## Friday, September 25, 2015

### School Days

Kal-El is reviewing long-multiplication with the flat bead frame.  He original learned this work in parallel with the checkerboard back in April of 2014.  However, he wound up preferring the checkerboard at the time and didn't spend as much time on this which makes it good for using for review.  We have a set of Nienhuis cards he is working through.

This time around I laminated a strip of paper that he can use over and over again with a dry erase marker rather than having to get a fresh strip every time.  Extra bonus, I don't have to keep making strips of paper just the right size again and again.

I do have to keep strips of paper stocked for logical analysis, but I don't have to fuss about the size.  Kal-El has mastered indirect objects and started adverbial extensions ("where" in particular) last week.  I might get a photo of that this week.

Both boys did really well with finding lowest common multiples and we finished that thread in the albums.

They did equally well with factors.  During this very first presentation, finding the factors for 18, they both figured out all of the factors in their heads while I was still showing them how to lay out the pegs on the boards to check if "two" was a factor.  So, I had them do the four remaining examples in their heads and write them all down on a piece of paper.  They made it into a race which Kal-El barely won.  So, we moved on.  I taught them how to use table C to find all of the factors for a number and then how to break down each factor into prime factors only.  This week I think we do something similar on the pegboard.  I can't wait to get past this.  I understand why we find all of the prime factors for a number but I don't understand why we break down the other factors into their prime factors.  Stuff like that makes me really dislike a lesson.  The last time I felt this way was some of the squaring and cubing games.

Me Too began the checkerboard.  We have cards from Nienhuis.  After the initial presentation he did about 15 cards over the course of three days in which he just had to build a number with beads on the board.  Last week he started doing equations with one-digit multipliers (Something that is in AMS albums but is skipped in AMI.  Probably not necessary, but we have the cards and they didn't take very long).   The hardest part for him is really writing down the equation and the product.  He is still learning how to line everything up vertically.  Both the stamp game paper and the large bead frame paper really take care of that for you.  He finished all of the one-digit multipliers this week and now can start two-digit multipliers next week.

We built a Roman road this week and I took lots of pictures.  Hopefully I can get those uploaded this weekend.

1. What a great week. I love you resources.
Blessings, Dawn

2. Laminating a strip for the flat bead frame is a good idea. That frame is so good for learning why we put a zero first when we multiply by the tens digit in the multiplier. We did the frame before the checkerboard, and Mr. Scientist can do the problems on paper no problem now, except for sometimes forgetting the zero...a couple of problems on the flat frame will fix that!

3. I think you break the other factors into their prime factors so that the learner can realize that they are always a subset of the prime factors of the original number. If I worded that confusingly, an example is 12 with composite proper factors 6 and 4 which have prime factors 2, 3 and 2, 2 respectively. 12's primes are 2, 2, and 3.

1. Thanks you for trying. I still don't understand why we we want to know that. LOL.

2. It's preparation for equations, a long way in the future. My daughter, who is 15 and doing maths GCSE this year has some algebra stuff where you have to know the factors of numbers.

3. Thanks Annicles! (and anon). I also noticed this week that an upcoming lesson has them use the prime factors, including the factors broken down into their prime factors (number of occurrences) to find the LCM. I feel better now.

4. Amazing week!! Love all your math works@!! Congratulations!!! OmG!! The boys are soooo big!!! LOL hugs