Tag Archives: Fractions

Our 3rd edition of Time 4 Fractions is ready to start: all aboard !

Please click here to follow Time 4 Fractions.

I am quite excited about starting our 3rd edition of Time 4 Fractions in the coming weeks. I should be able to update the posts from last year significantly, since I went to the conference dedicated to Cognitively Guided Instruction in June and I am taking a course on Children’s thinking this semester as a doctoral student.

As you may remember, I started Time 4 Fractions two years ago, after I read the book “Extending Children’s Mathematics – Fractions and Decimals” (Epson & Levi, 2011) as a M.Ed. student, thinking “This IS the way I would have liked to explore fractions! “. An ah-HA! moment, a true eye-opening: building up meaning for fractions through equal sharing problems. A wonderful approach to pursue at School. But also at home, I believe: the more opportunities to extend math reasoning, the better.

Over the twelve coming weeks, I am going to post a word problem that will take the kids to slowly, gradually, explore the concept of fractions. We will start our journey with multiplication problems (yes, even with lower graders, click here if you are not sure why !), division problems, then, finally equal sharing problems, the core of our journey, and the true beginning of our fraction exploration. The sequence of problems is based on the reading of two books, Children’s Mathematics (Carpenter et al, 2015) and Extending Children’s Mathematics – Fractions and Decimals” (Epson & Levi, 2011).

Whether your child is in lower grade or upper grade, I hope you join us. I share what I do with my own child as a illustration of what a child may do, but by no mean as what a child should do. It is not a test, it is not a race. Week after week, problem after problem, children practice their reasoning skills by creating their own strategies to solve problems.

In the previous year, I found it quite convenient to put together a “math box”. You may want to do the same before we start !

  • paper and pencils. Markers are also helpful to connect a visual representation to an equation.
  • manipulatives to model the problem.  You do not need the base-Ten blocks. Marbles, buttons can do the trick. I like Legos® and Duplos®, as you can stack them in Tens.
  • Containers (e.g. paper cups, Tupperware®), to model problems involving groups of items.
  • A stack of paper (e.g. blank flashcards), to explore fractions, by cutting parts of a whole, and putting them back together.Our math box

 

Most important, I will be here to support you in the journey. 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 !

Off we go !

References:

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2015). 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.

Update Time 4 Fractions : welcome aboard !

My daughter and I went on a 12 weeks journey in the Fall 2016 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 have little memory of studying fractions at School. I remember adding fractions, multiplying fractions, finding the least common denominator, but nothing about exploring the concept as such. It was last year, while I was taking a class about fractions, reading “Extending Children’s Mathematics – Fractions and Decimals”(Epson & Levi, 2011)  that I started thinking: “Ah ! This IS the way I would have liked to explore fractions !”. An ah-HA! moment, a true eye-opening. Using word problems to build meaning for fractions. Then, incorporate symbols and equations. A wonderful approach to pursue at School. But also at home, I believe: the more opportunities to extend math reasoning, the better.

Our journey is going to take us to slowly, gradually, explore the concept of fractions. Whether your child is in lower grade or upper grade, I hope you join us.

How is it going to work : 

  • Once a week, I will invite my child to explore a word problem and share my experience with you. We will start our journey, labeled as “Time 4 Fractions”, with multiplication problems (yes, even with lower graders, click here if you are not sure why !), division problems, then, finally equal sharing problems, the core of our journey, and the true beginning of our fraction exploration. The sequence of problems is based on the reading of two books, Children’s Mathematics (Carpenter et al, 2014) and Extending Children’s Mathematics – Fractions and Decimals” (Epson & Levi, 2011).
  • 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 a few days 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.
  • I found it quite convenient to put together a “math box”. You may want to do the same before we start !
    • paper and pencils. Markers are also helpful to connect a visual representation to an equation.
    • manipulatives to model the problem.  You do not need the base-Ten blocks. Marbles, buttons can do the trick. I like Legos® and Duplos®, as you can stack them in Tens.
    • Containers (e.g. paper cups, Tupperware®), to model problems involving groups of items.
    • A stack of paper (e.g. blank flashcards), to explore fractions, by cutting parts of a whole, and putting them back together.Our math box
  • Most important, I am here to support you in the journey. 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 !

Off we go !

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.

Time 4 Fractions : welcome aboard to our new math journey !

Please click here to follow Time 4 Fractions.

I have little memory of studying fractions at School. I remember adding fractions, multiplying fractions, finding the least common denominator, but nothing about exploring the concept as such.

It was last year, while I was taking a class about fractions, reading “Extending Children’s Mathematics – Fractions and Decimals”(Epson & Levi, 2011)  that I started thinking: “Ah ! This IS the way I would have liked to explore fractions ! “.

An ah-HA! moment, a true eye-opening. Using word problems to build meaning for fractions. Then, incorporate symbols and equations. A wonderful approach to pursue at School. But also at home, I believe: the more opportunities to extend math reasoning, the better.

So that’s where our next journey is going to take us for a while, to slowly, gradually, fully explore the concept of fractions. Whether your child is in lower grade or upper grade, I hope you join us. All aboard. From K to 5th. Ready?

How is it going to work : 

  • On Monday, starting next week, I will create and post a word problem. We will start our journey, labeled as “Time 4 Fractions”, with multiplication problems (yes, even with lower graders, click here if you are not sure why !), division problems, then, finally equal sharing problems, the core of our journey, and the true beginning of our fraction exploration. The sequence of problems is based on the reading of two books, Children’s Mathematics (Carpenter et al, 2014) and Extending Children’s Mathematics – Fractions and Decimals” (Epson & Levi, 2011).
  • Each problem will be differentiated to target lower elementary grades to upper elementary grades.
  • With each problem, I will include guidelines to follow, as well as a child’s sample. Invite your child to explore the problem on his/her own.  I wrote a post a few weeks ago about how we explore word problems at home. You may want to check it out before we start our new journey ! It is here. You can do it, too !
  • Problems will be quite short. A child may be done within 5-10 min, or may decide to take a few days 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 will strengthen their reasoning skills by creating their own strategies to solve problems.
  • The first problem will be posted on August 31, but if you want to start later on, no problem, you will just have to start with “Time4Fractions – Problem 1” and follow the sequence. I will create a link on the menu on the right for easy access.
  • I found it quite convenient to put together a “math box”. You may want to do the same before we start !
    • paper and pencils. Markers are also helpful to connect a visual representation to an equation.
    • manipulatives to model the problem.  You do not need the base-Ten blocks. Marbles, buttons can do the trick. I like Legos® and Duplos®, as you can stack them in Tens.
    • Containers (e.g. paper cups, Tupperware®), to model problems involving groups of items.
    • A stack of paper (e.g. blank flashcards), to explore fractions, by cutting parts of a whole, and putting them back together.Our math box
  • Most important, I will be here to support you in the journey. 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 !

Off we go !

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.