Practice Arithmetic with Geometric Dice



My daughter recently received a huge pack of cool geometric dice in several different colors:

  • An icosahedron (20-sided polyhedron) with the numbers 1 thru 20.
  • A dodecahedron (12-sided polyhedron) with the numbers 1 thru 12.
  • A decahedron (10-sided polyhedron) with the numbers 0 thru 9, and another with the numbers 0 thru 90.
  • An octahedron (8-sided polyhedron) with the numbers 1 thru 8.
  • A cube (6-sided polyhedron) with the numbers 1 thru 6.

These dice turned out to be really handy for learning addition and multiplication facts.


You can easily practice addition facts and multiplication facts with these dice.

Here are some examples:

  • ADDITION/MULTIPLICATION. Roll two decahedra, marked 0 thru 9. Add or multiply the two numbers to practice addition or multiplication facts 0 thru 9.
  • SMALLER NUMBERS. Roll two cubes, marked 1 thru 6. Add or multiply the two numbers to practice addition or multiplication facts 1 thru 6. The cubes let students focus on the smaller numbers first, before working with 7, 8, and 9. (If you want more basic practice, find tetrahedra—4-sided polyhedra—marked 1 thru 4.)
  • FOCUSED FACTS. Roll one decahedron, marked 0 thru 9. For example, suppose you want to practice your multiplication table of 4’s. Simply multiply the die by 4. This lets you concentrate on a single number’s addition or multiplication facts at a time.
  • 11 THRU 20. Advance to dodecahedra or icosahedra to practice the facts 1 thru 12 or 1 thru 20.
  • SUBTRACTION. Practice subtraction facts using an icosahedron and a decahedron. Be careful to subtract the smaller number from the larger number; sometimes, the number on the 10-sided die will be larger. (Advanced students who are learning about negative numbers can use these to sometimes subtract the larger number from the smaller number.)
  • TENS. Multiply powers of 10 using one decahedron with 0 thru 90 and another with 0 thru 9. Or roll one decahedron and multiply that by 10 for more basic tens practice.
  • POWERS. Roll a tetrahedron and a decahedron together to learn about powers. Let the tetrahedron serve as the exponent.
  • FRACTIONS. Roll four decahedra to learn about fractions. These will give you the numerators and denominators of two fractions. Then you can add them, multiply them, divide them, compare them (figure out which is bigger), or subtract them (but first find out which is larger).
  • DICE WAR. If you have several dice to divide equally, you can play dice war with a friend. Each player rolls two dice. Either add or multiply the numbers (choose one before the game begins). The higher sum or product collects both dice.


Another cool thing about using a variety of geometric dice to play math games is that kids get to hold various geometric solids in their hands, see how they look, get a feel for them, and after much use remember how many sides each shape has.

Better than just being told or shown what a dodecahedron is… hold one in your hands, roll it, play with it for months. Then you’ll ‘know’ that solid when you hear its name. (It helps when someone learns and uses the correct names while using the dice.)

Many of these dice packages are sold with role-playing games in mind, but there is no reason that you can’t use them for math practice instead.


  • Polyhedron: a three-dimensional solid.
  • Polygon: a two-dimensional object, not a solid; it’s flat.
  • Polyhedra is plural, polyhedron is singular.
  • Dice is plural, die is singular.


Copyright © 2015 Chris McMullen, author of the Improve Your Math Fluency series of math workbooks

Singing Arithmetic



Sound can be a useful learning tool.

I saw this firsthand a few weeks ago when I met a couple and their daughter at a local restaurant.

Their daughters were learning arithmetic, history, language, science, and other facts by singing.

They were using a special curriculum that included songs for many basic things that students learn in various subjects.

One of the girls sang a few different songs and it was quite impressive how much she had learned from singing.

My daughter enjoys singing, too. Recently, I heard her singing some of her multiplication facts.

You can simply sing facts in order, like the table of fours: 4 times 1 equals 4, 4 times 2 equals 8, 4 times 3 equals 12, etc. Or you can add an occasional phrase here and there, especially if it rhymes.

It’s good for patterns, too, like 5, 10, 15, 20, 25, etc.

Most children learn the alphabet song. There are many other songs available to help with learning.

I recall listening to the Schoolhouse Rock songs when I was a kid.

Most people learn better one way than another. So using a variety of teaching strategies helps each student learn through his or her strength.

But I think it’s also important not to let every student rely only on his or her strengths. It’s important to develop the other learning styles, too.

We become better students not just by focusing on improving our strengths, but also by improving our weaknesses.

Singing arithmetic isn’t for everybody, though. I’m sure nobody wants to hear me sing my multiplication facts—or anything else, for that matter. 🙂

Copyright © 2014 Chris McMullen, author of the Improve Your Math Fluency Series