Posts tagged preschool math
This is a story inspired by Vi Hart’s “Wind and Mr Ug” video. I so wanted to tell it to my son myself, but my drawing skills fall way short. So instead we talked about ants.
Once upon a time two ants lived on a strip of paper. A strip of paper has… how many sides? how many edges? [I drew two ants on a strip of paper] Each ant lived on his own side of the strip. They never saw each other, but since ants have an excellent sense of smell, they smelled each other. And they really, really wanted to have a playdate or maybe a tea party one of these days. They tried visiting one another, but each time they reached an edge of their little flat worlds and would get scared.
Then one day something happened. There was much shaking and twisting and the ants got scared and closed their eyes and covered their heads and tucked their antennas. When the twisting and shaking stopped, they opened their eyes and saw something strange. Their flat world was no longer flat. Instead, it became cylindrical [At this point I glued the edges of the strip together to create a cylinder]
Hooray! said the ants. Maybe now we can visit each other! One of the ants, who was a bit braver and more adventurous than the other, immediately set out on a round-the-world trip in hopes of meeting his friend. He crawled and crawled along, leaving tiny prints behind him [I'm drawing ant's path with a marker]. Will he ever see his friend?
Soon the ant came to a set of tiny footprints. At first he got excited. Was that the marks left by his never-before-seen friend? Is he getting closer? But soon the ant realized that those were his own prints and he’s been crawling round and round his little world.
But what about the other ant? He too sat out on a journey, crawling along. Will he have better luck? [I'm drawing second ant's path with a different colored marker]. Nope, he too finds no one, just his own footprints. Their world had… how many sides? how many edges?
Poor tired ants needed a rest. But just as they were going to take a nap, their cylindrical world shook and twisted again. Again they got scared and closed their eyes and covered their heads and tucked in their antennas. [Here I cut the cylinder to turn it back into a strip; then I twist the strip and glue to form a Moebius strip]. When the twisting and the shaking stopped, they opened their eyes and looked at their strange new world. Maybe now that it changed they will be able to meet each other.
The first ant, the braver one, set out on his round-the-world trip once again. He walked up the hill and down the hill and across the valley [I'm tracing the ant's path with a marker] until… he saw the other ant! Hooray, the two cried and hugged each other. And then they walked back to the first ant’s home [a child is tracing the ants' path with a different color marker]. Their world was no longer flat. Was it a cylinder? Nope, it became something called a Moebius strip. How many edges does it have? How many sides?
And that was the story. But then we experimented some more. We made another cylinder and another Moebius strip, each with its own pair of ants. This time my son traced ants’ paths all by himself. Then I brought out the scissors and both worlds underwent another cataclysm, this time it was a continental drift (thanks, Ice Age 3, for the idea) as I cut the cylinder and the strip in half. Want to know what happened to the ants? Try it for yourself. It’s really very fun!
I remember that when I was little, I derived a sort of enjoyment, a feeling of accomplishment, from doing math worksheets. For better or worse, my son is the exact opposite. Worksheets do nothing, but turn him off math. And so do most of the puzzles. But he loves stories. So a lot of what I do is tell stories.
The first time I told a cut-and-fold story was a long time ago. We were exploring symmetry, playing mirror games and building with blocks before. That first time I folded pieces of paper only 1 or 2 times before cutting while telling a story. My son really loved it, but then we moved on to other things…
But a few weeks ago I read a wonderful post on the Map is Not the Territory blog. In her Scissor Stories post, Malke not just posted the pretty photographs of symmetry art (like the one above), but wrote a detailed script, a story she told to a group of children. While my stories were monologues, she conversed with children, asked them questions, and helped them notice the math in the story. I encourage you to read Malke’s post. It was so inspirational to me, that the very next day I tried our cut-and-fold stories again, this time in a way Malke’s done it.
The story I told my son was about three friends. He immediately made it about him and his two best buddies and how they were ninjas. Each friend was represented by a square of origami paper. We then folded each square, trying to predict what would happen to them after each fold. Then each square ninja had some adventures along the way and made some tough choices. In the end, we tried to predict what each square would look like. Typically, my son does not like guessing, but he was so into the story, that he kept offering his predictions throughout the game. And, unlike his usual answers of “I don’t know” and “A million” and “17 million and twenty five” the guesses he offered were well thought-out and he could usually explain how he arrived at them.
Unlike Malke, I totally forgot to take pictures throughout the game or record the narrative. But honestly, if you read Malke’s post, you will know exactly what to do and will see all the opportunities for improvisation.
I promise that next time I tell math stories to my son, I’ll keep a better record of them. Would you be interested in these stories? Do you tell math stories to your children? Would you like to share them on this blog? If yes, e-mail me at yelena(at)moebiusnoodles.com If you already have your stories posted on your own blog, please share a link in the comments!
Lately my 5-year old has been very interested in signs – road signs, signs at the entrances to parks, museums, office buildings, etc. Which led to some really interesting conversations about how rules (and ideas in general) can be represented as symbols.
