Category Archives: Book

Exploring fractions with “The doorbell rang” by Pat Hutchins

You may know the author Pat Hutchins and her books for young children, such as Rosie’s Thedoorbellrangwalk, Changes changes, Clocks and more Clocks, etc. I bought a few when my children Rosie and Tom were younger, and “The doorbell rang” was one of them. I had almost forgotten about them, until I recently heard Rosie, second grade, say:

“I recognize this book ! We read it in math today !”

So we read it again. The text is attractive as it includes predictable sentences that young children enjoys repeating out loud. And for older kids, the story opens the door to math. Ma made cookies for her two children, Sam and Victoria to share (equally). The doorbell rings, and two more children, Tom and Hannah come and share the cookies. As the doorbell keeps riging, more children come to share the cookies, until twelve children have to share the twelve cookies.

As I was reading the story, Rosie modeled it. She used flashcards to represent the cookies, similarly to what she has been doing with Time 4 Fractions.

  1. At the beginning of the story, Sam and Victoria gets 6 cookies each. How many cookies has Ma baked?
  2. Now that they have to share the 12 cookies among 6 children, how many cookies does each child get?
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6 children sharing 12 cookies equally: each child gets 2 cookies

But a fun activity we added was to twist the story a little, and work not only with whole numbers, but also fraction. You may want to give it a try. I just let my child make sense of the problem, whether using paper to cut, or buttons to count, or the base Ten Blocks. Sometimes, she connects her model to symbols she has learned at school. But the goal is to let her make sense of the problem.

  1. What if Tom does not want any cookie, i.e. three children share the twelve cookies, how many cookies does each child get ?

  2. What if Peter does not want any cookie, i.e. five children share twelve cookies many cookies does each child get ?

  3. What if Tom, Peter and Victoria do not want any cookie i.e. nine children share twelve cookies many cookies does each child get ?

IMG_0042

9 children sharing 12 cookies: each child gets 1 whole cookie, and 1/3 of a cookie (or equivalents)

I always look for opportunities for my children to have fun exploring problems, and make sense of them.  “The doorbell rang” sure is a neat book to create such opportunities.

Give it a try ! I am here if you have any questions !


Small, 2012 – Reaching out to all children

Here is another book I studied as a graduate student that I found interesting to share.

FullSizeRender-2Small, M. (2012) Good Questions: Great Ways to Differentiate Mathematics Instruction, 2nd Ed., Teachers College Press, NY.

The author suggests 2 different types of math tasks to reach out children with different skills and needs. Makes sense in a classroom, of course, but it makes sense to me at home as I start seeing my son Tom, 4, willing to “do math” with his sister Rosie, 7 (see my previous post here on Doing Math outside, for instance).

Open questions:

The task is “framed in such a way that a variety of responses or approaches are possible” (Blanton, p6). Remember my post on Vygotsky  (here) ?  Well, the goal is to design the task “in the appropriate zone of proximal development for all students” (Blanton, p6), so that every student can be part of the discussion.

Here is an example of what we did recently:

“Go outside and take a picture of a pattern”.

Rosie came back with a pattern found on  a flower, while Tom came back with a  pattern he created with rocks and pine cones. Still, we were able to discuss patterns all together.

Parallel tasks:

It is a set of tasks that children can choose from, that are close enough to be discussed at the same time.

For instance, this afternoon, I asked Tom and Rosie to create a story out of:

  • Choice 1: 10 dinosaurs
  • Choice 2: 3 cars

Again, even if Tom used a number smaller than Rosie to create his story, they still were able to share what they did with each other. Also, Rosie was able to create a math problem, while Tom invented “just” a story involving 3 cars.

Of course, with Tom and Rosie’s difference of age/skills/grade, I may not always be able to provide them with tasks they can explore together, but I really like the idea, and will come back to it regularly.

You may want to  check out the book, too ! It includes hundreds of Open Questions and Parallel Tasks organized by math concepts and grade levels.

 


Math & Children Literature – Part II

A few month ago, I shared “The wonderful world of mathematics: A critically annotated list of children’s books in mathematics” (Thiessen et al., 1998), a helpful ressource to find children books that could be connected to math (here).

