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.
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?
What to do as a parent ?
As always, 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.
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 ?
With level Red, I left again the option open to pick the number of peg dolls and the number of bags. 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
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).
Click here to see a video of the exploration of 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.