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

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, in case you want to join us this year. I am adding videos this time :-) Click here if you want to know more about the journey.


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 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. Each problem is differentiated to target all elementary grades and is quite short. A child may be done within 5-10 min, or may decide to take more time to fully explore it with a visual representation and manipulatives. It is not a test, it is not a race. Week after week, problem after problem, children strengthen their reasoning skills by creating their own strategies to solve problems.

When children receive their formal fraction 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. They explore. We listen.

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 ?

What to do as a parent ?

  1. 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.
  2. I purposely stepped away from grade level. Each child should pick the problem that he/she feels like exploring. In the coming weeks, some upper graders may decide to pick a Level orange to model, represent, and write the equation. Some lower graders may decide to pick a Level Red and model it only.
  3. 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 !
  4. Our journey starts slowly, as children must explore a variety of problems, and build up strategies they can use with fractions later on.  If you child solve Level Red, providing an equation and another way of representing his/her strategy, you can always invite him/her to invent his/her own multiplication problem.
  5. One more thing, 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. 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.
I am including a link to 2 videos this  week:
  • Video Level Yellow : this short video (2 min) shows the material we use at home, and how a child may solve Level Yellow with a drawing
  •  Video Level Orange : this one (3 min) is an example of a child solving Level Orange with manipulative
These videos are just examples, but I hope they help you see what we do at home. It is all about the exploration. Your child may not use the same approach, but as long as he/she solve the problem a way that makes sense to him/her, it is all that matters.
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 weeks on Multiplication problems (see problem #1) above. Then, we will continue with 2 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.

Please, feel free to comment or email at journey2helpchildrenwithmath(at)gmail(dot)com if you have any question about our journey. The more feedback I receive, the more complete the next post will be ! Let’s build up a community of people supporting at home what our children learn during Math instruction !


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.

Would love to hear from you !

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