Magic Tens

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By Mike O’Hern, Center Director of Mathnasium of West Knoxville


Memorizing math facts can be quite an arduous process, and exceedingly few students actually like it.  Beyond that, what’s the value of memorizing a ton of math facts?  The student typically memorizes these facts for the moment, but then they quickly fade away.  Then if you ask “seven plus what number is 13?” and he doesn’t remember that fact at the moment, out come the fingers to count it up.

There is nothing wrong with memorizing math facts, but having a grasp on how the system works is the permanent solution to keeping math facts close at hand for a lifetime.  The magic key to the whole system is TEN.  Yes, once the student understands the ten-based system she will be able to figure out all kinds of things without having them memorized.

The first step in building this magical foundation is being able to visualize the complements of ten.  (“Complements of ten” is just our fancy jargon for the pairs of numbers that add up to ten.  Nine and one, two and eight, etc.)  Explore these things both orally and visually with little or no writing – we’re not trying to memorize numeral groupings, but visualize quantities.

Get a set of ten objects of the same size (buttons, blocks, coins, whatever) and arrange them like shown in figure 1.

Have your child count the items to see that there are ten.  (Notice, too, that later you can use this arrangement to start learning about counting by 2s.)  Now split off two of the objects so that it looks like figure 2.

Make sure your student notices that there are still ten objects, but they are in two smaller groups.  So, eight plus two makes ten.  Copy figure 3

with your objects, and continue to make various two-group combinations.  Soon it will be clear that 8 + 2 is the same as 2 + 8, which is a very important concept.

Now that our complements of ten are nailed down, let’s add up from ten.  For these, let the language help out.  Help your student notice that the numbers describe themselves.  “Sixteen” sounds like “six ten” and it is, in fact, six plus ten.  (Sure, eleven and twelve are a little tougher, but, hey, that’s English for you.)  Figure 4 shows our ten, plus a few more as an example of how to get the idea across.

Now the best part!  Back to our original question: seven plus what number is 13? Figure 5 shows how the “math brain” automatically figures it out.  First, from seven up to ten is three, then from ten up to 13 is three more, so that’s six altogether!

By working on and around the tens, even those facts that aren’t on the tip of the tongue will come out quickly.  But even bigger is confidence.  Memorizing packs facts in the brain, but understanding brings real confidence!


Mike O’Hern, Center Director of Mathnasium of West Knoxville, earned his Bachelor’s Degree in Metallurgical Engineering at the University of Tennessee, Knoxville in 1988. He pursued graduate studies in Materials Science & Engineering while on the Research Staff at Oak Ridge National Laboratory. Mike has had a life-long love of mathematics and teaching, and feels that math is not about learning to be ready for the next math class – it’s about learning to think.

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