Tag Archives: Reasoning

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.

How I support my child exploring word problems at home

I don’t really teach my daughter math. Well, sometimes I do, informally, when  the perfect opportunity to strengthen and connect a math skill to real life comes up, but most of the time, I don’t. I trust her teachers.

But there is one thing I try to make sure : that she has plenty of opportunities to explore math concepts at her pace. Away from peer pressure, or time pressure, she can model, draw, write equations. Few minutes here and there. Once a week.

I recently made a video of how we do that, with the example of my child exploring one of the Time 4 Fractions problems (Problem 10) in a meaningful way for her as recommended in Carpenter et al., 2014. And her Mom following her reasoning. Now, bear with me, it is quite unnatural to me to speak English to my child, but I thought the video could help you see what our journeys, such as Time 4 Fractions, or WedWoPro are about.

Enjoy !

Reference:

  • 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.

Drawing math with ballons

Drawing math is a … drawing that I make to discuss math with my children. My oldest (7) likes to invent a word problem that matches the drawing, while my youngest (4) likes counting items ! 

You can discuss with your child about any math in the picture (e.g. counting, patterns). You can also ask your child to invent a word problem that would match the picture. Here are some examples!

  • Addition – There were 2 yellow ballons, 4 green ballons and 5 blue ballons. How many ballons were there all together? (2 + 4 + 5 = 11)
  • Subtraction – There were 21 ballons. 9 were sold. How many ballons were left for sale?  (21 – 9 = 12)
  • Multiplication – There were 3 children. Each child had 3 ballons. How many ballons did the  children have all together? (3 x 3=9)
  • Division – 3 children wanted to share equally  9 ballons. How many ballons would each child get ? (9 ÷ 3 = 3)

Until next time !


Drawing math at the circus

Another picture to strengthen your child’s math reasoning skills and creativity !

Invite your child to invent a word problem that matches the drawing.

Circus

If your child is not sure how to start, you may invite him/her to write a problem involving addition at first. Then, let him/her try with subtraction, multiplication and division !

Here are a few examples:

  • On the ring, there were 1 illusionist, 3 jugglers and 4 circus musicians. How many people were on the ring ? (1 + 3 + 4 = 8)
  • There were 15 circus musicians leaving the ring. 11 were already behind the curtain. Some were still on the ring. How many musicians were still on the ring ? (15 – 11 = 4)
  • There were 3 jugglers. Each juggler had 4 balls. How many balls did the jugglers have all together? ( 3 x 4 = 12)
  • There were 180 spectators. Two third of them had brown hair. How many spectators had brown hair? (180 x 2/3 = 120)
  • 3 jugglers want to share 12 balls so that each of them gets the same number of balls. How many balls would each juggler get? (12 ÷ 3 = 4)

Until next time !


Drawing math with penguins

Remember last week (here) ? Here comes our second picture ! Invite your child to invent a word problem that matches the drawing.

Penguins

Here are a few examples:

  • There were 12 penguins on the ice,  4 penguins in the water, and 1 penguin jumping out of the water. How many penguins were there all together? (12 + 4 + 1 = 17)
  • There were 15 penguins on the ice. 3  jumped in the water. How many penguins were left on the ice? (15 – 3 = 12)
  • There were 4 penguins in the water. Each penguin ate 5 fish. How many fish did the  penguins eat all together? ( 4 x 5 = 20)
  • There were 16 eggs. There were 2 eggs under each penguin. How many penguins were seating on eggs ? (16 ÷ 2 = 8)

Until next time !


Drawing math in the ocean

After our last journey, T4F, ended,  I quickly started missing the special time my daughter and I had on Friday nights when we explored the weekly problem together.

Over our Thanksgiving break, I decided to try something new.

I drew a quick picture, and asked my child to invent a word problem that matches the picture.

It worked so well, that I am going to keep drawing pictures (with much more details!), and share them with you.

A – It gives a chance to children to explore word problems though a different angle. At first, my daughter wrote something that was quite close to what she does at school. But then, as she was trying something more complicated, reading her problem so I could solve it helped her see what information she may have forgotten, what she had to add to her text to complete her problem. At one point, the whole family gave a try to inventing a problem.  Even my almost 4 year old son asked a math question related to the picture. Here are a few examples:

  • There were 5 fish. 2 were pink and some were purple. How many fish were purple?
  • There were 2 pink fish, 3 purple fish. There were also 2 brown fish behind the rock. How many fish were in the water all together?
  • How many pairs of socks will the octopus need to buy when the water gets cold?
  • How many fish do you see?

B – The children can explore different formats of word problems (I don’t think I would have thought about an octopus in need of socks !).

C – The children can pick the operation they feel comfortable with, as well as the numbers (the rock can be used as a hidden place to work with higher number!). They can also try to come up with a word problem that involves a specific operation.  Next time, I will draw much more details that could be used, but here are some examples from that picture.

  • Addition: There were 2 pink fish and 3 purple fish. How many fish were in the water all together? (2 + 3 = 5)
  • Subtraction: There were 14 fish next to the rock. 9 fish left. How many fish stayed next to the rock? (14 – 9 = 5)
  • Multiplication: There were 3 purple fish. Each fish blew 2 bubbles. How many bubbles did the  purple fish blow all together? (3 x 2 = 6)
  • Division: Rosie has 17 fish. She wants to give as many fish as she can to her 6 friends, with each friend getting the same number of fish. How many fish can she give to each friend  ? Will Rosie have some fish left? (2 fish / friend, Rosie has 5 fish left)

If your child is not sure how to start, you may want to invent a first problem and ask your child to invent another one. That should do the trick.  I am going to post a new picture every week, so we can practice all together.

Beginning of 2016, I will start another journey, that will include exploring word problems on all operations, but I think these pictures could be fun as a transition.

Until next time !