My daughter and I went on a 12 week-journey last year to explore Fractions. We are doing it again this Fall/Winter. I am updating the posts, in case you want to join us this year. Click here if you want to know more about the journey and the previous problems.
Here comes our last Equal Sharing problem !
Time 4 Fractions – Problem #12 – Sharing cereal bars
Level Yellow – 2 people want to share 1 cereal bar so that each of them gets the same amount. How many cereal bar would each get?
Level Orange – 3 people want to share 1 cereal bar so that each of them gets the same amount. How many cereal bar would each get?
Level Red – 5 people want to share 3 cereal bars so that each of them gets the same amount. How many cereal bar 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 !
The problem will lead to a answer of each person getting 1/2 of a cereal bar (level Yellow) , 1/3 of a cereal bar (level Orange) or 3/5 of a cereal bar (level Red).
This is the last problem. What can you do now ?
The goal of T4F was to provide children with opportunities to explore fractions at home, so they have stronger foundations to build up on when they study fractions at school. This is our last problem, but it does not have to be the end of our journey. The set of problems was designed to provide a wide range of answers, to explore halves, fourths, thirds, fifths and so on, so do not hesitate to go back to these problems and provide one regularly to your child, until your child figures out that “a thing shared by b people is a/b” (Empson & Levi, 2011, p25). For instance, Problem 12, Level Orange, leading to an answer of 1/3 would be an instructive step towards Problem 8, Level Red, that leads to an answer of 2/3.
The level of difficulties can be seen as follow (Epson & Levi, 2011):
- Equal Sharing problems that lead to a whole number (i.e. Problem 8, Level Yellow)
- Equal Sharing problems that lead to an answer that is more than one, with the children having to decide what to do with any left over they may have (first in halves, e.g. Problem 8, Level Orange, or Problem 9, Level Yellow, then fourth e.g. Problem 9, Level Orange)
- Equal Sharing problems that lead to an answer that is less than one (first with halves or fourths e.g. Problem 12, Level Yellow, then thirds, e.g. Problem 8, Level Red, Problem 12, Level Orange, and so on)
I am including a table summarizing the problems and set of numbers we have exploring so far, I thought it might help.
|Problem 8 – Sharing paper||Level Yellow||2|
|Level Orange||2 1/2|
|Problem 9 – Sharing bananas||Level Yellow||2 1/2|
|Level Orange||1 1/4|
|Problem 10 – Sharing apples||Level Yellow||1 1/2|
|Level Orange||2 1/4|
|Problem 11 – Sharing clay||Level Yellow||3 1/2|
|Problem 12 – Sharing cereal bars||Level Yellow||1/2|
Hope you enjoyed our T4F journey ! As always, I appreciate any feedback you may have. Comment, or email at journey2helpchildrenwithmath(at)gmail.com.
Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.