## Secret 3-digit numbers

For the past two weeks, in my first grade math class, we had been playing with 3-digit numbers. Many of the students in this class are the same ones that participated in the lessons described in the posts 3-digit numbers are tricky!, Part I and Part II, from last year.

But now, 3-digit numbers are their old friends and they are ready to do much more sophisticated things with them. I have found a number of interesting activities in the Super Source – Base Ten Blocks book for grades K-2 for us to try out.

One of the activities was a particular hit with the students. Here is how it worked.

One student would go to the special table and build a 3-digit number inside a box using base-10 blocks. That student would then give out clues about the number until another student built the same number.

Here are lists of clues that three different students came up with. Can you guess the numbers? For reference, a unit is 1 little cube, a rod consists of 10 such cubes and a flat consists of 100 cubes.

Student 1:
Clue 1: The number of units is 1
Clue 2: My number is bigger than 100 and smaller than 500
Clue 3: The number of tens in the flats is 40.
Clue 4: There is only 1 rod.

Student 2:
Clue 1: There are 9 flats.
Clue 2: There are 14 blocks total.
Clue 3: The number is bigger than 909.
Clue 4: The number of rods is smaller than 6.
Clue 5: There are 5 units.

Student 3:
Clue 1: The number of units is smaller than 9.
Clue 2: There are 20 blocks altogether.
Clue 3: The number of flats is smaller than 7.
Clue 4: The number of rods is smaller than 7.

Notice that both Student 1 and Student 2 have redundant clues, which was very typical. But it was the clues of Student 3 that I found particularly interesting.
It was not immediately obvious, even to me, that they were sufficient to determine the number.

The “guessing students” took some time after Clue 4 to come up with a number that fit all 4 clues, but to my surprise they all came up with the same number, which turned out to be the correct one. Only then did I realize that the clues were in fact sufficient.

I tried to discuss this fact with the students, but I’m not sure that they followed much of what I said. They were excited to have guessed the number and the next student wanted their turn at the special table.

What are your favorite 3-digit number activities to do with this age group?

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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### 5 Responses to Secret 3-digit numbers

1. bovetsky says:

I believe that the discussion on a sufficient number of clues should be delayed at least until the third grade.

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I actually agree, and that’s why I didn’t really “discuss” it with them. I just thought I’d mention it in case it made sense to someone. But it didn’t 🙂

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2. That’s a really nice activity. Thanks for sharing. I wonder if it would be possible to adapt it to an algebra game using Cuisenaire rods for example.

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