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.

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?

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