Math talk: Which number doesn't belong?

A key theme of the Common Core State Standards for Mathematics is the need for students to use deeper mathematical thinking and reasoning skills (rather than just memorizing procedures) -- and to apply their understanding of mathematics by justifying conclusions and communicating them to others.

What I think this means is that the Common Core math classroom is going to be a much livelier place, full of discussion and teamwork and talk. That's a wonderful thing.

Here's a fun math conversation starter:

Which of the following numbers doesn't belong? 9, 16, 25, 43.

Let us know what you think. And remember, EXPLAIN YOUR REASONING!


43 - The other numbers can be reached by multiplying a number by itself. 3x3, 4x4, 5x5

(I apologize for my English before I start, I am from Argentina)

At first glance, we could say 43 doesn't belong because it is not a square number (that means there is no n that n*n is our number): 9 = 3^2, 16 = 4^2, 25 = 5^2.

But as any list, there is no a defined pattern, there are as many patterns as we want to discover!

I could say 9 is the number which doesn't belong. A simple reason would be "Because it only has one digit". I think, in fact, 9 is the number doesn't belong, but for another reason:

All the digits of 16, 25 and 43 sums to 7. 1+6 = 2+5 = 4+3 = 7.

This is a nice excercise to show how can, in the same sequence, be different patterns. This is a problem in cryptography, for example.

Isn't it awesome how you can be correct in so many different ways? We often think of math problems has having only one correct answer.

Your English is perfect!

9 doesn't belong, because if you add up the digits in all of the other numbers, they give you 7. 9 is the only number that doesn't give you 7.

I say 16 is the number that doesn't belong because 9, 25, and 43 are all odd numbers and 16 is even.

the number that does not belong is 43. It is not divisible for only Number like the others. It is still have remainder.

I'm going to say 16 because it's the only even number, and all my other ones have been taken already!! =)

The number I first looked at was the number 16, because it is an even number and the other numbers are odd. But then I really digged deeper into these numbers and came up with the number 43 because the other numbers are square numbers and this made more sense. So depending on where the student is in Math would be how they look at these numbers.

Sorry for my English, I'm from Russia.
I think number 25 doesn't belong. In each number, except 25, we can divide last number on 3. 9/3=3. 16 - 6/3=2. 43 - 3/3=1. And you also can see, that there is decreasing arithmetic progression

25 doesn't belong because the product of the digits of all the numbers is a multiple of three; except 25.

9 = 9
1*6 = 6
2*5 = 10
4*3 = 12