Don’t Let a 6-year-old Do Your Taxes

The Activities

  1. Topic: Proofs:The Boy Who Cried Ninja” by Alex Latimer.
  2. Topics: Multiplication, Teamwork, Counting: Working as a group, evaluate 29 times 73 using Base Ten Blocks.
  3. Topic: Programming: More programming problems like the previous week.  This week, we had a new chart for keeping track of the program variables and output and introduced multiple variables and assigning one variable to another variable or itself.
    Program 1:
    ———-
    Print “Joe_has_”
    Box_A = 3
    Box_B = Box_A + 1
    Print Box_B
    Print “_dogs.”
    Program 2:
    ———-
    Box_A = 5
    Print Box_A
    Box_A = Box_A – 1
    Print Box_A
    Box_A = Box_A – 1
    Print Box_A
    Box_A = Box_A – 1
    Box_A = Box_A – 1
    Print Box_A
    Program 3:
    ———-
    Box_A = 10
    Box_A = 10 * Box_A
    Box_A = 10 * Box_A
    Print “Sabrina_ate_”
    Print Box_A
    Print “_cookies.”
    Program 4:
    ———-
    Box_A = “Shannon”
    Box_B = “Lucy”
    Box_A = “Sophia”
    Print Box_A
    Print “_ate_”
    Print Box_B
    Print “‘s_lunch.”
    Program 5:
    ———-
    Box_A = 3
    Box_B = 5
    Box_B = Box_A
    Box_A = Box_B
    Box_B = Box_A
    Print Box_B
    Program 6:
    ———-
    Box_A = “John”
    Box_B = “Monkey”
    Print Box_A
    Print “_eats_bananas.”

    Program2Program5

Preparation

The programming worksheet is available here, and the programming problems are available here.  We used the kids’ names in the problems (anonymized in the link) — they loved this!

How did it go?

We had all 6 kids this week.

The Boy Who Cried Ninja

This is a light retelling of “The Boy Who Cried Wolf”, with a twist.  It’s vaguely related to the idea of proofs.

Large Multiplication

First I asked them what multiplication is.  Some knew, although they mostly only knew the word “times”.  The best definition was adding the first number the second number of times (3 x 4 = 3 + 3 + 3 + 3).

Then, I gave them the problem 29 x 73.  I initially gave them 10 minutes.  I put the whole box of blue blocks on the table.  One of the kids said they should do 29 73 times.  I suggested they might want to do 73 29 times.  I don’t think they understood why, but they took my suggestion (which is good, because it would have taken forever the other way).

They started by each separately making a few piles of 73.  After each kid had made about 3, they got kind of stuck; many of the kids stopped making piles.  Kid #1 started changing their tens into hundreds.  I suggested they could put their groups on the island in the kitchen.  Mostly they didn’t listen to me, but kid #2 said a little later they should put their groups on the ground.  They didn’t listen to kid #2 either, but I encouraged kid #2 to start doing it by themselves.  Once the other kids saw what kid #2 was doing, they began to join in.  They weren’t very careful about blocks that weren’t part of groups though, there were some random 100s that kid #1 had moved which didn’t end up being used, had I not cleared them away they probably would have included them accidentally.  10 minutes was up by this point, so I added 10 more, and then later, 10 more (they ended up finishing almost exactly at the 30 minute mark).

When they were at about 20 piles, kid #1 started to trade in some of the existing piles.  Kid #2 said not to do that, and I agreed.  Kid #2 started counting the piles over and over seeing if they had gotten to 29.  They actually overshot by 3 or 4 piles, because kids #3 and #4 were still busily making piles.  I suggested they might want to come up with a better way to count, but kid #2 wasn’t interested.  Kid #1 suggested grouping into fives, which I said was a good idea, but by that point kid #2 and others had decided that they had 32 (I don’t know if they were right).

Then they started trading in, beginning with 1’s.  I think? most of the kids understood they were supposed to be trading, but they were pretty bad at it.  Almost all the kids picked up a pile of 1’s, took it over to the table, and counted it.  Of course, they didn’t have multiples of 10, and so who knows what happened to the extras.  Also, they were really worried about the uneven 1’s — kid #5 got the big bag of extra 1’s and brought it over to start counting out new 1’s until she got to 10!  Kid #1 said “No! No!” so that didn’t end up happening.  Once they got to 10’s, kid #1 went over and grabbed a stack of 7 100-plates, and then took them off the pile one at a time, measuring against the bars (rather than counting out 10).  Only after (physically) measuring out the bars did kid #1 take them to the table, which of course is a procedure with a high risk of error, plus the extra 100’s appear to be part of the total.  Some of the kids did the trades correctly, picking up 10 bars, taking them to the table, and bringing back a 100.  But I’m pretty sure kid #4 was just taking stacks of 10 bars to the table (I caught kid #4 doing this at least once and made sure they took a 100).

Kid #1 was able to read the number correctly (they’ve had trouble with this in the past).  Their final answer was 1757 (correct answer: 2117).  Not at all surprising.  I think that if we set up one person to be the “trader”, they could get much closer to the right answer, but not sure if we should do that.  Another interesting note is that had they realized that 10 * 73 is 730, they could have skipped a lot of work.

Programming

This was the same as the previous week, except that I had a new sheet with a clearer section for the variable boxes and for the output.  There were two new concepts: multiple boxes (which our daughter had suggested), and setting one box equal to something based on either itself or another box (e.g., Box_A = Box_B + 1 or Box_A = Box_A – 1).  I accidentally used * for multiplication, but once I said it was times they were able to do it.

This time, I think all the kids got the idea.  Kid #1 (different numbering from previous problem) really liked this problem.  We did the first couple programs in sync, and then people started working at different pace.  Everyone but kid #2 and #3 were able to consistently make independent progress.  Kid #2 was able to do it, but would sometimes pause until I encouraged them to do the next step.  Kid #3 got distracted by kid #1 (who was able to guess most of the programs just by thinking in their head).  I think kid #3 also had a bit of trouble determining what the next statement was.

As before, the kids loved having their names in the problems.  I did the problems out of order, because problems 2 and 5 were trickier.  We were out of time after the 3rd program, but kid #4 was sad because we hadn’t done the one with their name yet, so I brought that one out.  Several of the kids finished the 4th quickly, and did the 5th as well; they wanted to do the 6th problem too, so I sent it home with them.  On the problem with B = A; A = B; B = A; they thought it was very funny that you kept crossing off 3 and writing 3.  Kid #5 had an “optimization” in the cookies problem where instead of crossing off 10 and writing 100, they added a 0.

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