# Category Archives: Book

## Exploring the math shelf #3 – “The Grapes of Math” and other Greg Tang books

“Exploring the math shelf” is a journey that takes us weekly to our public library to explore their selection of math books. Click here to follow it from the beginning. Whether you are a parent, a teacher, someone supporting a child’s math thinking, I hope you find our books review helpful !

This week, we had fun exploring several math books written by Greg Tang.

• The books “Math Fables” and “Math Fables Too” present short stories about 1 to 10 animals gathering in a single group first, and then breaking down into two smaller groups.
• The books “The Grapes of Math”, “Math for All Seasons”  and “Math Potatoes” invite the reader to count items, suggesting strategies to count them other than by Ones (e.g. grouping items in a special way; counting by 5s or 10s, etc).
• The book “The Best of Times” reviews the multiplication facts from 0 to 10 through short riddles.

1. As often with the math books we take at the library, we did not read any of the books from the beginning to the end. Rather, we picked a few pages to discuss at night, or when we had  few minutes to spare here and there. These books have a perfect format to do so, and get a daily dose of math.
2. We spent most of our time with the books “The Grapes of Math” and “Math for All Seasons”, discussing strategies to count. The books give clues leading to one in particular, but we did not read it right away. Rosie came up with her own strategy, and shared it with me first, then, I offered mine, and finally, we reviewed the strategy from the book. It seems a good way to help a child not only build up his/her own mathematical thinking but also make sense of a strategy that may be different from his/hers.
3. Although the books are mostly focused on thinking, a few “tricks” can be found. I decided to skip the ones connected with concepts that Rosie has not fully explored yet. For instance, my hope is that by providing Rosie with plenty of opportunities to explore multiplying by 10, she will notice on her own the particularity of the products. Therefore, telling her now that she can multiply any number by 10, by just adding a 0 at the end seems going backward in our home journey of making sense of math.

I encourage you to check these books out. And if you like them, there are two more (“Math-Terpieces” and “Math Appeal”) you can explore !

## “1+1=5”, by D. La Rochelle & B. Sexton. It is all about the units !

Last month, I attended a presentation about units (Cipparone & Bass, 2017). When C. Danielson (“Talking Math with Kids”) mentioned the book “1+1=5”, I quickly wrote the title on a Post’It, knowing that as soon as we were back home,  I would check it out.

I am so glad I did. Such a fun support to make children think about units.

Each page presents a drawing and an equation, such as a unicorn and a goat and “1+1 = 3?”. On the next page, the equation includes the units i.e. 1 unicorn + 1 goat = 3 horns. Indeed, 1 + 1 = 3 :-)

You may have read it in some of my previous posts, I always remind my daughter Rosie, 8, to provide the unit at the end of a word problem, and even invite her to write the units in her equations. This book was just perfect to reinforce my point, and led us to an instructive talk about the importance of the units.

Rosie LOVED that book, and could not stop talking about it for a week, finding new examples on her own. In fact, if you meet a little girl who claims, with a mischiveous grin, that “1+1 = 3”, enjoy: you may have just met Rosie :-)

Reference:

Peter Cipparone & Hyman Bass, 2017. Bringing Out the “Unit” Across Mathematical Domains. Cognitively Guided Instruction. 2017 National Conference, Seattle June 26-28.

## “Exploring the math shelf #2” – Building Blocks of Mathematics

“Exploring the math shelf” is a journey that takes us weekly to our public library to explore their selection of math books. Click here to follow it from the beginning. Whether you are a parent, a teacher, someone supporting a child’s math thinking, I hope you find our books review helpful !

Our weekly trip made us discovered a series of books called “Building Blocks of Mathematics” (by Joseph Midthun and Samuel Hiti).

The series comprises six books

• Numbers
• Subtraction
• Multiplication
• Division
• Fractions

I highly recommend them.

