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.
Here is Problem #5, a partitive division problem. Last week, with the measurement division problem, children knew the number of items in each group, and needed to find the number of groups. This week, children know how many groups they have, and have to find out how many items are in each group. Just another way to keep exploring division and mathematical relationships.
Time 4 Fractions – Problem #5 – Peg dolls
Level Yellow – Peter and Julie made 6 peg dolls. They put them into 3 gift
bags with the same number of peg dolls in each bag. How many peg dolls are in each bag?
Level Orange – Peter and Julie made 18 peg dolls. They put them into 6 gift bags with the same number of peg dolls in each bag. How many peg dolls are in each bag?
Level Red – Peter and Julie made ___ peg dolls. They put them into ___ bags with the same number of peg dolls in each bag. How many peg dolls are in each bag?
As always, invite your child to solve one of the problems 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.
When your child is done, invite him/her to share his/her reasoning with you.
With level Red, I left again the option open to pick the number of peg dolls and the number of bags, as my child seems to enjoy the freedom. You may want to invite your child to explore Level Yellow or Level Orange first, though, with modeling the problem with manipulative or a picture. Be aware though, that depending on the numbers the child picks, Peter and Julie may have some peg dolls left (e.g. 13 dolls to put into 5 bags), or may not have enough dolls (e.g. 6 dolls, to put into 12 bags). Let me know how it works !
Sharing my experience (Fall 2015)
My child solved Level Yellow first by modeling it, though dispatching 6 marbles into 3 containers, one marble at a time. She also did a representation of the problem, and wrote an equation (repeated subtraction).
For Level Red, she picked 20 peg dolls, and 4 bags. Then, she asked me to solve it. But I am glad she did, as we ended up talking about how different people may use different ways to solve a same problem, and how she will learn additional strategies and symbols at school (i.e. division instead of repeated subtraction, multiplication instead of repeated addition).
Sharing my experience (Fall 2016)
Here is Rosie exploring Level Orange with buttons. As always, it is just to provide an example of how a child may explore the problem.
Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.