Sometimes, we need to do what we've always done, just jazzed up a bit.
Sometimes, ramping up an old idea is just what we need to increase learning in our classrooms.
Plotting numbers on a number line is not a new concept.
We've been doing it for years.
I reinstalled this simple, yet eye-opening, idea back into my classroom.
We were able to take many side trips of learning through the process.
How to convert a fraction to a decimal.
How to use the square root sign on our calculator.
How to set up a number line.
How to plot numbers on a number line.
But then I took this simple activity and used it to introduce rational and irrational numbers.
However, it wasn't as straight forward as that.
Each group of students got two groups of cards that they had just previously put in numerical order.
All they were told was to sort these into groups and share their reasoning behind each group.
As I walked around, listening to their reasoning,
I would have to agree that they did a good of sorting the cards into two groups.
But since I was the only one with knowledge of where this was going, I could get them to think even deeper.
With every group, I was able to switch a few cards around so what the students had in front of them was a pile of rational and a pile of irrational numbers.
Remember...they didn't know this.
They then had to re-analyze the two groups.
In most cases, I was able to move the square roots of perfect square numbers into the rational category...totally uprooting their whole theory behind their groups.
On the board I had a huge Venn Diagram drawn.
I had the first group take magnets and stick up their two groups.
As a whole group we talked about what we saw.
Not much discussion at this point.
So we moved on to the second group.
This group had it a littler harder.
They had to put up their two groups, but now it would have to make sense with what was already up there.
We discussed that since we were placing them up there with magnets, that even if they were wrong we could easily change it.
We went through about four groups, after each time, the students would write down the new numbers in their personal Venn Diagrams in their notes.
I would always ask, what does this group have in common?
Why is this group difference than the other group?
Finally, one student noticed that in one group they were all square roots...but WHY were there some square roots in the other group???
He had hit upon the essential question.
What was different about these square roots?
All of a sudden, one student noticed that the square roots in the "rational" group were all perfect squares thus ending up as whole number answer!
After all the cards had been successfully sorted,
We wrote out a bulleted description for each group.
We also talked about why nothing was in the center area. We had to refer back to our descriptions several times before the students understood the reason it was blank.
We then watched two short videos (Video 1 and Video 2) with the instruction that students were to find the names of each group.
By working backwards...by starting with the numbers, then sorting into groups, writing out descriptions, and finally labeling them with the proper vocabulary...students were able to get a better understanding of each term then had I just introduced it and given them some examples. By getting a little messy and using various math tools aka a calculator (MP5), asking some good questions (HOM , persevering (MP1), analyzing structure of the numbers (MP7), and justifying their answers (MP3), students definitely moved their thinking in the right direction!
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