This is the second of a series of blogs regarding fluency of basic facts.
Memorizing any operational facts can be easy for some (who have photographic memories) and difficult for others. I tried and tried every type of “flash card” with my oldest and all it did was provide frustration, tears, and dislike for the math. We tried flash cards, memory games, on-line shoot the sum games. And none of them worked. I freaked out, knowing that if he didn’t get these facts down, it would be an uphill battle. But is it really? Do we need to focus on memorization or understanding???
This blog is about understanding and a teeny tiny bit of memorization. Please feel free to disagree, as this is a blog after all and participation is encouraged! However, at least read on before fighting the fight for memorizing only.
Depending on whether you live in a Common Core state or not, typically we want children to know fluently all of their facts to five by the end of Kindergarten and all of their single digit facts (10 + 10 is cool too) by the end of grade 1. Note I wrote “fluently” versus “to automaticity”. So what’s the difference? It means I get three whole seconds to figure it out. I may not be able to see the answer in 0.5 seconds, but using some strategic thinking I can get it. That’s the goal. Anything beyond is cool, but this is for all children.
Fun fact: If all you are going to do is memorize the sums for two single digit numbers, the amount of facts you need to memorize is 81. 81! That is a LOT! Have fun making 81 flashcards! No thank you!
So let’s dwindle the amount to memorize. Below are two strategies to teach your kiddos to make that 81 significantly less. (There are others, but if you focus on these two you are waaay ahead of the game!)
- Commutativity. This is a property (a rule that ALWAYS works in mathematics) of equality. Think about the distance you drive to work. And the distance you drive home. Now if you take the same route both times, you go the same distance. No matter if you start from home, or you start from work, your commute distance is the same. Commutativity works the same for numbers. I can add 3 + 5 or 5+3 and my result (the sum) is the same, 8. So if I use my commutative property, I now only have to memorize one of the two facts! I am now down to 45 facts! (You may think, “Hey, why isn’t it half of 81?” Well, the doubles such as 2 + 2 and 3 + 3 do not numerically have a commutative fact, so you are stuck with them.)
- Making 10. This is a big stinking deal. Your kiddos need to get under their belt the ways to make ten. (1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 and the reversals based on strategy #1.) Why? For starters, we live in a base ten world. Once you hit 9, the next number literally moves over one spot to the left and now you have a double digit value. Once you hit 99, you move over one spot to the left and you now have a triple digit. And so on. Really though, let’s be practical. Is it easier to add 9 + 8 or 10 + 7? 10 + 7, because you can add the 0 + 7 easily. So if I can manipulate my digits to make a 10 +, I am good to go. Example: 9 + 6. I know that I only need one more to make 9 a 10. So I am going to take it from the 6. 9 + 6 = 10 + 5 = 15. If I know how to make a 10 + expression from the addition fact I am working with, I now go from 45 memorization facts to 25!
What are those 25 facts? 1 + 1, 2 + 1, 3 + 1, 4 + 1, 5 + 1, 6 + 1, 7 + 1, 8 + 1, 9 + 1, 2 +2, 3 + 2, 4 + 2, 5 + 2, 6 + 2, 7 + 2, 8 + 2, 3 + 3, 4 + 3, 5 + 3, 6 + 3, 7 + 3, 4 + 4, 5 + 4, 6 + 4, 5 + 5 (Notice the largest sums are 10, because all others can be made using a 10 + strategy.) So could your child learn these facts? ABSOLUTELY! Just remember to include the others for them to practice their two cool strategies with!
Next Blog: Fun games to play to work on making ten!
HUGE NOTE: Please do not time your children. For many, it stresses them out and they lose focus. Also, if you time children before they master the strategies, it will encourage them to count on their fingers. Though that may work for these small values, it will not help them in the long run when adding much larger numbers.