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Posted in Newsletter
Press Here
Have you read this book? Maybe “read” is not exactly the word here. Have you played this book yet? If not, go ahead and give it a try. The idea is simple – each page of the book tells you what to do, but doesn’t tell you why you are doing it or what to expect. You discover what has happened only after you flip the page.
This is not a math book. Yet there is a lot of fun math hidden in it. In just a few pages you play with iterative functions, several function machines and a fun pattern.
Even better, the book ends with an invitation to play it again, looping back to the first “press here” page.
This book gives a child a perfect opportunity to figure out patterns of action and to predict outcomes. “What do you think is going to happen now?” is a question that is ingrained into the book.
After going through it a few times, children might feel inspired to create their own books similar to “Press Here”. All it takes is a few sheets of paper, stickers and markers.
One thing I haven’t tried yet, but that sounds intriguing is to see what happens if you stop in the middle of the book and go back to beginning and repeat the instructions. For example, what if we stop on this page with a pattern and then go back to the beginning, follow the instructions and press yellow dots only. I think it would be a fun way to explore algorithms with nothing but a large piece of paper and a few Dot Dot markers (or regular markers or stickers).
httpv://youtu.be/Kj81KC-Gm64
Have you played this book? Share your ideas and experience with us!
Posted in Grow
No Manipulatives Days
These have been our math manipulatives for the last couple of weeks. Here they are lined up from largest to smallest.
We usually use a lot of manipulatives with my son. But not this week. It was interesting to see how a 5-year old deals with something very abstract, such as numbers.
Last week, while grocery shopping, I asked him what was bigger, 8 or 14. Without hesitation he responded that 14 was bigger. Distractedly, I asked him why did he think so. The answer was “14 is bigger because I can count to 8, but I can’t count to 14”. The reasoning sounded both unexpected and logical to me.
This week started with my son asking me to write down a story he made up about his collection of toy garbage trucks. It started with
At first Mark had 0 garbage trucks. Then he found out about them, started watching videos about them. Then he had 1 garbage truck. Then he had 2 garbage trucks because he got a gift from a store. Then he had 3 garbage trucks…
on and on it went like this until he got to 7 because that’s how many trucks are in his collection. So it was basically a counting story.
Then today he wanted to write down the same story again, but I approached it differently. Instead of writing it down, I gave him a pencil and paper and we worked out some basic equations:
0+1 = 1
1+1 = 2
2+1 = 3
3+1 = 4
4+ 3= 7
(because he found 3 trucks at a garage sale all in one day)
After he was done writing it all down, he reviewed his work, then looked at me with a puzzled expression and asked “I don’t understand, Mom. Where are all the words?” Which gave me a chance to explain a bit about how equations can tell a story. He seemed to be happy to discover a way of writing things down in as few signs as possible.
Both stories seem trivial when I re-tell them. But when they happened, I was reminded of how abstract the concept of numbers and manipulating with numbers (as opposed to quantities) can be for a child. And for me, as an adult, it is a difficult one to relate to. It’s been a while since I was 5 years old. I simply don’t remember myself not knowing numbers. Do you?
Posted in Grow
Greedy Triangle Math
We’ve had such a great time with Marilyn Burns’s The Greedy Triangle book that I want to share it here on the blog.
If you haven’t read this story, it is about a triangle that one day got tired of doing the same old things. It thought that if he only had one more side and one more angle, its life would become much more interesting. Luckily, a local shapeshifter was there to help and turned the triangle into a quadrilateral. Things went along just fine until one day the quadrilateral became unhappy again and went to ask for just one more side and one more angle. It was turned into a pentagon first, then – a hexagon and on and on.
So not only does this story helps a child understand better what a polygon is – a shape with sides that are straight line segments. But it helps children understand that polygons can have 3, 4, 5, 10 and more sides and angles.
This book is a great jumping-off point for many games and activities.
Shapes Scavenger Hunt – we looked for shapes from the book wherever we went, but also in our house (the story gives lots of examples).
Polygon Builder – try to build a polygon out of a certain number of craft sticks or crayons. What would this shape be called?
Polygon Races – this is just an extension of the Polygon Builder. The idea is pretty simple – once the shape is built, hot glue the craft sticks together. Build a few different polygons and try to figure out which one would roll faster and why. This led to a quick search on Internet for a square-wheeled bicycle and another one from the Museum of Mathematics and a bicycle from China that has both a pentagon wheel and a triangular one.
Geo Board Builder – this was largely a self-directed activity. We just had a geo board and rubber bands laying around.
Mirror Book Shapeshifter – the book has some suggested activities, including asking a child about why a shape with many sides and angles would roll more easily than a shape with fewer sides and angles. We used the two square mirrors taped together and set up as a mirror book to explore the answer. We taped a piece of painter’s tape on the table in front of the “book” and opened the mirror pages so that the tape and its reflections formed a triangle. Then we started closing the pages until an extra angle and an extra side was added. Wow, we were the shapeshifting magicians now!
At the end of the Mirror Book game, when we had too many angles and sides in our polygon to count, I asked my son why a shape with many sides would roll more easily than a shape with fewer sides. His answer was “it has all these short sides and it looks almost like a circle now“.
Now, we didn’t do all this in one day. Nor did any of the games last very long. We did read the book a dozen times or so in just three days. And then it was all over and my son moved on to different books. But a few days later he picked up a small flat rock on a walk, showed it to be happily and said “Mom, look, it’s a quadrilateral!” and it sure was!
As the author explains, the book’s main goal is to “engage and delight children, stimulate their imaginations”. She also reminds parents “At all times, follow the child’s lead.”
Posted in Grow
