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Real Math Mastery, Part 1

One of the best educators in the world of math, Marilyn Burns, has been working for years on quick ways to check whether children have grasped the big ideas of math. Her conclusion? Often, students with fantastic test scores still lack basic concepts! To see the difference between understanding and merely calculating!

If your child is struggling to memorize math facts, chances are the real problem is one of the big math concepts I’ve been discussing in my last couple of blogs. And you’ve got the best tool right in front of you at all times to check for understanding of the next big concept: combinations that make 5 and 10. You have your hands that naturally make these combinations!

What are combinations that make 5? Knowing that 4 + 1 and 2 + 3 and 3 + 2 and 1 + 4 all equal 5. Once your child masters this basic concept, remembering all of the addition facts becomes easier. The same is true of combinations that make 10. These are the building blocks of computation. If your child is struggling with addition, hold up 2 fingers and ask, “How many more do you need to make 5?” They’ll see the quantities, not just numerals on flashcards, and start to make sense of it all. Think of it this way:

We all know that memorizing some of the bigger numbers such as 8 +7 gets tricky for a lot of students. But, once they understand that 8 + 2 = 10, they have two ways of getting the right answer. Memorization of course, but if they forget, they can talk themselves through, “Well, 8 + 2 = 10. And 7 is 2 more than 5. So if I recombine I’ll get 10 + 2 = 15.” Sound like too much work? Not if you forgot the basic fact.

“Combinations” help students see the patterns in the facts. Brain-wise, accessing numbers in various ways means your using different parts of the brain. That makes for more synapse connections—and multiple ways to retrieve that information.

But that’s more than you need to know. More important, when a group of 8th graders struggling with algebra spent time mastering combinations of 10, guess what? All of a sudden algebra made sense as well.


In this case it’s okay to use your fingers. It’s no accident we work with base 10 numbers; those hands will work wonders in helping your child make sense of addition. And, therefore, subtraction! But here are two more ways to play with this idea:

  • Play “concentration” with just the 1-5 or 1-9 cards. Children keep cards that add to 10
  • Play “Go Fish”. Children have to ask for the card that will make a five or ten.


By Jane Kise, Ed.D. – Educational Advisor and Consultant, 
Jane  writes an insightful post every Tuesday for Kidtelligent. Jane is an educational consultant, specializing in teambuilding, coaching, and school staff development. She is also the coauthor of more than 20 books. Jane’s website  is