Well, there is more !IMG_1500

“Exploring Mathematics though Literature” is another book from the National Council of Teachers of Mathematics (NCTM). It includes a selection of articles previously published by the NCTM, categorized by math topics: Number & Operations, Algebra, Geometry, Measurement, and Date Analysis & Probability. Articles may discuss a book, a math activity connected to the book and strategies children may use, etc. This book is a gem to me: not only it gives me ideas of books to read in connection with math, but also activities to implement. And cherry on the top for me so interested in how children think, it provides student samples. A great source of inspiration for our math journey 🙂

Also, Math Solutions, CA, published a series of books connecting fiction/non-fiction books with math lessons for different grade levels. I sure will try some of their recommendations throughout Summer.

If you love connecting books to math as much as I do, you may want to check these books out !

References:

Burns, M & Sheffield, S. (2004). Math And Literature, Grades K-1: Math Solutions, CA.

Burns, M & Sheffield, S. (2004). Math And Literature, Grades 2-3: Math Solutions, CA.

Peterson, J. (2004). Math And Nonfiction, Grades K-2: Math Solutions, CA.

Thiessen, D., Matthias, M., & Smith, J. (1998). The wonderful world of mathematics: A critically annotated list of children’s books in mathematics. Reston, VA: National Council of Teachers of Mathematics.

 


Is your brain thinking about it ?

Here is another book I am reading as a graduate student in math elementary education: “Why don’t students like school”, by D.T. Willingham. I enjoy the cognitive approach the author takes to explain how to better support children’s learning.Willingham

One thing I noted is how your brain has to think about what you try to learn in order to retain it :

“Thus, your memory is not a product of what you want to remember or what you try to remember: it’s a product of what you think about” (p53)

And it is actually quite easy for children (and adults!) to get distracted from  thinking about the concept they intend to learn. Quick example from the book (p64): a math problem involving cell phone minutes in High School may have students think about… the last text they received rather than thinking about… math. And it may be tricky to motivate children with a topic of interest, or add some fun to help them learn without crossing the line of distracting them.

Indeed, I had the perfect example with my child this week.

Rosie came back home one night, and  recognized the symbol “<” in one of my books left on the table. “We just started learning about that symbol at school !” she said. So of course, I asked her to tell me more about it. To which she answered… “I am not quite sure yet, but it is like an alligator. And I love alligators !”

Zoology: 1 – Math: 0

alligator

 

 


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


Exploring money a little further …

Quick post to complete what I wrote earlier this week (here). Somehow I forgot to include another relevant book about money. Let me address that.

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Indeed, the book “If you made a million” (by D. M. Schwartz and illustrated by S. Kellogg) provides a nice support to extend the discussion my child and I started with Dollars and Cents for Harriet (B and G Maestro). It goes from coins, to bills, to checks, or how $10 could be paid through 1 ten-dollar bill, 2 five-dollar bills or… a 5-inch pile of dimes. It even includes bank accounts and interests, as well as choices you have to make when you have money (e.g. spending, saving, both).

Another great resource to explore money !


Exploring coins

My daughter has been expressing interest in learning more about coins. I thought I should share what we have been doing !IMG_4118

We started the exploration with the book Dollars and Cents for Harriet, from B and G Maestro. It is one of the books listed as highly recommended in The wonderful world of mathematics ( Thiessen, D., Matthias, M., & Smith, J. (1998), see here ). Indeed, I like how the concept of money is introduced through the story of Harriet, a young elephant who wants to buy herself a gift (suspense until the end of the book !). Through small jobs, she collects a variety of coins until she has enough to purchase her gift. My child loved the book, and have read it on her own several times since (on a side note, there are more Harriet concept books, including some on Time. I am going to check them out, as my child is studying this concept this year at school. Stay tuned…)

Then, we looked at the coins my daughter has been gathering around for years, and sorted them. We identified them in the book. We discussed the value by using the base Ten blocks (not familiar with the base Ten blocks? Click here). For the record, you can use paper clips or Legos®, as long as the child sees visually that different coins have different values, it should work as much.IMG_0617

After that, we played ! My child decided to sell tiles. How much for 5 pink tiles? How about this precious lonely brown tile? And so on.

And finally, we went on a field trip. And a hunt for items that would be less than $1. I must admit I was surprised, we found more items than I thought (made sense once I realized that many fruits were sold by the unit). 19 cents for a banana, 79 cents for an orange, 29 cents for a lime. We could not find a box of cereal for less than a dollar, but we did find a pretzel stick for 99 cents i.e. almost a dollar. We noticed that it was cheaper to buy a sweet onions than a red onions.IMG_0637IMG_0636

We ended up paying… with my credit card. That’s what you get, kiddo, when you have a mom who grew up with Francs, switched to Euros when she was 26, and switched again to Dollars when she moved to the U.S.  🙂