Fractions Day 11: ‘One More’ Than a Whole

Note: The title is not mathematically accurate, but since my tiny kept using the phrase I figured it was an appropriate way to express the meaning behind the lesson.

So often when students learn about improper fractions and mixed numbers, it is smooshed together as one lesson. I disagree. I think we should focus first on a little bit (unit-fraction) more than the whole to really understand how the whole number relates to our denominator. So though this lesson may seem unnecessary, I think it is a critical first move for children who are learning the relationship between fractions and whole numbers.

Thinking about 3-halves.
  1. Played the first version of “Cover it Up!” See Fractions Day 2 for directions on how to play the game. (We play 3 times.)
  2. Show me 4-thirds. (Chris laid them out side-by-side). How would we write that number? (He wrote ‘4/3’ on his whiteboard.) Is this more or less than a whole? How do you know? (It is more. He showed the whole strip, blue for us, and compared.) How much more? (1 more. ) One more of what? (1 more third.) So how can I write 4/3 in a way that tells me it is a whole and a third more? (He wrote ‘1+1/3’.)
  3. I showed him the very fancy worksheet. (Pencil and paper my friends are amazing!) The first one is 4/3. He wrote in ‘1 + 1/3’. I was going to start the same way with the next improper fraction, 9/8, but he said, “I can do it without the fractions, mom!” And he did! What amazed me was that he didn’t notice the pattern that they were ALLLLL a whole and 1/denominator more. He always said the whole number as a fraction (Example, 1 is the same as 8/8.) and added the unit fraction to it. (So 8/8 plus one more eighth is 9/8.)
  4. I flipped our fancy worksheet over and modeled for Chris the 1 whole strip and 1/3 more, laying them out as one long strip. How could I name this? (1 and a third more). If I want to name the length just in thirds, how many thirds would I need? (4-thirds.)Though I showed him the first two (Please see video below for 1 + 1/6.), he did the rest of them without needing the physical fraction strips.
Thinking about 1 1/6.

As I noted in Fractions Day 10, spending so much time at the beginning with the physical fraction strips and really exploring how the different size pieces relate was extremely important for this lesson. He ‘sees’ the pieces in his head and can mentally find relationships without needing procedures or sets of rules he may (or most likely may not) make sense of. This understanding will continue, as you will see tomorrow! Be well!

For the sequence of the fractions (both sides) on my fancy worksheet:

Renaming improper fractions as 1 + a unit fraction more.
Renaming 1 + unit fraction as improper fractions.
Fractions Day 11: ‘One More’ Than a Whole

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