### Tag: short bead chains

Horray for having a curriculum!  Sunday night I looked on my presentation calendar and realized I was supposed to present skip counting on Monday.  I hurriedly looked at the ideas from What Did We Do All Day and made my own set.  She also has a second post on a game you can play.  I didn’t even bother doing a bunch of research.  We ended up with about 9 ideas from her website.  I got both kids to work on them yesterday.

What’s Skip counting?

Skip counting is a state standard for Kindergarten (or it was last year).  It is the precursor to learning multiplication and comes after your child has mastered counting.  In Montessori, you show the kids how to count these short and long bead chains.  The short bead chains are squares of a number, (so for 9, you would be able to count to 81) and the long bead chain are cubes of a number.  But you don’t show the kids how to skip!  They’re supposed to arrive there on their own after getting tired of counting one by one.  Makes sense from a development point of view.  It is how you know that they’re ready to move on from counting.  Of course in practice I don’t know if it’s really true.

I want to emphasize this because if you teach the trick to skip too early, you could end up with a child who knows how to skip count but not know how to count well.  Knowing how to count is important because it helps the child know the relationship between two numbers.  It’s the foundation for all math.

I had one epiphany yesterday watching the kids skip count.  There are two aspects to multiplication.  One is learning your multiples, and the other is knowing the result when two numbers are multiplied together.  To me, they’re related but different.  So for example, the What Did We Do All Day activities are asking the kids to recite their multiples, for example, 3, 6, 9, 12, etc.  But that doesn’t tell me off the top of my head that 12 is 3×4.  What it tells me is that 12 is a multiple of 3.  Useful when you have to learn Common Multiples.

On the other side is learning your multiplications table.  This is what you need when you are doing equations like (1234 x 4321=?)  Multiplications table is pure boring memorization.  I don’t know of any activities, short of singing, that will make it more fun.  Whereas learning multiples there are a variety of activities that I see online.

Where the Kids Were

Last year Thumper got to memorizing 6 and then got stuck, could not remember multiples of 6,7,8,9.  I was going to “force” her to continue.  Hey, I remember standing next to my mom memorizing them when I was 7, she can do it too!  But thankfully I read Life of Fred math.  It basically split up what you would normally think of as a complete concept to learn, like learning to add up to 20 all at once, or learning multiplication table up to 9 all at once.  Rather, kids have difficulty the bigger the number so they could do well with the beginning numbers (addition up to 10, multiplication up to 5) and then need to wait a year for the rest. So I let it go.  This year Thumper is more willing to learn the rest of that multiplication table.

As for Astroboy, he knows his numbers up to 1000 for sure, 10000 sometimes, so we’d been working on counting the bead chains.  But I needed more variations.  I think the fact that Astroboy is now also adding small numbers together is another good indication that he is ready to figure out the next number in the sequence without counting.

What We Did

I looked through all of the link’s activities and printed them out.  I ended up with the following work:

• 選一個數字。 可以丟骰子選。
1. 數長的跟短的珠串
2. 在一百板上每數到這個數字，用筆塗顏色，念它的乘法表出來。
3. 把數字寫下來在空的一百板上，每遇到他的倍數，用新的一行。
4. 在珠串復習紙上寫數字。
5. 玩迷宮遊戲。
6. 看電視，唱九九乘法表歌。
7. Astroboy： 寫 數字在空的一百板上。
8. 描寫數字。
9. Thumper：把20個數字寫在筆記本。

Age: 4.5 and 7.5

Presentations: Making Geometric Shapes, Association of squaring chains with bead stairs (primary), Concept and notation of squares, Notation of squares layout, Finding the totals of squares, Power scales, Chain of 1000 (just work)

Because I’m in the squaring and cubing section part of the album right now in class, I’ve been giving the kids some presentations in this area recently. Last week, I presented the introduction section of squaring and cubing, which are extensions of the short chain work: Making Geometric Shapes.  This is where we bring out the short bead chains, fold them into different polygons, and introduce the nomenclature.

You can see typical Thumper reaction here at the face of new materials; she wants to play with it and make a star with the 9 chain instead of a nonagon. The other thing we did that day was Circumscribing One Figure Around Another.  For this presentation, you show them how to circumscribe one shape inside another and introduce those two vocabularies (circumscribed and inscribed).   Astroboy worked on this again today (Thursday).   Because he did this after my attempt at giving him the Bead Cabinet presentations that were at the end of my primary album (whereas this activity is in my ELE album), he put all those bead bars around the circumscribed shapes.  And of course he was no where super interested in my presentation.  Though he was game and allowed me to finish my presentation and even helped me count.  (He does love anything that has to do with pretending to be a train and lining things up.) My sister asked me what the point of this work is, circumscribing figures.  I think it’s just a sensorial activity.  Letting kids play with their geometric shapes.  The kids also figured out by playing with it that as the shapes got larger by one unit on each side, the difference in area between shapes got larger.

Finally splurged last week and purchased the bead cabinet.  I forgot to buy the arrows so now I’m busy making them.  This required some research into what’s included and it’s actually quite confusing.  So I thought I’ll write it down here for reference.

The bead cabinet contains the following.

1. Short Bead chains has square chains.  So 1, 2/2, 3/3/3, 4/4/4/4, etc.  The golden Bead Chain of 100 is also sold separately.
2. Bead squares  are square representations of the short bead chains #1-#10.   #10 is basically hundred square.
3. Long bead chains has are cube chains.  So 1, 2/2/2/2, 3/3/3/3/3/3/3/3/3, etc.  The golden Bead Chain of 1000 is also sold separately.
4. Bead cubes are cube representations of the long bead chains #1-#10.  #10 is basically thousand cube.

The reason I got confused was that I wanted to make the arrows myself.  I couldn’t bring myself to spent \$45 (including shipping) to buy the cheapest set from Kid Advance.  But in doing research, I found that most free printables don’t do it up to the standards of Nuinhuis.  The arrows have different widths to help the child.  The Nienhuis and Allison’s Montessori ones have cursive numerals printed.

In the Nienhuis catalog description it says:

• 1/4″ for units
• 1/2″ for multiples
• 3/4″ for squares
• 1″ wide for cubes

What are multiples???  Since I haven’t actually used the material, I had no idea.  Good thing Montessori Materials actually has printables.  I wish people make their numbers in cursive.  It’s very important to me because Astroboy constantly tells me that is not how 4 is written when I show it to him the cursive way.  It’s the little details like this that makes Nienhuis so expensive.

Combined with repeated staring of catalog pics, here is what I made: