First, a bit about what factors and multiples are. They're easiest to explain with examples instead of definitions.
- The FACTORS of 15 are 1, 3, 5, and 15, because 1 x 15 = 15 and 3 x 5 = 15. 7 is NOT a factor of 15, because 7 doesn't divide evenly into 15 (you'd have a remainder).
- The MULTIPLES of 8 are 8, 16, 24, 32, 40, etc. (going on forever). That's because 1 x 8 = 8, 2 x 8 = 16, 3 x 8 = 24, and so on.
- Remember multiplication tables? Go look at my favorite multiplication table. Can you tell what's going on there? Great connection to area of rectangles, huh?
- Another great way to represent factors is this visual illustration of divisor pairs (which is prettier than it sounds). Select one or more of the factors shown and see what happens to the picture. If you can't tell what's going on, try entering 12 or 18 or 28 in the number box.
- Next, check out this Composite Number Tree. "Each number branches from its largest divisor," says the caption. Can you figure out what they mean? (I think it actually would be more correct to say each number branches from its second largest divisor.)
- Now take a look at the number patterns showing up here on the curves, and move your cursor around to explore. Can you tell what's going on? It may help to notice the "n=" entry at the bottom of the page.
OK, on to the games. These games help you practice multiplication facts online, but remember: if you find a game on this list is stressing you out, or you're just learning how to do some task fast but not actually improving your recall of any new math facts, the game is not making your life easier and maybe you should go do something more fun or thought-provoking! Just make sure to stop and think every once in a while about whether the game is helping with your learning goals or not, and try to check them all out at least a little bit. Anyway, on with the list:
- Multiples Frenzy at Sheppard Software: You shoot fruit (just go with it) that shows a multiple of your target number. Math concept level: medium. Strategy level: medium. Time pressure: high.
- Times Square at Calculation Nation (where you can click on Guest Pass): Tic-tac-toe with times tables, basically. Math concept level: medium. Strategy level: medium. Time pressure: low.
- Factor Dazzle at Calculation Nation (where you can click on Guest Pass): Get points by finding factors, and keep your opponent's score low by giving them numbers without many factors. Can you figure out ahead of time how many points you will get from a certain move? Very similar to NCTM Illuminations' Factor Game but has a little extra fun. Be sure to read the game directions. Math concept level: high. Strategy level: medium. Time pressure: low.
- Penguin Jump and Swimming Otters: Crowd favorites, especially for students playing each other. For your 12 x 12 multiplication facts, check your knowledge (and speed) in a competitive way. You can join a game or create your own. If you create a private game, you can play against the computer. You can also make custom settings to play (for instance) only up to 10 x 10. Math concept level: low to medium. Strategy level: low. Time pressure: high.
- Sigma Prime at Mangahigh.com: Shoot the appropriate factors at the invading number ships. Math concept level: medium. Strategy level: medium. Time pressure: high.
- KenKen puzzles: To practice multiplication and division, be sure to select the puzzle type that only has those operations. You can also pick the size and difficulty level that works for you. Click on How to Play if you're not sure how KenKens work. Math concept level: high. Strategy level: high. Time pressure: optional.