Time 4 Fractions – Problem #1 – Walking along a pond

This is the second post related to our Time 4 Fractions journey. Please click here to start from the beginning.

Welcome to our first problem ! This week will be a warm-up, as I want to make sure we are all aboard and comfortable with pursuing the journey from home. Bear with me with the length of this post, next week will be one much shorter.

The goal of this journey is to provide opportunities for children to explore word problems in “any way that they wish” (Carpenter et al, 2014, page 80), extend their reasoning skills, and gradually strengthen their foundation in fractions. When children receive their formal instruction in class, they will have a stronger background to build upon. If you decide to take the journey with us, from home, I hope you will enjoy observing your child’s thinking as much as I do with mine. It is fascinating.

One last thing, our journey will start slowly. It has to, if we want as many children, and as many parents, to benefit from it. We can’t just jump into fractions. Children must explore a variety of problems, and build up strategies they can use with fractions later on. Slowly, but surely.

So, here we go:


Problem #1 –  Walking along the pond

  • Level Yellow : Mr. Wood is walking along a pond. He sees 3 waterlily pads. On each pad, there are 2 frogs. How many frogs does Mr. Wood see ?
  • Level Orange: Mr. Wood is walking along a pond. He sees 4 giant waterlily pads. On each pad, there are 5 frogs. How many frogs does Mr. Wood see ?
  • Level Red : Complete the problem with the numbers of your choice. Mr. Wood is walking along a pond. He sees ____ giant waterlily pads. On each pad, there are ___ flies. How many flies does Mr. Wood see ?

Invite your child to solve one of the problems. He/she can model the problem with some manipulatives ( such as buttons, marbles, etc, and small containers), represent the problem on a piece of paper, write an equation. When your child is done, invite him/her to share his/her reasoning with you. If he/she writes only an equation, encourage him to share his/her strategy another way (with a visual representation, or with manipulatives). Enjoy following his/her way of thinking. Just resist teaching him/her symbols ! They will come in time !

I purposely stepped away from grade level, or an obvious nomenclature such as Level 1 to 3 or A to C. Each child should pick the problem that he/she feels like exploring.  It is not a test, I am not giving grades. In the coming weeks, some upper graders may decide to pick a Level Yellow to model, represent, and write the equation. Some lower graders may decide to pick a Level Orange but model it only.

I thought the Level Red could be great for children who are already used to explaining their thinking, representing the problem with a picture or a diagram, etc.  Just make sure your child does not get frustrated by picking numbers that may be too high !

You may want to find an example on how fractions could be useful in your child’s life. For instance, my child loves working with me in the workshop, where we measure, add length, etc. Fractions are key ! That way, even if the problem is on a topic that may be less appealing to her, I can remind her why, in the long run, it can contribute to her learning all the same.

Sharing my experience

  • I did my best to pick the right time for my child to solve the problem, and I stayed with her the entire time (5-10 min max). A special one-on-one time that we both enjoyed.
  • Most of the time, I just observed what she was doing, and learned a lot from it.  IMG_0470For instance, she stayed focused on Math while using buttons and cups, and solved the problem quite rapidly, counting the buttons by 5. With the visual representation, though, she got distracted with adding a flower on the water lilies, the water, etc. I have to keep that in mind next time she brings a worksheet from School. Does she do it there too?
  • She was not sure which kind of equation to write, and that is totally fine. Eventually, she will.IMG_0471
  • Doing Level Red was quite fun ! My child picked 2 leaves and 5 flies. How about yours?
  • I know we are all busy, having to be here and there, but I have found it so rewarding as a parent to just sit down for a few minutes and observe my child’s reasoning. I hope you do to. It can be a very special bonding time !

Questions you may have ?

I do not see any fraction in this problem !

Good point ! Just remember that we are going to explore the concept gradually.

We will start with  2-4 weeks on Multiplication problems (see problem #1) above. Then, we will continue with 2-4 weeks on Measurement Division problems (Carpenter et al, 2014).

E.g. An elf has 10 berries and some bags. He wants to put 2 berries in each bag. How many bags can he fill?

Finally, we will explore Partitive Division problems and Equal Sharing problems, the core of our fractions exploration (Epson & Levi, 2011). When we reach that step, our children will have developed/reinforced the habit of modeling directly a problem with manipulative, or representing the problem on paper,  and will naturally continue to do so with fractions.

E.g. An elf has 15 berries. He puts the berries into 3 bags with the same number in  each bag. How many berries are in each bag ?
 E.g. Two elves want to share 5 berries so that each of them gets the same amount. How many berries would each get?

My child does not know how to start

If your child is not used to solving multiplication problems, it is to be expected ! You may read the problem again, and say things like “I am wondering if these cups and buttons could help us solve the problem” or “Do you think it would help to draw the situation? What should we draw?”. Level Yellow is great for that.

My child provides the answer straight away

Remind him/her that the answer is important, but how it was obtained is even more important. That’s when learning happens ! Invite him/her to model and/or represent the problem with a drawing or a diagram. Invite him/her to write an equation and connect each part of the equation to his/her model and/or representation.

Questions ? Comment or email (journey2helpchildrenwithmath@gmail.com) ! Any feedback would be highly appreciated. This journey is our journey !


References:

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.
  • Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.

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