15 Heads in a Row

The Activities

  1. Topic: Algebra: Book: The Yum-Yum House by Walker.
  2. Topic: Algebra: Work together as a group to solve simple algebra problems.
    1. y + 11 = 32
    2. y + 68 = 72
    3. y + 22 = 100
    4. 2 * y = 40
    5. 3 * y = 12
    6. y / 2 = 10
  3. Topic: Programming: Trace more complex programs, then try to write your own programs.

    1. Box_X = 1

      Print Box_X

      Box_X = Box_X + 10

      Print Box_X

    2. Box_Y = 1

      Do 10 times {

      ____Print Box_Y

      ____Box_Y = Box_Y + 1


    3. Write a program that prints out “Hello”.

      One student's program to print "Hello"

      One student’s program to print “Hello”

  4. Topic: Probability: Experiment with coin flips to figure out how many flips it takes to get 3 Heads, and how many it takes to get 3 Heads in a row.

How did it go?

I led the big kids circle this week. 5 kids attended.  At the start of circle we had a discussion about how wild circle got last week. I explained that I want kids to talk, but they should talk about the activities, not about other things. Two of the kids suggested I should say “1, 2, 3 Silent!” and then everyone should stop talking.  This worked well this circle…there was still lots of talking, but it didn’t get out of control.

Book: The Yum Yum House

The kids all really enjoyed this book. It has a lot of story, and a little math.  It centers around 2 kids who want to get at least 83 pieces of candy so they can make a gingerbread house that is fancier than their friend’s.


I asked the kids if they had ever heard of algebra, and they all raised their hands excitedly.  Apparently all of the their schools have introduced simple problems like x + 10 = 17.  The first 3 problems about addition were very easy for the kids, though some were faster at mental arithmetic than others.

2 * y = 40 was more difficult. None of the kids had seen multiplication in an algebra problem.  Several kids were able to explain that if you make 2 groups of y blocks each, you should have 40 blocks.  They were able to guess 20, and we verified it using Base 10 Blocks.  3 * y = 12 was also quickly solved.

y / 2 = 10 was actually  much trickier. One kid really wanted to answer ‘5’ to this.  The other kids realized that it should be a number that can be broken into 2 groups of 10, and came up with y = 20 on their own.  I then showed all the kids the difference between y * 2 = 10, and y / 2 = 10.

One kid complained that this activity was too easy, though she stopped complaining when the problems involved multiplication.  Another kid kept asking if we could do programming or compasses next.


All the kids were excited to do programming.  I handed out the materials and the first problem.  It turns out that a statement like:

Box_X = Box_X + 10 is confusing to about half the kids. Most kids were able to get through the first program with a couple questions to me.  One kid wrote “11 11” for the output, because after the value of Box_X changed, she also changed the value that had been printed.

The second program (which should print the numbers 1 through 10), was much trickier for everyone.  Only one kid was able to do it totally independently. Two kids understood what was going on after a bit of help from me, and the last two kids were really pretty confused.

The confused kids did not understand which lines we were supposed to do 10 times, or which order to do them in.  3 kids thought they should print “1” 10 times in a row, but then I showed that we have to do Box_X = Box_X + 1 in between the prints.  Then they guessed “1” 10 times, followed by “2” 10 times.  We’ll have to work on loops a bit more.

Next I said the kids would get to write their own programs.  They were excited to do this, but my daughter started crying when she heard it should do something specific…she didn’t think she’d be able to do it.

The first program was supposed to print “Hello”.  Most of the kids quickly caught on, and several came up with interesting ways to do this.

I suggested: “Print “Hello””.  Two kids independently came up with “Box_X = “Hello”; Print Box_X”.  One kid came up with the complex program pictured above.  I like how that program uses a loop.

After this, the kids started writing their own programs to do whatever they wanted. They loved to have me follow their programs and write the output. Nobody wanted to stop, but it was time to move on to the last activity.

Coin Flips

I handed each kid a small cup with a quarter in it. I showed them how to flip the coin by covering the cup with their hand, shaking it, and then looking at what side the coin is showing.

First I asked the kids to write down their flips until they got 3 heads.  This took between 4 and 8 flips.  Next I asked them to keep flipping until they got 3 heads in a row. Three of the kids took 24, 28, and 25 flips, which seems reasonable.

One kid kept getting Tails, like 15 times in a row. I’m not sure if he was intentionally cheating, or not shaking the cup hard enough, or what.  Another kid kept getting Heads.  So their results were a bit suspect.

The kids explained that it is harder to get 3 heads in a row than it is to get just get 3 heads. One girl mentioned that if you get 2 heads and then a tails, then you have to start over to get 3 in a row, but the 2 heads still count if you just want 3 heads total.


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