My daughter and I went on a 12 week-journey last year to explore Fractions. We are doing it again this Fall. I am updating the posts from last year with videos, in case you want to join us this year. Click here if you want to know more about the journey and the previous problems.
Another Equal Sharing problem (Empson & Levi, 2011) to help children make connections with fractions.
Time 4 Fractions – Problem #9 – Sharing bananas
Level Yellow – 2 children want to share 5 bananas so that each of them gets the same amount. How many bananas would each get?
Level Orange – 4 children want to share 5 bananas so that each of them gets the same amount. How many bananas would each get?
Level Red – 5 children want to share 4 bananas so that each of them gets the same amount. How many bananas would each get?
Invite your child to either model the problem (with paper and scissors for instance) and/or represent the problem with a picture. If your child has learned about fractions at school, invite him/her to connect symbols to the model or picture. And as always, invite your child to share his/her reasoning with you !
Level Yellow involves halves, level Orange, fourths and Level Red, fifths. Level Yellow leads to a mixed number (2 1/2) although it may make more sense to some children to give each child 2 bananas, and have a banana left. Level Orange leads to a mixed number (1 1/4), level Red to a proper fraction (4/5).
Sharing my experience (Fall 2015)
My child got a little frustrated with Level Red. If it happens to your child, you may want to start the problem with 5 children sharing 1 banana. It was a good alternative for us.
Sharing my experience (Fall 2016)
We continued modeling the different levels with flashcards, through folding/cutting paper similarly to what we did last week, each flashcard representing a banana. It is a good way to explore half, fourth, or fifth, depending on the level, with the option to going back to a “whole” banana if need be. We also took the chance to compare a fourth of a “banana “to half of a “banana”, or “two fourth” of a banana to half of a “banana” (“it is the same!”), etc.
Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.