Easy Fraction of a Set Game

Fraction of a set can be a challenging concept for fourth grade.  Often they are still trying to understand the idea of fractions dividing a whole into equal sized parts.  So looking at a given number of equal sized groups that relate to one as "one whole set" is very confusing.

To begin, we go back to the division dots task cards that we used earlier in the year.  This review with the concept of arrays gets them comfortable.  I much prefer the "we did this already" as opposed to the, "I don't get it."  Because the moment they are bored I tell them, "Good, you remember.  Now we're just going to add one more step, which is to color a certain number of sets after you circle them."  And they are on their way!  There are 3 levels of practice in my fraction of a set task cards.

In order to help them conceptualize fraction of a set without a visual, I came up with a quick review game you can do with your class, and all you need is masking tape!  

Here's how I explain and scaffold for the game.  Right before Morning Meeting, I used thin masking tape and divided the rug area into a large area and a small area.  That day I had 16 students.  I told them "I want 1/2 of the class in the large area, and 1/2 in the small area."  They quickly and easily got into 2 groups of 8. 

Next, I asked each group to line up in their section.  I wrote "1/2" on the board and explained that there were TWO lines, because 2 is the denominator.  I asked if they thought they could get into FOUR lines, with only 1/4 on the small side and 3/4 on the large side.  Once that was done, we determined that 1/4 of 16 is 4.  I asked them how much 3/4 of 16 was, and they counted 12.

The next day I pushed them a little further, asking for 3/8 of 16.  They needed some reminding about getting into 8 rows, but what most of them COULD do independently was to get 3 of those lines in the smaller side and 5 on the larger size.  I asked how many kids were in the 3/8 of 16 section and they counted 6.

The final variation of this game was to find a "mystery number."  In Math in Focus, Chapter 6 (Fractions) they have to basically "do fraction of a set backwards." 

In other words, I tell the class that I am thinking of a certain class size that is SMALLER than the number of students present today.  That number is a mystery.  However, I will tell them that 3/5 of that number is 9. 

Again, to start out they need reminding that they need to get into 5 rows.  They remembered on their own to have 3 rows on one side with 2 rows on the other.  Then I reminded them that there should be 9 kids on the side with 3 rows.  At that point, they remembered they needed equal sized groups.  

When there was a single student left over, not in a row, they determined that the class size I was thinking of was one less than 16:  15. 

In the end, we discuss 3 ways to find fraction of a set.  I had a few kids find the algorithm (method 2) on their own as they were working on the task cards!  They really feel like they "own" it when they "Find a method."  

Do you have any tips for teaching fraction of a set?