Fractions: The Set Model with “Eggs”

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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