# Category Archives: PreK

## 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 !

## It sure is a journey !

When I decided, a couple of years ago, to start this blog, I saw it as a journey, my journey as a parent helping my children with math at home, willing to share all the good stuff I would learn as a M.Ed. student in math elementary education to, hopefully, inspire other parents.

It has, indeed, been an instructive journey. And attending recently a conference dedicated to Cognitively Guided Instruction (CGI) makes me feel like embracing the journey even more. In the past two years, I have enjoyed listening to my children solving problems “a way that makes sense to them” (Carpenter et al, 2014) and meeting the CGI community deeply confirmed my beliefs in such approach. CGI can be complex to describe, but in the context of this blog,  I would define it as a math instruction focused on how children think in math i.e. children’s mathematical thinking: children are invited to explore problems prior to receiving any formal instruction, prior to being introduced to any symbols or procedures. While children make sense of a problem, adults listen. In a CGI classroom, as children share their work, teachers embrace opportunities to build up their math instruction. At home, of course, one may not expect a nurturing classroom discussion. Still, I believe the exploration as such, without time pressure or peer pressure, the “out-loud” thinking is quite valuable. I have opened the door of my house to CGI, and I have enjoyed sharing my experience as a parent on this blog.

I often wonder, though, how I can reach out to more parents. Because it was, of course, my main goal in blogging: helping other parents. I use pen names, which makes it trickier to use social media as a megaphone, and I am more of a “behind-the-curtain” kind of person. So I guess the key will be to get back to more regularity  in my posts. Luckily, I came back from the conference with plethora of new activities to do with my kids, new blogs and resources to explore. So from now on, you can expect to find, once a week, at least one of these posts :

• “Solve and Share”:  I will continue to post word problems to explore across elementary grades but I will include additional children strategies from the literature to complete the experience I have with my own children. Hopefully, these posts will inspire you to welcome CGI at home.
• “How many?”: I am super excited about sharing this activity as I have done it a couple of times with my kids, and they loved it. I will dig further to let you know the genesis of it and explain it in further details when I write our first post but basically, you show the kiddos a picture, and ask them “how many?”. And they can count … whatever they want. They may start with counting items one by one, but the picture can open up to counting by groups, finding arrays, discussing fractions, etc. Here is a picture to help you start thinking about it.

• “Exploring the math shelf”: I naturally add math questions to any book I read to my kids, but I discovered an entire shelf dedicated to math books at our library (I know, it is about time). I started reviewing them, I have to say that some are much better than others. No wonder why kids get easily confused with math ! So each time we go to the library, I will bring a few math books and share my thoughts with you.

Of course, I will continue to post about any relevant matter for parents I read  as a doctoral student. Please, do not hesitate to share your thoughts as well, and raise any questions you may have. Time to fully connect with the math e-community !

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 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 !

## 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.

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.

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 !