Every kid needs to learn their times tables at some point, and this means practice. Unfortunately, practicing times tables can be unmotivated and boring for kids. We adults, rightly, ask, “How can we make it fun?”(Important note: **times tables are not math**. Math doesn’t need to be made fun; it already is fun. Memorizing your times tables is a rote activity, it requires a fair bit of repetition for most, and it may need to be made fun. Just saying.)

Well, here’s an idea: play a game that requires multiplication. Of course, there are literally bajillions of multiplication practice games available online. (Ok, not literally. But google returned 820,000 hits on a search for “multiplication games online.”) I guess these games are ok, and some kids like them, but I honestly don’t care for them so much. They’re more time looking at a screen, to start. Also, the multiplication is totally arbitrary. If you’re just sticking some packaging around it, I don’t think you’ve solved the fundamental problem. To wit:

Principal Skinner: Here’s a whole box of unsealed envelopes for the PTA!

Bart: You’re making me lick envelopes?

P.S.: Oh, licking envelopes can be fun! All you have to do is make a game of it.

Bart: What kind of game?

P.S.: Well, for example, you could see how many you could lick in an hour, then try to break that record.

Bart: Sounds like a pretty crappy game to me.

P.S.: Yes, well… Get started.

Can we concoct fundamentally more interesting games that still give multiplication practice? Well, here’s my latest, so you can tell me what you think.

It’s called **Damult Dice**.

The Rules: Each player takes turns rolling 3 dice. First to break 200 (or 500, etc.) wins. On your turn, you get to choose two dice to add together, then you multiply the sum by the final die. That’s your score for that turn.

Simple; no bells, no whistles. For example, I roll a 3, a 4, and a 6 on my turn. I could either do (3+4) times 6 for 42 points, OR (3+6) times 4 for 36 points, OR (4+6) times 3 for 30 points. I’ll take the 42 points.

I spent some time playing this with kids the other day and I saw that (1) it was genuinely fun, and (2) it gives you almost all the multiplication practice you could ask for. In fact, it gives even more, because the choice of which dice to add and which to multiply reveals some interesting structure of numbers. Seriously, get a kid hooked on this game, and it’s the equivalent of dozens or hundreds of times table practice sheets.

Maybe I’m speaking with a bias of someone who learned his arithmetic from games and then went on to become a mathematician, but games like this are great. If you know a kid, try this game out on them, and let me know how it works! I need to know if it needs tweaking.

I have three variations on Damult Dice, but I’ll save those for later. Did you come up with a cool augmentation of the game? Let me know in the comments.

Even better is when kids start inventing their own games. I met with a student who invented two dice games in less than an hour this week! I’ll share those soon as well.

## Comments 33

Good stuff. I like the mix of operations especially. I only see two downside. The first is that the person not rolling is just watching. The second is it getting bogged down while someone goes through every possible iteration, like playing scrabble with my dad.

At first I thought maybe you could have both players “claim” a combo on each role, but then imbalances in skills are pretty impossible to overcome.

A better solution might be if the person just watching found a higher scoring combo, they could claim it and steal those points. But again, you’re stuck with it getting bogged down while the roller triple checks each iteration so I guess a time limit would be necessary.

In dominoes you only score in multiples of 5. It might be interesting to role dice and you can use any operation but you only score if the total is a multiple of 5. Maybe an additional bonus for a total of 1 or 0. I’m not sure how many dice you’d need to make this playable though.

Again, really good stuff. I’m interested in seeing what you came up with and to hear about Dice Poker and Dice War.

Author

Wow, Jason–those are excellent suggestions. Particularly the stealing of points if you can find a larger product.

One thing I did in practice was have both parties roll at once, which addresses your first downside.

For the second downside, you could add a time element, where the first person to say their point count from the roll gets a 10 point bonus, and if there’s an error, they lose ten points, or get no points for that roll.

If the speed element is too nerve wracking, well, I don’t know another way to get people to move fast in Scrabble either.

Author

Here’s another idea for a Damult Dice add on… let’s call it Double Down: Roll all six (or n) dice at once, and both people can use any combination of {+,-,x,/} to get the highest number they can. Whoever gets the highest number scores as many points as they beat the other person by.

And of course, you need a restriction:

Variation 1: You have to use each operation at least once.

Variation 2: You only use + and x, but you have to use + at least as many times as you use x.

Why damult?

Author

The inspiration for the name was ADd and MULTiply, but in the order you want… DAMULT. I thought it was catchy.

A bidding system might be interesting. I’m thinking something like the game BS. You could even have any number of players. Roll dice. First player calls out a number. Second player has X number of seconds to call out a higher number or call Prove it. (or whatever the math equivalent of BS is). If they can solve it they get the points, if not, the other player does…or perhaps they get the highest amount they can prove. Maybe if they got caught in a lie they get those points subtracted. I dunno. Still thinking out loud here.

