Picture Books
There are a couple of good picture books for younger students about probability. The first is the MathStart book Probably Pistachio by Stuart J. Murphy. This is really not one of my favorites in the series, but it does introduce the concepts, especially about using probability to predict what comes next. It’s Probably Penny by Loreen Leedy is similar in concept, and readers who like Leedy’s classic picture book about measuring will recognize the same characters. However, my favorite was A Very Improbable Story by Edward Einhorn from Charlesbridge. This one is more clever and introduces a lot more basic vocabulary to start talking about probability, not only for what happens next but also for games.

Chapter Book
Of course there’s a Murderous Maths book for kids who are just a little older. Are You Feeling Lucky? is yet another excellent resource. We have been loving the Murderous Maths series. This one, like the one about shapes, asks readers to try a number of things out and I think it’s best when you do the activities with the book, such as flipping a coin or rolling a die. The book also covers some combinations math, which is nice for us as a follow up to some of the Beast Academy combinations math. If you haven’t yet discovered the Murderous Maths books, know that they often cover some surprisingly complex and difficult math, far beyond what kids would typically do before high school. However they cover it in such a friendly and humorous way that it feels approachable and enjoyable.

Activities
The GEMS guide In All Probability is an excellent one. It’s intended for students grades 3-5. I think the activities could be done more quickly for older kids who need an introduction to the subject as well and perhaps beefed up a little. There are five sets of activities that include flipping coins, making spinners, rolling dice, and making game sticks based on a Native American game. I really like the thought behind the GEMS Guides in general, however, as always, you have to adapt them to homeschool use since they’re really set up for a large class. In this book, some of the activities assume that you’ll gather lots of data from the games. Also, I wish the books were organized with the math more clear and more in depth. There is a teacher section in the back that explains the math behind the activities in more depth, but, for example, the number of chances in the Native American game sticks activity is tied to Pascal’s Triangle, yet it never mentions that. Still, I like the way the investigations are set up for real discovery math and Mushroom and BalletBoy both enjoyed building the spinners, making game sticks, and playing all the various games.

I wanted some pages to practice probability problems, so I had Mushroom do some of the pages from MEP Math that deal with probability. You can find them in the 5b book at the end of this section and the beginning of this one. An alternate source of probability problems and text could have been the NCERT 7th grade math book chapter on data, which covers a variety of concepts, including probability. You can find that here, if you’re interested.

Of course, since probability is in our lives so much, it’s good to look at other places it appears. We started with something greatly revered in our house: game shows. In case you didn’t know, the Husband won us the down payment on the rowhouse many years ago on a game show. Thus the game show’s exalted place in our hearts. It’s fun to look at the odds on nearly any game show. However, the classic game show problem is the Let’s Make a Deal problem, which has been written about a ton, most famously by Marilyn Vos Savant and Martin Gardner (if you’d like to be a math nerd and don’t know who Martin Gardner is, you need to remedy that, by the way). It’s great to actually watch the show and learn about the problem. I saw a great demonstration of it by Ed Zaccaro of the Challenge Math books at a conference once, using envelopes instead of doors. With three envelopes, it’s not clear which one to choose. However, with a hundred envelopes, it’s almost immediately clear. We tried that and talked a little about how probability is one of those things that can be tricky to think about sometimes. This was followed up on nicely by the Murderous Maths book when it talked about how pennies don’t have memories.

If you look up probability lessons on Pinterest, you’ll find lots of options. However, the classic probability lesson that I wanted to be sure to do was with M&M’s. There are many variations, but essentially you have students calculate the probability of drawing an M&M out of the bag. The more bags you calculate, the closer you can start to get to what is, presumably, the actual ratio in which M&M’s are actually produced. You’re finding the experimental probability, so this is a good activity to introduce this term. The theoretical probability can also be found just by looking up in what ratios the M&M/Mars company actually makes the M&M colors. It’s slightly different for each type of M&M, but you can find it easily online.

Finally, we simply tried to be more alert to probability in our lives, such as in weather forecasts, board games, video games, and random events. It’s nice when kids can see math in the real world, especially when it’s things that aren’t money. Overall, this was a good unit for us.

Math App Explosion

We have an absurd number of math apps on our iPad and I thought I’d give a rundown of what we like and find useful.  If you’re like me, you’re always adding more apps, especially when they’re free or only a dollar.  A few of these are more, but they’re all ones we found to be worth the price.

Rocket MathRocket Math
This is the math app we’ve had the longest and we love the designer, who also made Stack the States.  The format of making your own rocket and testing it is appealing.  The math is mixed.  I wish it was easier to customize the math to focus on different skills and skip others, but overall, it’s a fun app worth buying.

Sushi Monster
I like that this app asks you to start with the answer and find the numbers that make it instead of vice versa.  There is an addition and a multiplication option.  It’s a simple game, but the graphics are offbeat and cute.  Plus, you can’t beat the free price.

Math Motion Wings
This game asks kids to visualize multiplication and numbers as you fly a bird around.  It’s not about knowing the exact answer quickly, it’s about comparing values and knowing which is greater.  There’s some fun bits where you get to customize your own bird nest as you go along.

Marble Math
The graphics on this game are just okay, but it’s a clever little concept.  The marble in the maze needs to hit certain numbers before the hole opens up and lets you win.  Almost everything about the game, from the color of your marble to the whether you tilt the screen or use your finger to the math practiced is customizable in this app, which makes it good for more specific practice.

