Door-2-Math Blog

(I’m writing a bit long article today on introducing fraction to a young child.  For best result, this should be done at home when you have more time and space.  Good luck!)

Fractions are an important building block in Algebra, introducing it properly can help your child to progress along in mathematics smoothly. One way that I’ve found works the ‘magic’ is a simple hands-on introduction. The idea is to show your child how and why fraction is used, what does the numerator (I call it the ‘number on top’) mean and how it’s different than the denominator (i.e. ‘the number on the bottom’). Before starting this exercise, it is very important that you’re not stressed with math yourself – any stress you have will transfer to your child. Our kids are remarkable in picking up stress signals (especially non-verbal ones). Be aware.

Starting with a single piece of 8×11 paper on a large, non-cluttered table. Have a pencil handy. Ask your child to tear paper into half. You can either help your child fold the paper along the short side or longer side (easier along the short side) and tear it into two halves. Hold the two halves up and ask ‘if 1 is the whole piece paper, what do you think this is?’

Most kids (3 grades or up) will answer ‘half’. Write ½ in one of the half piece you’ve just made with your child. Now, take the half that does not have any marking on it, and ask, ‘what’s a half of half?’

Depending on your child’s grasp, some will answer ‘a quarter’. If yours didn’t, do not panic. Excuse yourself from the table and get 4 quarters from your purse (or wherever your family keeps the coin draw) and calmly show your child ‘four quarters make a whole dollar – and that is why they call a quarter a quarter 1/4 of a whole dollar).

Observe your child carefully; don’t rush to the next step unless you feel your child can connect 1/4 with ‘four of these 1/4 pieces make a whole’. This is important because mathematical concepts are build on top of each other, missing one link usually leads to breaking the whole chain of reasoning. The whole point is to build bridges from ‘known’ to ‘new concepts’ and no hole on this bridge is too small! (Maybe this will help: imaging your child is crossing the math bridge you’re building with tilts – you never know how a tiny whole will get him stuck!)

If you’re convinced that the concept on 1/4 is firmly established, then write 1/4 on one of the quart piece and tear the other one into half again. Show your child that half of 1/4 is 1/8 since now it takes eight of 1/8 pieces to make the whole 8×11 paper. A good leading question here is ‘what do you think the bottom number mean?’

What you’re looking for is a connection between ‘bottom number’ determines the size of the torn paper ( 1/2 is bigger than 1/4 and 1/4 is bigger than 1/8, etc). My experience has been if they can see it in their minds eye, they can picture it when they are starting to work on fractions. Having addressed what the bottom number mean in a fraction, the next natural question a student usually ask is ‘well, what does the top number mean then?’ If your child ask you that question, congratulations! That means that he/she is actively thinking and digesting the material you’re presenting. Fear not if yours is not asking what the top number means. What you need to do is then go back, re-enforce the concept on what the bottom number means and gently guide your child to the question ‘if the bottom number means this, then what about the top number’. A fraction is made up with two numbers: one on top and one on the bottom. Sooner or later, your child is going to wonder… ‘Okay, I get one of the two numbers, what’s with the other one?’

The logic answer for what the top number mean in a fraction is ‘how many pieces of certain sized paper do I have’, where the size of the paper is determined by the bottom number. For example, 3/4; means that one has 3 pieces of paper that’s 1/4 in size. Having address your child’s questions on ‘what does a fraction mean’, now it’s a good time to show how adding fractions (which requires finding common denominators in most of cases) is really nothing but a counting game. Here is how I proceed:

Holding up a 1/4 piece, I wrote down 1/4; on it and holding another 1/2 piece with ‘ 1/2′ written on it, I ask my students, now how much paper do I have? Most students respond “oh, this is adding fractions’ and they draw a line on the 1/2 piece diving it into two 1/4 pieces. Then majority of them, at this point, tells me the answer to 1/2+ 1/4=3/4. I then show them that when they dividing the 1/2 piece into two 1/4 pieces, math follows the similar procedure, and that procedure is finding the common denominator: If this is the first time you’re explaining fractions to your child, it is probably best to leave finding least common multiple (LCM) and greatest-common-factor (CGF) to another day. Introducing new concepts to young children, it is very important to keep it bite-size, so your child will not be overwhelmed

“What does Fraction really mean?” Alexa asked today while I was dropping her off to her school.Thus far, I’ve covered 2-digits multiplications (26 x 32 on paper), divisions (321 divided by 3 mentally; and 4225 divided by 65 on paper) with her and she was ready to move on.

“What do you think it’s about?”  (I wanted to see where her understanding was and go from there)

“It’s about how much you have in a group?”  (This is how most school textbooks introduces fraction — though not entirely untrue, it is not the clearest way to introduce Fraction — in my opinion any way).

“hm…well, remember that big chocolate cookie daddy makes in the big pot?”

“yeah”

“well, if all four of us spilt the whole cookie evenly, how much cookie do each of us get?

“a quarter!”

“Right!  so in fraction we say it like this ‘ we each get 1 over 4′, which is exactly like you said, ‘a quarter’”

“so fraction means splits cookies?” (only if she knew how close she was to the essence of fraction!)

“Right on!  Fraction means ‘A part of a whole’.  Now can you tell me when splitting cookies, do you want more people splitting it or less?”

“Less of course!  I’ll have more splitting an olive with me” (she does not like olive as you might’ve guessed).

“So if we bring a cookie made of olive to your school, and all the kids there splitting it evenly, how big of chunk do you get?”

“hm…1 over 32″ (there are 32 kids in her combined 1st and 2nd grades).

“Right!”

“Now going back to the cookies with chocolate, if I didn’t want mine and give my share to you, how much would you have?”

“Two quarters of course!”

“Right again.  So we say ’2 over 4′.  Now do you know how we write 2 over 4?”

“2 with a line and then 4.”

“Good!  Can you tell me which number is on the top? The 2 or the 4?”

“2.”

“So when you want eat more, do you have the bottom number big or top number big?’

“The bottom number is how many people splitting it, so I want the bottom number small and the top number big, since the top number is how many slices I get to have.”

“Very good!”

“Okay, Mommy, my head had enough math now.”

That was a good start on fractions.

Happy Zen Math!

(c) Feenix Pan, 2007.  All rights reserved.

Today during the drop off, Byron announced that he is tired to adding with 9’s. I promptly asked him ‘oh, yeah, what’s the trick with adding 9’s?”

“Borrow 1, make ten and add ‘teen’.’ (Not bad for a 4-yr old, I thought).

“Cool! Do you want to know what to do with adding 8?”

“ Then, we are done?” (Boy, he really didn’t want math today).

“Yep.” (I’m a firm believer that there is absolutely no point in dragging a non-thirsty horse to the riverbank!)

“All do you with adding 8 is ‘Borrow 2, make ten and add ‘teen’.”

“that’s it?” (Kids are always amazed that math can be so simple!)

“That’s it with 8. wanna do some tomorrow?”

“of course!” We then moved onto who is doing what at his pre-k grade at the Montessori Schoolhouse.

Happy Zen Math!!

(c) Feenix Pan, 2007.  All rights reserved.