3 thoughts on “Rational and Irrational Numbers- Open Middle Problem”

Okay I like this series a lot. The only the thing bothers me (and maybe it only bothers me) is that I’m to use the numbers 1-9 but there are only eight positions. If it were “use the numbers 1-8” or if there were nine blanks, I’d feel nicely pigeon-holed.

Understandable, I normally don’t buck things like that because I like the options for discussions in class. It can work smooth without the extra place, so I can live with that.

This is a general observation about irrational numbers and the CCSS document. I would be very pleased to have your opinion on these matters.

The CCSS document says “Know that √2 is irrational.”
Are the students expected to follow the proof of this (actually easy) or is it an act of faith?

In the previous section I found this as a way to estimate root 2:
“For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.”

I was under the impression that the decimal expansion of root 2 went on for ever, and was therefore unavailable for truncation. The procedure for estimating root 2 or any of the others (can’t do this with pi very easily) was to start with an approximate value, and then repeat the “test it, modify it” activity until the desired approximation is reached.
It is quite a philosophical stance to assert that there are numbers whose decimal expansion does not repeat. Not a safe place for a beginner at all.

Okay I like this series a lot. The only the thing bothers me (and maybe it only bothers me) is that I’m to use the numbers 1-9 but there are only eight positions. If it were “use the numbers 1-8” or if there were nine blanks, I’d feel nicely pigeon-holed.

Understandable, I normally don’t buck things like that because I like the options for discussions in class. It can work smooth without the extra place, so I can live with that.

Here goes:

This is a general observation about irrational numbers and the CCSS document. I would be very pleased to have your opinion on these matters.

The CCSS document says “Know that √2 is irrational.”

Are the students expected to follow the proof of this (actually easy) or is it an act of faith?

In the previous section I found this as a way to estimate root 2:

“For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.”

I was under the impression that the decimal expansion of root 2 went on for ever, and was therefore unavailable for truncation. The procedure for estimating root 2 or any of the others (can’t do this with pi very easily) was to start with an approximate value, and then repeat the “test it, modify it” activity until the desired approximation is reached.

It is quite a philosophical stance to assert that there are numbers whose decimal expansion does not repeat. Not a safe place for a beginner at all.