Tag Archives: math discussion

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.

Want to do math at night? Try Bedtime Math® !

Another book I have discovered recently: Bedtime Math®, by Laura Overdeck and Illustrated by Jim Paillot. It is series of books, actually, but I just bought the first one for now.

Each page includes a short text about a fun fact (e.g. “exploding food”, “extreme vehicles”, etc) , and  3 levels of word problems (one for the “wee ones”, one for the “Little Kids” and one for the “Big Kids). Click here to see an example of pages displayed on Amazon.

My daughter (1st grade) and I have been doing it at night for a little while, and I must admit, we are having a good time.  My child might get frustrated exploring some of these problems on her own because of the wordings, and the format, rather different than what she does at school. But to discuss and explore informally together, before turning off the lights, it is a neat book. I do like the idea of combining reading and math. The “Wee ones” problems are the ones we usually discuss at night, as most of the time, we would need at least paper, if not manipulatives to explore the “Little Kids” level. That would be more a “Daytime” Math for us. The “Big Kids” Level is most of the time, out of reach for us. These problems cover indeed a wide range of skills !

You may want to give it a try ! If you are interested, check their website here, the books can be bought on Amazon or Barnes & Nobles.

BedtimeMath


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.

Hooked on Anno books

A few weeks ago, I wrote a quick post about my recent discovery of Anno books (here). Now that I have had a chance to look at several of them, I can definitely claim, loudly and clearly, how instructive and entertaining they are.

Anno’s Counting Bookthumb_IMG_0370_1024

The book starts with an empty landscape, with the numeral 0. The next page, numeral 1, includes a house, a cloud, a bridge. One child, one grown-up. On the next page, a second house can be seen, two trucks. And so one until the page with the numeral 12.

I have always enjoyed counting book, but I would put this one on the top of my list.

  • The drawings are quite appealing to me, and to my children.
  • Page after page, you can see the landscape changing with the seasons, filling up with all kind of items, full of little details that my kids love exploring.
  • There is a neat connection, on the left, to the counting blocks children use at School (e.g. 3 blocks on the left, the drawing in the middle, and the numeral 3 on the right).thumb_IMG_0381_1024
  • Similar items are not always all together, providing support to discuss not only counting, but also adding. For instance, on page “4”, there are 3 birds on one corner, and one more on another corner. My son Tom, 3, would count them one by one, while Rosie, 6, would see it as  adding 3 to 1.

I just wish I have found this book a few years ago, when I started reading books to Rosie or when I was teaching PK and K. A must have for young kids, in my opinion !

Ann’s Math Games and Anno’s Math Games II

These two books include a series of activities to strengthen mathematical skills.

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Ann’s Math Games relates to comparing, adding/subtracting, ordering, and measuring. Ann’s Math Games II goes further, deeper. I found the chapter on Counting with circles quite interesting, showing that a group of children to be counted, can be represented from a complete drawing with all details, to something simpler, to a circle. A helpful transition to modeling and symbolics, that Rosie would have benefited from a few months ago (see here, first and second bullet point).

FullSizeRender

“Parents, Teachers and Other Older Readers” can also find additional information about the math concepts presented in the book at the end of each book.

Anno’s Magic Seeds and Anno’s Mysterious Multiplying Jar

These stories relate to more advanced concepts (multiplication and factorials). However, I like to give opportunities to my kids to informally explore math concepts on their own before learning them at School. Anno’s Magic Seeds is a fun way to do so with multiplication. I just need to remember to come back to it when Rosie is in 2nd grade !

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To sum up: Anno books, I am hooked !