My daughter and I went on a 12 week- journey the past two years to explore Fractions. We are doing it again this Fall. I am updating the posts from our previous journeys, in case you want to join us this year. Click here if you want to know more about the journey.
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).
Yellow : Mr Moose has 4 eggs and some baskets. He wants to put 2 eggs in each basket. How many baskets can he fill?
Orange : Mr Moose has 12 eggs and some baskets. He wants to put 3 eggs in each basket. How many baskets can he fill?
Red : Mr Moose has 20 eggs and some baskets. He wants to put ___ eggs in each basket. How many baskets can he fill?
What to do as a parent ?
As with Problem #1, invite your child to solve one of the problems, and listen to his/her way of solving it. He/she can make sense of the problem while using small objects (such as buttons, marbles, etc, and small containers) or drawing a picture. He/she may write an equation. Each child should pick the problem that he/she feels like exploring.
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.
If your child calls out the answer right away, remind him/her that the answer is fine, but how it was obtained is even more important in this journey. How would he/she explain it to a younger child? Could he/she represent the problem with a drawing? a diagram? Using small objects ?
Enjoy following his/her way of thinking !
Sharing my experience
- Click here to see a video we did last year. Just remember it is just an example of how a child may explore the problem. Your child may approach it differently!
- 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.
- I am also including a example of how a child, like…. Rosie, may represent her thinking on paper. The picture on the left may look “messy” for some, but I think it illustrates well what may be going on in a child’s brain while making sense of a problem. The twenty eggs are presented in four groups of five before an equation is written (a division, but also a repeated addition (making group of 5s from the 20 eggs), a repeated subtraction (taking away groups of 5s out of the 20 eggs).
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.