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.
Hope your child had fun exploring Problem #1, and Problem #2, two multiplication problems. Here is Problem #3, a measurement division problem (also called quotative division problem), our second step towards Equal Sharing problems (Empson & Levi, 2011, p 9).
Level Yellow : Mr Moose has 4 eggs and some baskets. He wants to put 2 eggs in each basket. How many baskets can he fill?
Level Orange : Mr Moose has 12 eggs and some baskets. He wants to put 3 eggs in each basket. How many baskets can he fill?
Level Red : Mr Moose has 20 eggs and some baskets. He wants to put ___ eggs in each basket. How many baskets can he fill?
As with Problem #1 and #2, invite your child to solve one of the problems (you can pick one, or let him/her pick one) by
- modeling the problem with manipulatives (such as buttons, marbles, etc, and small containers),
- representing the problem on a piece of paper, and/or
- writing an equation.
With Level Yellow and Orange, all eggs will be dispatched in a basket, and Mr Moose will have no egg left. With Level Red, invite the child to pick the number of eggs he/she wants to put in each basket. Depending on the number he/she picks, though, please note that Mr Moose may have some eggs left.
When your child is done, invite him/her to share his/her reasoning with you. If he/she writes only an equation, encourage him/her to share his/her strategy with a visual representation, or with manipulative.
Enjoy following his/her way of thinking !
Sharing my experience (Fall 2015)
- Since it was our first division problem, we spent a lot of time modeling, with marbles and containers. We did Level Yellow, Level Orange, but also Level Red, with 5 eggs per baskets. And when I said “we”, it is my child leading her exploration, and myself saying “tell me about what you are doing” from time to time. Nothing more, really. Symbols she may not know yet, formal teaching will occur in time, at school.
- An observation I found quite comforting regarding our journey is my child saying “You see, the more eggs you put, the less baskets you need !”, noticing the relationship between the number of items, the number of groups of items and the number of items in each group. Do you see how this kind of connection relates somewhat to fractions, and the fact that sharing an item in 8 (1/8) provides smaller pieces than sharing the same item in 2 (1/2), i.e. the number 1/8 is smaller than the number 1/2 ? It is all about mathematical relationships.
Sharing my experience (Fall 2016)
- Click here to see a video of one of our explorations this week. Hope it helps. Just remember it is just an example of how a child may explore the problem. Your child may approach it differently !
Have fun, and see you next week for Problem #4 !
Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.