## Tuesday, July 23, 2013

### Classifying Real Numbers Foldable

The first foldable for next fall has been made!  The first lesson that I teach in my algebra text is on sets and real numbers.  When I think about classifying real numbers I always get the image of nesting cups that you used to be able to buy for toddlers.  I wanted to somehow bring that idea to the foldable that we made for this part of the lesson.

Now, I have seen the traditional Venn diagram of the sets.  My problem with it is that I have noticed that my kiddos have trouble picturing the sets of numbers and being within each other.  They often forget that 7 is an real number, rational number, integer, whole number, and natural number.  They will usually just say that it is a whole number.  I wanted them to see that whole numbers contain the set of natural numbers in a way that was different from the traditional diagram.  So I started by folding a piece of paper in half and putting real numbers on the outside of it.

When the students open the foldable they see that real numbers contain the set of rational and irrational numbers.

Now I realize that not all of the sets show up at once.  That is what I am going for.  Rational numbers have many subsets.  So to show that rational numbers hold the integers, the students have to lift the flap.

Continue opening the flaps and you will see all of the subsets appear.  In each flap, I have the definition of the set, examples of what is included, and non-examples to try and help the classification process happen smoother.
Just through the assembly of this foldable there are so many opportunities to reinforce that a natural number is also a whole number or that a negative number is part of the integer, rational, and real numbers, but doesn't fit the definition of a whole or natural number.  I also like that it shows that the set of rational numbers holds integers, whole numbers, and natural numbers, but not irrational numbers.  Yet, at the same time, the kiddos see that real numbers hold rational and irrational.

Update:

I added this post to the Interactive Linky Party at 4mulaFun.com (http://www.4mulafun.com/).  Go and check it out for some other great ideas related to INB!

(8-10-14) I was going through Pinterest and I came across this slideshare at http://www.slideshare.net/ProfessaX06/real-number-system-foldable-5151675.  In it, there is a foldable very similar to the one that I created.  I must have seen this at some point and have forgotten when I made my version of it above.  My apologies to the authors below for using their idea and not giving them proper credit.

1. I just found your blog today and am so glad I did! I nominated you for the Liebster Award! Find out more at: mrshester.blogspot.com/2013/07/thanks.html

2. What type of post-its did you use for the subsets?

3. Thanks for the question Anika!

I actually didn't use post-its for this foldable. I used some scrap paper and folded it in half. I made the rational numbers diamond shape first and then reduced each nesting one by 2cm.

For the students, I am going to copy the design as many times as I can onto a piece of paper and then photocopy it. That way, the students will only have to cut out the shapes and not design them too. This will speed up the process, I hope!

1. So helpful! Thanks! Love this foldable!! :)

2. I'm glad that you like the foldable! It is one of my favorites!

4. This is exactly the thing I was searching for! This is my first year moving up to 8th grade math. I am excited but in new territory... I will definitely be stealing this one for the math journal.