*[Photo by geishaboy500 (CC BY 2.0).]*

Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.

Here is the newest entry, a variation on #10, the “Race to 100” game:

**(11.5)** Play “Odd-Even-Prime Race.″ Roll two dice. If your token is starting on an odd number, move that many spaces forward. From an even number (except 2), move backward — but never lower than the first square. If you are starting on a prime number (including 2), you may choose to either add or multiply the dice and move that many spaces forward. The first person to reach or pass 100 wins the game.

[Hat tip: Ali Adams in a comment on another post.]

And here’s a question for your students:

- If you’re sitting on a prime number, wouldn’t you always want to multiply the dice to move farther up the board? Doesn’t multiplying always make the number bigger?

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A thought and an idea — both all yours, if you want them!

Thought:Your fifth question, “How many numbers are there from 11 to 25? Are you sure?”

The way that I typically tackle this is by talking about “shifting” the numbers (this relates to the distance interpretation of subtraction; good to point out if you are working with students). In particular, we can shift the labels on “11 to 25” down by 10.

Now the labels are from 1 to 15. And this, in effect,

countshow many numbers there are (imagine “1” means “first” all the way up to “15” means “fifteenth”). So the answer is 15.As another sample problem: How many numbers are there from 13 to 26?

Answer: Shift down by 12. Now we have the numbers 1 to 14, which means there are a total of 14 numbers.

(Hopefully this is clear; if not, let me know and I will clarify further!)

Idea:One of my favorite activities is what you list as #7. The context in which I use it, though, is the multiplication table: Consider a 10×10 multiplication table. If you have a 2×2 puzzle piece with one 9 marked in it and the other three squares blank, then can you be sure (thinking about the 10×10 times table…) how to fill out the blank squares? [Answer: It depends on which of the blank squares has the 9 in it! Only in one of the four cases can you be

sureabout how to fill out the puzzle piece. Why? And how does this work with numbers other than 9?]Maya,

The problem is that counting from one number to another is not a well-defined operation. Depending on the context, you may or may not want to count the numbers on the end. The option you describe is inclusive counting, since you have included both of the endpoints.

The same shifting method can be used for the other types of counting, but the first step in any counting-from-A-to-B problem is to determine which numbers we really need.

I *like* the idea of playing with these hundred-chart activities on a multiplication table! I wonder how many of the other games would work that way…

What if on the even numbers you could choose to move backward or move your opponent forward?

And I like the prime special places. That makes me wonder about a version where you move back if you roll a divisor, forward otherwise.

John,

Having choices is usually good in a game. Especially if your opponent is sitting on a prime.🙂

The original version (in Ali’s comment) did offer some choice: the players could choose between addition and subtraction for the regular moves. It offered a strategic option (try to hit a prime), but I wanted to save space in my long article. At the end of Ali’s version, you had to hit 100 exactly, so subtraction would come in handy there, too.

I like your divisor variation, because it connects the concepts better. With addition and subtraction, there seemed to be no logical reason for the primes to be a special case. And it would make the game move faster, without so many backwards moves.

RE: multiplication table

Manyof the games would transfer or could be altered (though perhaps for a slightly different st/age of mathematical thinking).For example, the even/odd game suggested here as #11.5 (by the way: counting from 11 to 25, inclusively or exclusively, is complicated by the presence of a number like 11.5!) would be affected by working with the times table.

In particular: 50% of the Hundreds Chart is even; the other 50% of the Hundreds Chart is odd.

Contrary to the initial intuition [of most] this is

notthe case with a times table. I’ll leave to you the puzzle of finding the percent breakdown for even and odd in the times table, and an explanation of why it is so. (I think this is a fun activity!)Yes, decimals and fractions do complicate counting tremendously!

I did modify one of my hundred chart games (gomoku) for playing on the multiplication table: Times-Tac-Toe.

The share of odds/evens in a multiplication table is a good question for kids. I’ll have to remember it next time we have a math circle…