1. The books are amusing, cute, strips books. Once we started with the first one, Rosie, 8,  could not wait to read the next ones.
2. We started with Addition, Subtraction, Multiplication and Division, as Numbers was not available initially, but I do not think it matters. Numbers can be read independently.
3. The book Numbers presents a variety of counting systems, and invites children to create their own. I remember having to create my own Base System as a M.Ed. student, it was quite an instructive process, to say the least ! Rosie started by making random symbols for each numeral she would think of. We started discussing about patterns that usually occurs in counting systems.  Her second attempt was quite close to our decimal system, but in her third attempt, a different logic started to appear. Her reflection is far from being completed, but I can see how the book Numbers could indeed lead to a powerful activity around counting.
4. The book Numbers also goes into place value, presenting how some systems have place value while others do no. I have to say that I had never really thought about it. For instance, the counting symbols used by the Egyptians could be written from left to right, or right to left, each symbol keeping the same value no matter its position. With the Arabic numerals, however, the value of each digit depends on its place in the number (e.g. the 5 in 53 has a value of 5 Tens). Interestingly, it seems to me that the Roman numerals are kind of in-between: V has always a value of 5, but IV and VI have different value, depending on the position of the symbol I (4, when I is placed before V, and 6, when I is placed after V). Place value is a concept so often misunderstood, Numbers provides an opportunity to approach it through another angle that would be helpful even in upper elementary grades.
5. In Numbers, there is even a WHOLE page on Zero, a numeral so often forgotten!!!
6. My hope when I pick a book series, is to find some connections between the math concepts presented in each book (e.g. a link between geometry and fractions, or multiplication and repeated additions, etc). This series exceeded my expectations on that front. The character “+” leads the story in Addition, but is also part of Subtraction aside the character “-” and Multiplication along character “x” . In Division, all characters are present (“+”, “-“, “x” and “÷”) illustrating well the relationship between the four operations.
7. The books contain reassuring words (the character “+”, for instance, saying “It never hurts to slow down when you are doing math”, or “you can always use me to check your work” in the book Multiplication).  I have to say that Rosie is not the most confident person around (the apple doesn’t fall far from the tree), and she found it quite comforting to read that when you are stuck in one operation, you can always go back to another one.
8. The characters “+”, “-“, “x” and “÷” discuss different ways to solve problems, using drawings, number lines, equations, etc. A good review of strategies to discuss with your child.
9. Rosie has not been talking about division at school yet. Still, she was fully engaged in the book “Division”, as the concept is clearly presented, and well connected to the other operations she is more familiar with. I decided not to read the whole book “Fractions”, though. It is well written, but I  want Rosie to keep exploring fractions a little further without going to rapidly into their symbolic representation. I look forward to doing our Time 4 Fractions in the Fall for the third time, I may go back to this book once we are done.
10. Cherry on top: the book Cognitively Guided Instruction (Carpenter et al, 2014) is referred as a resource for educators. If you have been following my blog, you know how highly I recommend this approach of instruction :-)

I could still add to the list,we had so much fun reading them. I hope you do to !

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.

## “Exploring the math shelf #1” – How to pick math books for a meaningful discussion

I often write about how much I enjoy listening to a child making sense of a math problem. But something I find quite fulfilling as well is reading books with my children (any child, actually). No need to say that I am quite excited about our new journey, “Exploring the math shelf”, that takes us weekly to our public library to explore their selection of math books.

Before I start discussing books we have checked out, I thought that sharing our book selection process could be helpful as well. It has indeed been working quite well for us, considering the math discussions that have popped up at our house in the past few weeks.

At some point, I expect, well, I hope, my kids will be naturally attracted to the math section, and pick math books on their own. For now though, I think they count on me to do so :-).

1. I usually do not have any specific math books in mind when I arrive at the library. I like to browse the shelf.
2. Often, I take several books around a math concept my kids have been talking about, such as place value, multiplication or fractions.
3. I try to mix stories (e.g. “Earth Day – Hooray”, by S. J. Murphy and R Andriani, a story illustrating place value) with books specifically detailing a math concept  (e.g. Place Value, by D. A. Adler). That way, we can have an informal math talk while reading a story, and have access to other more detailed sources if my children raise a particular math question.

Once home, we read books when we feel like it. Sometimes at night, sometimes during the day. Unlike with the story books, we rarely read our “math” books from beginning to the end. Rather, we discuss a page or two at a time, such as page 8-11 in Place Value, where the number system is compared to the alphabet. But we go back to the books several times during the week.

One more thing: I do read the math books with my kids. Indeed, you would be surprised by the imprecision, and even inaccuracies you may find in math books. I checked out recently a book about multiplication, and was quite excited to see that the equations included the units. I always encourage my child Rosie, 8,  to do the same when she solves problems (e.g. 2 cats + 3 cats = 5 cats). Indeed, there is no need to wait for a Chemistry course to begin such a helpful habit. Alas, in the book, to illustrate 2 baskets containing each 7 tomatoes , the equation was:

7 tomatoes X 2 baskets = 14 tomatoes.

Somehow, magically, the “basket” unit disappeared (to produce more tomatoes???). Now if the equation had been written as follow, I would have highly recommended the book:

I have to say, though, that once you are aware of possible misconceptions, and discuss such eventualities with your child, it opens a new door to more meaningful math. Rosie is now on a new quest:  “See, Mom?  They say that you have to use the zero mark when you use a ruler. But you don’t have to ! It is easier, but you don’t have to !”. Never too early to become a critical reader.

## 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 walk, 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?

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 ?

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.

Small, 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.

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 !

“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.