Wednesday, January 15, 2014

School Days: Fractions

After a long Christmas break the boys have had a good four or five days back in the school room. We were ready to get back to work on the 6th, but the Polar vortex kept Dad home from work.  We generally keep the same calendar as Dad.

The have been on a huge fractions kick. Apparently Me Too has been feeling taunted by the site of his own face stalled on drawer number one of the fractions cabinet and wanted to change his position:

We reviewed equivalencies and moved on to the addition of fractions with like-denominators.

We used laminated blank tickets, construction paper fraction bars, our signs and symbols box, and the fraction circles.

Above is a peek at his notebook from his first day of this work.  Me Too is happy to report that his "face" has moved forward several drawers on the fraction cabinet.

Kal-El was either inspired or threatened by Me Too's advancing mug.  He has been avoiding fraction work, but sat down and worked through four drawers while I taught Me Too.  The mopped up all of the remaining subtraction of fractions with like denominators.  There are at least 150 equations in the final subtraction drawer because it contains all possible equations each in six different formats (combinations of:  difference first, difference last, numerator of difference missing, numerator of subtrahend missing, numerator of minuend missing).  I told him that he only needed to do about 30 of those and that if they went well the rest would be saved for occasional review work.

Kal-El has since moved on to multiplying fractions by a whole number.

Me Too still enjoys tracing the fraction insets, particularly those in the triangular or square frames.

I can tell the boys are comfortable with fractions now because they have started using them effortlessly in daily life.  Today Kal-El reported that at dinner last night (I was at the gym) Dad filled 1/3 of his plate with broccoli.  Me Too, not to be left out, added that 1/12 of their plates was full of coleslaw.  Yesterday in the car they were spontaneously inventing fraction story problems.  Kal-El said, "Mom, if Dad gives you a dozen roses and a one-half die, how many roses do you have left?" Me Too, not to be left out (again), countered, "Mom, if Dad gives you TWO dozen roses and 1/4 die how many do you have left?"  I don't think he knew the answer (When I said "18" he said "correct" but would have agreed with anything I said.)  but I enjoyed the spirit of the question.  Kal-El was miffed because he knows Me Too will just agree with anything I say.  He asked Me Too, "If *I* had said 19 would you have said 'incorrect'?"  Me Too didn't answer but Kal-El knows that Me Too DISAGREES with everything Kal-El says.

1. Your boys always make me smile. Where did you get your cut outs?

1. Thanks Abbie! I'm pretty sure they are from iFit.

2. Thanks for the tip. Where did you get the montessori compass? is that what it is called? I've seen it on Alison's for a huge price.

I found last Oct/Nov that both T and S already just knew the basic operations for fractions smaller than one. Or just got it intuitively. Again, they don't like repetition much so there wasn't any revisiting this work back then. I plan/hope to delve back into fractions again next month with new lessons that include the cut-out fraction circles.

3. They are from either iFit or Kid Advance. Both carry it and I can't remember where I got it. It will be listed as a "protractor."

For the boys, I found the *concept* of operations with like-denominator fractions was so simple they understand immediately. However, without the practice using and writing the equations they looked at them blankly even a few days later. My boys need a lot of practice writing them. We're not the fastest antelopes in the pack.

4. For example, Me Too has been working on these daily for about five days. On DAY FIVE, just like every other day so far, the first few equations he wrote down had no denominators on one side of the equation and he reversed the order of addends (understands that commutative property I guess). Other days he has left off the fraction bars. He knows how to do it, it's recording it that's the challenge for him.

Kal-El can do the equations lickety split, but after a few weeks away from fractions forgot all about reducing to lowest terms.

Oh, and the compass is that two legged thing for drawing curves and circles. The protractor is the thing that measures them.

5. A yes, the notation of fractions. T did that fine, but at the time I introduced this, S was refusing to write anything. I'll probably have to review this with her in depth. How did Me Too do with your handwriting boot camp a few months back?

Oh, and do you have a theory, or know, why notation is more difficult for your guys? I am wondering if some of this might crop up with S and am trying gain some strategy about how to handle it if it does.

On another aside, I think I have an idea about getting the kids, T especially to engage with works a bit longer, and do more problems. I understand now from the KoTU albums that it IS sometimes the guide who will say, okay, you need to do some follow-up work for that lesson we did yesterday, when are you planning to do that? And then actually plan with the child when that follow-up work is going to happen. Somehow I don't think that T would mind this too much since this kind of planning would give him a good blueprint of what works he should be doing. Interesting. Thanks for planting this seed in my little brain.

And thanks for the protractor vs compass thing. :) The only thing I remember from my HS geometry class was the proofs. (I was much better at calculus.)

6. Me Too is not done with his boot camp yet. From what I can tell so far it has had no discernible effect. If you saw the post with Kal-El's recent poem you can see HIS current handwriting and I'm happy enough with it. I'm thinking Me Too just needs more time. I read somewhere recently that 5th grade is often the time when boys' handwriting blossoms.

Ack. I started calculus the same year I realized I was going into music. In one week I determined calculus was unnecessary and dropped it :)