And yes, why Damult?

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I have the same question as Sue, where does this name come from? I like this game because of the strategy to figure out the most points and the math that they would be doing to figure this out.

I saw one suggestion about stealing points but I would only use that with certain students. I have had students, that if that were part of the game, they would begin to disengage because they would be afraid of trying and losing points. Perhaps you could encourage the students to help others out and split the difference. For example if the possibilities were 30, 36 and 42 and a student calculated 36 and their partner helped them figure out 42 they each would get 3 points (half of 6). Just a thought.

Author

Very good point, Cathy. One does have to be careful on the competition front. I like your cooperative suggestion.

I just found your site and will definitely play this game with my daughter. You may have said this elsewhere, but an important principle with drills of any kind – even fun ones – is the student must first understand what they are drilling. It may sound obvious, but how many kids are asked to memorize math facts without really understanding what they are memorizing?! :0)

Author

I’d love to know how your daughter takes to the game.

It seems like an advantage of games that the goal is clearer than it is with drills. I personally learned to add very quickly as a child by playing endless cribbage games with my brothers. And I wasn’t trying to memorize my math facts–it was just a natural effect of repeated exposure, and possibly teasing from my brothers if I was too slow counting up the points in my hand.

It need not be so radical. There is plainty of math in the multiplication table. There are a few examples at http://www.cut-the-knot.org/blue/SysTable.shtml

Besides, there so many games out there that could serve as an arithmetic exercise. One can roll dice of course, but there are more.

http://www.cut-the-knot.org/ctk/March2001.shtml

And this is not all.

Author

You’re right, of course, that there’s plenty of math in the multiplication table. I recently was counting the number of rectangles on an n by n chessboard with a student and noticed that the answer was the same as the sum of the numbers on an n by n times table. Something interesting is clearly going on there.

But the “radical statement” that times tables are not math still stands, I think, though I may be overstating it. There is a distinction between mathematics and computation, and I think that the line between them is often blurred. In most schools, times tables contain information to be memorized. Your site contains some great examples of how to treat it as a mathematical object instead, but that isn’t the common usage. I wish it were.

I like your idea of using iterative games as a way to get kids motivated in math, with the byproduct that they practice arithmetic (happily). I myself gave a talk at a recent MATHCounts competition on the Collatz Conjecture (aka the 3n+1 problem) which you mention on your link. I’m trying to do something slightly different with this game, but I think it’s great to have as many tools in your belt as possible when it comes to teaching math.

I actually could argue that the multiplication table contains more maths than the activities you, I and many others have discribed because the latter, in themselves, are nothing more than a game-coated drill. The point of the argument is then that it is not a curriculum item that makes the difference but the method of presentation and the associated expectations of the results of student activities. Focusing on a curriculum item diverts attention from the real problem. There are pros and contras of teaching the long multiplication as there are in omitting to teach it. The trouble is in the rigidity of the system when it’s either this or that.

Author

I absolutely agree, Alexander. And that’s one of the reasons I like games: they emphasize play rather than rigidity.

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There are some pretty good 2 player multiplication games to download on BEAM Maths of the Month. Have a look around http://www.beam.co.uk/mathsofthemonth.php

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Hi there fellow blogger! I’m a newbie to the blogosphere but I just wanted to say how much I enjoyed your blog here about math games uk, it kept me reading all the way to the end… And then I went and searched for some more posts after that. Keep up the good work, I’m always looking to learn more about Math Games, especially.

My siblings had little dice-holding things that allowed the dice to rotate freely–I don’t remember how many dice, but two were black, with 1-6 and 10-60 on them, and you were to use all the other numbers and any operators you chose in order to make an expression adding up to the black dice “answer”. I’m thinking 5 dice total. You can do it with any dice, but the benefit of the holder was the game could travel in your pocket, and a simple spin between the palms gave everyone a quick problem to try to figure out while waiting somewhere.

Another, non-dice-related multiplication game is the one from Square One with the board of answers, and the numbers 1-9 in front of the two contestants. The first contestant gets to ring two numbers and “claim” the product on the board, and then the other player moves only his ring to form a new product and “claim” a new spot on the board, and so forth. I think the goal was to make 3-in-a-row or something like that… You can play the same thing with addition, with a different board.

My year 7’s (11-12 yo) love this – the gave an average rating of 4.1 out of 5. We tried variations including: you have to make 200 exactly so you can subtract your answer instead; if you roll a double, you get another go; you can choose to go again but if your answer is smaller, you lose your scoring options etc. They came up with excellent variations and were all active all lesson. Thank you!

