Skip skip skip ….counting!

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。

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1000 and 100 Bead Chains, counting to 10000.

Last semester Astroboy was on a counting spree.  By the end of the semester, we’d kind of covered the end of “counting” as it was presented in my album.  But he still wanted to count.  How much does he like to count?  On our drive to swimming, he’d suddenly start counting from 1 to whatever he can get to.  He managed to get to 300 with very minimum help for me.  When we do any other math materials (addition, multiplication, operations), you can see what he really enjoys is counting the beads.   I did not see this before with Thumper.  It’s fascinating to watch a child at work in their sensitive period.

But what materials can I use in the classroom?  I was at a loss as to what to do until I bought the bead cabinet for Thumper to learn skip counting since she’s doing multiplication.  During my research of the bead cabinet arrows, it finally dawned on me that I should introduce linear and skip counting because the beads are way longer.  Now, if you read the Australian Montessori Council and their National Curriculum guide, or even Info Montessori it’s spelled out right there, Counting or Continuation of Counting.  I don’t know why it didn’t occur to me other than the fact that linear and skip counting is all the way at the end of my album and I was told during my training that kids don’t really get to linear and skip counting.  Plus, it’s all the way at the end of my album!  Somehow I thought that meant it’s the end of the sequence.  We rushed through these presentations during training since it was the last day.  If you look at the album though, it says age of introduction is 4.  Maybe the instructor was really talking about the concept of squaring and cubing.

Anyways, so now I know if someone were to ask me.  For counting, after the intro materials, teens and tens, hundred board, use the bead chains.

During prep week, Astroboy said he was bored and was happy to do the 1000 bead chain work when I suggested.  Now, before Christmas break, we played a lot of Hundred Board games.  He got really good at reading up to 100, 200, and 1100.  It doesn’t mean he knows what comes before or after a number, how to count that high, he’s just good at reading them.  However, I’m glad we did all this prep work because he didn’t have to learn how to read the numbers on top of counting the numbers.  This is why I suggested the 1000 bead chain.  Thumper wanted to join in as well.  Which turned out to be a good thing.

Because the classroom is a mess, I had the kids lay out the beads in a circle over two rugs.  The kids had fun laying out the beads together.  Once I dumped the bead chain arrows out, Astroboy got discouraged.  Too many arrows.  Thumper on the other hand, got right to work sorting them.  It’s obvious she has a better grasp of the numbers and their relationship with each other.  After showing Astroboy laying the arrows for #1-#9, #10, #20, he and Thumper worked together to lay out the rest.  He laid the arrows for the first few 10’s then got tired.  That’s what he says when he doesn’t want to do a long work.  So I gave him sets of numbers in hundreds (110, 120, 130, etc) and had him find them in order to give to Thumper, who for some reason really wanted to lay them out.

1000 Bead Chain

When they were done, we admired their handiwork and counted backward.  Though he found the work of laying out arrows from 1-1000 tedious, he painstakingly walked and counted backward along the chain.

I wanted to talk about Thumper’s counting and counting in Chinese.  You’re supposed to introduce that huge cube to count to 10000, or was it 1,000,000 in Elementary.  We haven’t gotten to it because I haven’t had time to make the material.  But Thumper’s been showing her sensitive period for counting as well, in a not as noticeable and different way.  Several times, she counted spontaneously in the car to measure how long it takes, in seconds, to get home from swimming.  She goes along with Astroboy when he counts and goes higher.  Both kids like to use big numbers, even though they have no concept what they mean when they say “I love you 100,000,000 times.”  What was evident though, through a bit of assessment last semester, was that Thumper didn’t have a firm grasp of reading and counting in the 1000s nor does she know how to count to 10000.  10,000 is actually the highest number you count to in Chinese before the counters “repeat”.

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