Math

One of the beauties of homeschooling is that you are not confined to a classroom.  My daughter and I took a bus to the Philatelic Museum today (to support her new-found hobby, stamp collecting – anyone out there willing to send us stamps?) and we played a few number games whilst waiting for/taking the bus.  We played a game where we would look at the 4 digits on the license plate of each car and guess whether they added up to an even number or an odd number.  I had the unfair advantage of knowing that if they were all odd/even OR if 2 were odd and 2 were even, their sum would be an even number, but we had fun.  She then changed the game to subtracting the second 2 digits from the first 2 digits (eg 48-27).  Then we got to dabbling with negative numbers and multiplication tables.  I’m beginning to suspect that her memorization of the tables is limited, but since her interest in math is high, I am going to just offer materials for her to do but not push the issue.  I suspect it’ll come through using the other materials (eg checkerboard etc).  But I’ll still try to incorporate a variety of ways to allow her to memorize the tables, if I can find them….

One of the things I just realised (i.e. learnt from her) is that the way we write the “carry-overs” in our math operations can really confuse the child.  No wonder my trainer does not use the conventional method.

Let me explain:

If we have, say 834-256 (written vertically) – we will “cancel the 3” and write a small 2 in its place and write a small “1” next to the 4, so that it is 14-6 and so on.

So in effect, the “1” becomes a “10”. It’s just that it is written next to the 4.  Meanwhile the “2” written in place of the cancelled “3” remains a “20” and not a “200”.

However, for addition, when we carry over the 1, it is only an additional number for the next place value (eg in 246+358, 6+8=14 so we write 4 under units but the 1 that gets carried over next to 4 is really just another ten and does not make the number 14).  The same problem occurs with multiplication and is further compounded by the fact that the number you carry over does NOT get multiplied by the multiplier.

Of course if a child has had enough work with the materials, he/she understands what is really happening.  However, I can SO see how this method of writing the “carry-overs” can still add to the confusion of the child.  Unfortunately, I have to prepare these children to enter middle school/high school where this method of writing is a requirement.  I just need to figure out how best to help them get over any hurdles, if necessary.

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