Using the Set Model to Understand Fractions

Fractions are all around us. At first the Magical Minds did not believe me, but within two minutes we had a good list of where we can find fractions in our everyday lives:

- cooking (measuring ingredients)
- building a home (measuring rooms)
- measuring with rulers
- making choices between things
- sharing food with friends

Having established why it’s important to know about fractions, I gave the third graders “eggs.” My intention was to help the Magical Minds **think of fractions as part of a set**. In this case, the ‘eggs’ were the set.

Counting "Eggs"

We imagined using six of our dozen eggs (not an Estonian custom, hence the lack of egg cartons) to bake a cake. “What fraction of the eggs are still in the carton?” I asked. 6/12. A few kids noticed that this was the same thing as half of the eggs – our first hint at the concept of equivalent fractions (to be covered more completely while studying the length model of fractions.) Using a guide sheet, the Magical Minds played with several different fractions, removing different numbers of “eggs.”

4/12 of the eggs remain. What fraction are missing?

This is also 4/12 . It may look different, but the fraction is the same. It is the same number of parts of a set.

We explored how fractions can have many names, but still be the same fraction (equivalent fractions). For example 4/12 is the same as 2/6, which is the same as 1/3. We found these different names by drawing lines.

Having mastered the dozen eggs, I challenged to the Magical Minds to make fractions using a set of 18 “eggs.”

Half of the eggs are missing.

After creating fractions by adding and removing “eggs,” I asked the Magical Minds if show me they could figure out how many eggs are on the paper if I gave them a fraction. I started our simple, calling out numbers such as 5/18 and 10/18. It got a bit trickier when I asked them to show me 2/3.

Colored teddy bears help show 2/3

As the third graders wrapped up their work, I challenged those who were finished to find fractions around the room. J found the following fraction in our place-value blocks:

What fraction of the hundred blocks are yellow? I think she said it was 11/ 68

NOTE: The lesson I used with this class was adapted from a lesson on the NCTM: Illuminations website.

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