Space Math
If you remember Math Blasters, then this is pretty much the same concept, shooting things and all.  Simple but fun as a way to practice basic math facts.  There’s a lite version and a full version.  We have so many others that we haven’t sprung for the full version.

Numbers League
This game plays off of comics and superheros and has one of the best looks to any of the apps listed.  It’s also a more involved game that feels more like a game in places than a math drill app.  However, math is still at the heart and there’s a lot of good basic math fact practice built into this app.

Dragon Box
This app is set up like the popular puzzle apps with different levels that build on each other.  The goal is to learn, through little cards and pictures, how to isolate unknowns in algebra equations.  This game was incredibly fun for the kids and has been good for referring back to.  I wish it had more levels and more puzzles, especially for the somewhat high price, but it’s still a really innovative app – one of the most innovative that I’ve seen.

24
This is an extremely simple app, intended for the iPhone, that lets you simply play a round of 24, where you use the four basic operations to make the number 24 from the four numbers the card gives you.  There are absolutely no settings.  You draw and play eight cards and the game times you.  I wish there were some settings (it would be nice to be able to choose how many dots you want for your challenge, for example), but at 99 cents, it’s worth buying.

Math Evolve
This is one of the newest buys at our house.  It’s basically another Math Blasters style app where a character swims through the right answer, but it has more levels as you “evolve” your character.  The kids like it and it practices basic facts.

Pick a Path
This was a quick free app where you pick a path with different numbers and operations to try and reach a target number.  The levels are limited and they get too difficult for Mushroom and BalletBoy too quickly (multiplication and division by fractions and decimals are introduced just a few levels in).  I wish there were more boards though because it’s a clever little puzzle.

Coop Fractions
I discovered this little app by accident.  The chickens lay eggs that you have to catch in a moving nest that you place on a number line.  It’s a great game for teaching fractions values and has a bunch of options of how to use it.  I do find the look on the chickens’ faces a bit disconcerting as they lay their eggs, but as it’s a free one, I’m not going to complain.

Math Board
Despite the price tag, this is the best app I’ve seen for just straight math drills on the iPad.  I’ve mentioned it before, but I really like how it lets you customize exactly what you want to drill.  There’s a “chalkboard” space to work out longer problems and an explanations function for more difficult ones.

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.

A Rambling Post About Weekends, Math, and Waffles

On Sunday, we had a lovely school morning, reading picture books for Story of the World and playing a math game I stole from the blog Tinderbox and tweaked a little.  I know what you’re thinking.  You’re thinking, they do school on Sunday?  Yes, I’m a mean mama who makes her kids do school on the weekends.  But honestly, in our house, there is no Saturday and Sunday.  The husband works double shifts on the weekends, meaning that this isn’t really family time, so it’s easier for me if we just continue with our routine.  It’s only for an hour or two on any day.  Besides, if we do school on the weekends, it gives us the flexibility to not do it on other days if we’re busy or just need a break.

So here’s the game.  We’ve been working on greater than and less than with MEP.  I wrote down math problems in chalk in our backyard.  A wizard bewitched the backyard to protect his magic stone on the other side, but he had to leave himself a path.  To get across, you have to step only on problems with sums greater than 5.  On the way back, it’s reversed and you can only step on sums less than 5.  If you make a mistake, a magic bird (aka, yours truly) swoops down and carries you back to where you started.  By the way, if you’re wondering how big a rowhouse backyard is, well, that’s our whole space you see in the pictures.

The other day, I asked why is math so much easier with M&M’s.  Now I ask, why is math so much easier with sidewalk chalk?

They liked the game so much, that they wanted more math problems and circles to jump on.  Then they played for quite a long time.  The other day, Smrt Mama had a post about working independently.  Mushroom and BalletBoy aren’t quite there yet for long stretches of seatwork.  They can work a little handwriting or math alone, but I still need me to be pretty close at hand.  BalletBoy will read a book by himself, but I can’t count on more than ten or fifteen minutes of independent work at the most from the two of them.  That’s something I’m very much looking forward to building up over the next few years.

However, every once in awhile, we do something that sparks them to play with it for ages as was the case with this math game.  Taking advantage, I came inside to make our favorite breakfast: whole wheat peanut butter waffles!  I experimented with this recipe for pumpkin waffles, but they honestly weren’t all that, so I think I’m sticking with the peanut butter waffles and I’ll save my hoarded cans of pumpkin from the pumpkin shortage for muffins.  I like to make a huge double batch and freeze them so we can eat them for breakfast every day.  Just like I always feel better when I’ve got a pile of school things ready to go for the next few weeks, I feel better when there’s a fat bag of peanut butter waffles in the freezer to make our mornings go smoother.

I never do recipes on this blog, but I love this so much, I always want to share it.  Here’s hoping you’re not peanut allergic or gluten free or anything.  I add a little extra sugar so we can eat them plain, without syrup or honey.  However, you could cut the sugar down to a tablespoon if you wanted to top them more traditionally.  One of the best things about waffles is that the recipes are pretty generous.  If your batter’s too thick, you can add extra milk.  If it’s too thin, you can add extra flour.

Whole Wheat Peanut Butter Waffles

1 1/2 c. whole wheat flour
3/4 c. white flour
4 tsp. baking powder
generous 1/2 c. peanut butter
generous 1/4 c. sugar
2 eggs
2 1/2 c. milk
1/4 c. oil or melted butter
1/4 tsp. salt

Combine all the ingredients.  If you’re super awesome, I guess you can whisk up the wet then fold into the dry, but I find it’s not needed for waffles.  Then cook ’em up in your handy waffle iron of choice and let them be fuel for doing math problems!