Author

Hi V,

Glad it was a hit! I love your variations. I’m going to suggest them next time I play this. Having to hit a number exactly so you have to subtract is especially good because it makes the game more subtle than “always pick the largest product.”

I teach adult education and recently expanded the Damult Dice game to meet my students’ needs. Not only do they need to improve their mental math skills, they also need to learn to use the calculator.

I had the students work in pairs, giving each pair a set of three dice–2 red and 1 white. I then gave them a worksheet with the formula [a(b+c)]2 and 12 blank lines. They were to throw the dice, and student A would mentally add the two red dice and multiply by the number on the white die mentally. Student B would then take that answer, use the square function on the calculator, and enter the answer in the memory function. The numbers were also entered according to the formula on each blank line, and the sum was also recorded on the worksheet. The students were to take turns finding the mental math answers and using the calculator. When all blank lines were complete, they added the column of answers and compared the total with the memory total.

Everyone practiced mental math and calculator skills. They found that mental math can be faster than calculators, and they discovered that calculators are only as reliable as the person entering the data. It was a great exercise.

My students LOVED this game! They did not want to stop playing! I learned about it from one of my “tweecher” friends and went in and played it the next day. What an exciting, fun, way, to learn multiplication!

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I grew up playing Rats a$$. Way before farkle ever came to be. it is quite

Similar except five dice and rules a bit different. It’s a great game especially

When it gets all exciting after you keep getting to roll as long as you have doubles, triples or a five or one. So, your turn can go on a bit and at the end keep the score, or risk rolling again and losing it all. So, of course my son grew up playing rats ass as well.

Which is great for addition. Of course, kids getting to holler rats ass on a roll of 3 1s and the excitement of continued rolling and risks and quick playingade it more fun.

I can see a way to do this with multiplication as well perhaps. I love the idea

Of the game you’ve created!

My question is this. If your child hasn’t quite started memorizing the tables, is there an easy way to help them memorize them? You need a bit of knowledge of the tables to play this game. PC Games and apps .. Most are boring. One player. And seem, to my child at least, almost as grueling as just memorizing the tables alone on paper or drills.

Maybe we haven’t found the right games. But we’ve literally tried around one hundred and never found anything that wasn’t seriously boring or the format so messed up it wasn’t playable. I’m new to blogging and just found your blog googling for help memorizing tables in a fun way. Glad to have found your blog and game! Do you have any suggestions for help memorizing the tables quickly without being too grueling? One on one? Thank you! I can’t wait to try your game! Sounds like it could be a blast and truly helpful! I’ll let you know when we play!

P.s. He does seem to have the same issues I had as a child with math. Frown which is what I call “math anxiety” so I don’t do a huge amount of timing or drill super fast and hard until he’s feeling some confidence. Which is what I would LOVE to see him have with math. Math can truly be enjoyable and fun and even though I’m in my 40s, I buy algebra books to challenge myself lol I’d love him to get over his anxiety with math and have confidence. Math can truly be used in everything throughout your whole life. Many would debate that, but I see it to be true.

I like the simplicity of this game. I have played other dice-based math games with my students and, while they are fun, the more complicated they are, they more down time there is for the other kids. I’m excited to try this one with my students in the near future… hopefully tomorrow.

As a possible fun addition, consider using a variety of dice types. Groups/students that have mastered their times tables could up the challenge level by playing with 8, 10, 12, or even 20 sided dice. Of course, you might have to up the point goal. It might be even more fun to use a combination. Who doesn’t like rolling cool dice?

I tried this game with my students but not as a game as it is described but simply as a work to be done.

I rolled the dice. We have our numbers. Now, all of them work on them at the same time on the same numbers.

They are young people and don’t get it right first time so I help.

No one has to wait, no one has to rush, no one has to fear of losing the game. All have to work and help is there.

If they can’t add or multiply, not a big deal.

We set a time – say 15 minutes or until they say they don’t want to play.

Well, if they don’t want to play before 15 minute slot is over, they are not off the hook.

If they choose not to play, they get a regular practice sheet to work on!

After playing this in our 1st and 2nd grade classes, I created a little pencilcode program (Logo-inspired, based on Coffeescript) to analyze damult dice throws: Damult Frequency Charts.

One of the things we noticed was that multiples of 3 are quit common, especially when you are trying to maximize the score from each throw, hence the choice of coloring.

Author

Fascinating distribution graph, Joshua. Thanks for sharing this! I’d never considered the question of the odds that the best move is a multiple of three. When I tried it with your program, I saw that the chances of getting a multiple of 3 was 67%, a 2/3 chance! I wonder if there’s some elegant way to see this in the probability calculation itself.

I would have never considered that question without your graph. Really cool.