Fractions Day 12: Renaming Mixed Numbers and Improper Fractions

Children often struggle with understanding how to rename an improper fraction to a mixed number (and vice versa). They learn ‘slick tricks’, such as Around the World or The Circle Method (I have no idea what that means). In fact, when I googled how to change a mixed number into an improper fraction, the first dozen (I stopped looking) used titles with “Easy”, “Trick”, “Fast”, and “The Neat Way”. Who are these ways easy for? Certainly they are easy to learn…and then forget.

My stance is to take time to work with small whole numbers (1 and 2, for instance) and concrete models (such as our fractions kits) and let children figure it out for themselves. It may take time, but in the end they will remember and will figure out a ‘slick trick’ that works for them.

  1. Played “Cover it Up”, first version (Please see Fractions Day 2 for directions) three times. He still wants to play, so we still play!
  2. Wrote 5/3 on his whiteboard. How many wholes could we make? (1) How many thirds would we have left? (2) So you would have 2-thirds? (Yeah. That is what I said, mom!) How could we write that amount? (1 + 2/3) So you have 1 AND 2/3 (That is what I wrote, mom!) Clearly I was annoying today. However, I wanted to make sure we restated the ideas clearly using appropriate language. He didn’t hear the difference, but I did.
  3. We continued with renaming improper fractions as a whole number + fraction. I tried to continue the questioning, but he worked so quickly I didn’t have time to question as he did some of them. He got stuck for a quick moment on 4/2. (It’s just 2 wholes, right mom? Because 2/2 = 1 and if I double that I get 2, right?) Otherwise, this progressed much faster than I thought it would!
  4. We then moved to renaming mixed numbers as improper fractions. I started with the same number as before: 1 2/3. Show me 1 whole and 2/3. (Mom, I can do this without the fractions (strips). Okay…Then if I want to rename this in all thirds, how many thirds would I have? (3/3 is a whole, so two more would make 5.) Five of what? (5 of the thirds) How would I write that? (Wrote 5/3 on the paper.)
  5. Again, I was surprised at how quickly he grasped this and was able to reason out each one without the fraction strips. Below is a clip of him reasoning out 7/3.
Renaming 2 1/3

It is important to note that Chris didn’t use the fraction strips, but could have. Each child is different and needs different representations to understand the math. If your child would like to continue using the fraction strips to work through the problems that is awesome! They are still gaining understanding regarding equivalence and renaming fractions greater than 1.

Below are the improper fractions and mixed numbers we explored.

Renaming Improper Fractions
Renaming Mixed Numbers
Fractions Day 12: Renaming Mixed Numbers and Improper Fractions

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