Door-2-Math Blog

Once your child gets the gist of breaking 5 into groups (1 + 4, 2 + 3), move on to working with the other hand also.

Start by sticking both hands out but only extend 6 fingers. Here you’re demonstrating 1 + 5 = 6.

Alternate different fingers to get the point across that 6 can be regrouped into 1 + 5. When your child is ready, gently nudge him/her to see of (s)he can come up with another way to make 6. (2 + 4 = 6)

What other ways to make a 6? (3 + 3 =6)

Resist the temptation to rush ahead. Take your time and give your child all the patience you can muster. The reason we settled down on fingers is this: we can carry them with us all the time! Do this in the car when you’re dropping him/her off to school. Do this when you’re in the check out line. The point is that there are no flash cards, no props. And you can do it for a 5 minute session or a 30 second session, the choice is yours.

The reason that we start with “Adding to 5″ and ask you not to skip this one is that as simple as it may sound to you, connecting the “math verb” of ADD is not a natural thing.

Earlier, in the section on counting, we mentioned that the need to know “how many do I have” is a natural human behavior, but adding is not. “Adding” is to put two or more numbers together and do something with those numbers. To “add” is to count forward, to “subtract” is to count backward, to “divide” is to “share” and to “multiply” is to add quickly. Introducing this first mathematical “verb” correctly and efficiently is well worth the time and effort.

Start by sticking your hand out. Ask your child to count the number of fingers on your hand and then on his/her hand. Count thumb first and then count pinky first. Try a few times. When it’s apparent that there are 5 fingers, move on. (piece of cake!)

Now extend your thumb as far as possible, so you can demonstrate 1 (thumb) + 4 (fingers) = (total of) 5 fingers.

What you want to get across is that to make a total of 5 fingers, one can split 5 into a 1 and a 4. That is to say 1 + 4 = 5. This simple regrouping will help your child tremendously when later on (s)he is faced with an addition problem, say, 9+5. Kids who can’t add by regrouping will have to count on fingers or use cards or be forced to do endless repetition. If your child can picture that 5 can be regrouped to 1 + 4, then 9 + 5 becomes 9 + 1 + 4 which gives 14 because 9 + 1 is 10 and 10 plus any number is “teens”.

Adding by regrouping helps to set a young child away from memorizing “math facts”. As mentioned earlier, sooner or later memorizing math breaks down. For some, it breaks down when trig identities are introduced in 11th grade; for some it happens when fractions are introduced in 5th grade; and for some it happens when multiplication is introduced in 3rd grade. Contrary to conventional wisdom, the earlier it breaks down the better because of  the amount of material to be relearned. What could be even better? Not to get your child to memorize in the first place.

Double checking is a critical test-taking skill. The earlier a child can get in the habit the better. While some schools of though argue that it’s more important to focus on a child’s “effort” than on “results”, I disagree. Mathematics is an exact science – “close enough” just doesn’t cut it. Focus on getting the right answer only. And I emphasize here, it can be done without harming a child’s enthusiasm.

Since addition is the very first mathematical operation that a child encounters, we can gently introduce the “ugly” fact that, in math, there is only one right answer and getting the right answer requires one to “pay attention to details” and a skill like “double checking” is our friend. Yes it requires extra effort and yes, it is tedious., but it is necessary.  It is as necessary as brushing our teeth twice daily, making our bed daily and washing our laundry weekly. The sooner you can help a child to realize and accept the need to “double check” the smoother the math journey.