Equivalence is everything when it comes to fractions. Kids who understand which fractions are the same size and how to create fractions that are the same size are the ones in math class that say, “It’s easy!”. It’s not easy; it makes sense to them. Since I am at home with my tiny human for A-WHILE, I decided we would spend a good grip of time on equivalence. The next 3 lessons (and many more after introducing the family of thirds in Lesson 8) will focus on understanding equivalence with fractions.

Play “Cover it Up!” twice. Please see Fractions Day 2 for how to play the game. My questions to Chris focused on when our amounts were the same, or how to make them the same. How much more would I need to tie you?Which fraction would you need to have the same amount as me? I still had him write the addition sentence once he covered up the whole.

I asked him to pull out one of his half pieces. How many eights would I need to cover up the half? (2). I then directed him to do the same with each fraction size. He had to cover up with only that size piece. We counted them out (One-eighth, two-eighths, three-eighths, 4-eighths…4/8 is the same as 1/2.) and wrote down each fraction amount that was equivalent to half. See image above for our work.

On the whiteboard, I wrote 3/4. How many eighths would it take to cover 3/4? How many eighths are the same as 3/4?

We continued looking at different fractions and finding the equivalent amount. The fraction sequence is below (See Equivalent Fractions Practice doc.), but looking at it now I would suggest less sixteenths and more fourths and eighths. Will need to do that tomorrow.

I let him create two of his own. This was not easy. He just kind of stared at me. (Soooo tough not to just tell him, but the struggle is good for him!) I rephrased: Choose a fraction and find another that is the same size. Though this limited him at first, it helped get the ball rolling. He chose 1=2/2 for his first one. Though not what I was looking for, it is true! He second was more interesting (Wish I had asked for 3!) He chose 2/1=4/2. I was shocked, because we haven’t even talked about anything over a whole. However, when concepts make sense to kids, they can naturally apply them to unique situations.

Hope you have a great day exploring new ideas and making fractions fun!

Love seeing Chris work it out on video. And love question 3 – very natural to have division language show up in determining equivalent fractions.

Wonder what would happen if you varied the format of the equations.. like ___ fourths = 2 eighths. or 3 ____ = 6 eighths.

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Ooohhh! We can totally try that with the thirds and sixths!

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