Unlike written words or letters (which are symbols as well), well-designed signs are much more intuitive and easier for pre-readers and early readers to interpret independently. By the way, have you ever noticed how many of the signs we encounter are the ones that prohibit something rather than inform or encourage? I never did until my son pointed it out saying “see, this sign says no smoking, this – no drinking, this – no music, this – no guns. Signs are for saying “no” to things.”
So back to the conversation that we, my son (S) and I (M for Mama) had a few days ago:
S: Mama, when my tree house is finished, I’m going to invite all my friends and put a big sign “no girls allowed”
M: How would you make a sign like that?
S: Easy, I’ll just make a big red circle with a thick line across like that (draws in the air) and there will be a girl on it, like on bathroom doors.
M: Ok, but what if your cousin A comes to visit? Can she play in your tree house? (My son loves playing with his oldest cousin)
S: (after some thinking about it) Sure!
M: But then you need to make a different sign. What would it look like?
S: (after some more thinking) Ok, I’ll just put her picture next to the other sign. It has to be a smiling picture.
M: What if (names of a couple of girls he knows well from playdates) want to come play? Will you let them into the treehouse?
S: (after even more thinking) Yes. All girls I know can come and play. Only girls who are strangers can’t come. And if they are not very little.
M: Ok, but then you have to change the sign.
S: (sounding a bit weary) I dunno. Put more pictures. (runs away)
We had a few more conversations about signs that were similar to this one. My son would come up with a very broad rule and a sign for it. I would then suggest scenarios that did not fit the rule and he’d adjust the rule. And we’d try to figure out how to create a sign that would accurately reflect the new rule.
Since all these conversations were completely “on the fly”, usually while walking or right after reading a bedtime story. Which, I figured out, is not the best time since we don’t get to put any of the sign designs on paper.
But now I’m thinking what kind of a sign-making game can I put together (something that wouldn’t take too long). Any suggestions? Please share!
Today’s game comes from Julia Brodsky, the creative force behind The Art of Inquiry math circle in Maryland. Started several years ago by Julia as a thinking circle for her own children and their friends, it grew quickly. Julia teaches children the skills of solving non-standard open-ended problems using critical thinking.
While Julia’s thinking circle is for elementary school age children, she is sharing a game for younger children that she played when her kids were smaller. Without further ado, here’s the Magic Transformations game.
Pattern, prediction, transformation, unknown, input, output
How to Play
Prepare a big “wizard” hat and a “magic wand.” Prepare a set of small toy figurines (Safari Wild Tube, animal counters, matchbox cars, or something like that).
Show a toy to a child. Turn the hat upside-down. Put a toy under the hat. Say a spell and touch the hat with a magic wand. Put your hand under the hat and take what was hidden under the hat beforehand out of the hat. Voila – the toy turns into a different toy!
Ages and Stages
Baby: Start with just one item. The babies are just learning about the predictability of the events. They love when nothing new happens! The doggie goes in, the doggie gets out – let the baby watch it enough times, and watch the baby’s enjoyment. Just as the baby starts losing interest in the game, add another item – let the doggie turn into something else, different in size and color, and watch your baby’s reaction.
Toddler: Ask the toddler not to touch the hat – explain, that if the hat is touched, the magic will break. Decide on the rules of the transformation, but do not let your toddler know that rule – i.e the 4-legged animals always turn into 2-legged animals, and 2-legged animals always turn into toy cars. Make sure your hat has enough resources inside, and do not forget to “recharge” your hat after each manipulation, as needed. Ask your toddler to do something to distract his/her attention during this moment. See if your toddler will figure out the pattern, and will be able to predict the next transformation result.
Older child: Show the trick with the hat to an older child. Wait till the child figures out the transformation rule (you may come up with a 3- or 4-step rule). Now, ask the child to come up with another rule, and try to figure out that rule.
This is a perfect opportunity to use all those little toys children accumulate and love to play with. And how about using cartoon time to get inspired for more magic transformation play with this Moomin story?
I recently borrowed a large basket full of Mr. and Mrs. Potato Head parts and my son and I played a fun game with lots of math in it. It went something like this:
Step 1 – I taped out a small grid on the floor using blue painters tape – this was Mr. Potato Head’s apartment building
Step 2 – I placed different elements in the cells in the column and row headers – different types of hats, shoes, different noses
Step 3 – I asked my son to put together a Mr. Potato Head that lived in a particular
I explained how a Mr. Potato Head in each cell would have a combination of two elements from a row and a column that, intersecting, form his apartment. Once these two elements were in place, my son could choose whatever other parts he wanted to complete a Potato Head (the funnier, the better).
Once all apartments were occupied, we took a few Potatoes out of their cells (the more active and adventurous few since the rest turned out to be couch potatoes). Naturally, after a while they had to be returned to their exact apartments. It was like playing the game in reverse and it was much harder (to simplify the task, make sure that the rest of the Mr Potato Head’s parts are the same – same eyes, ears, arms, etc).
This game can be played with just a couple of Mr. Potato Heads (you can change the scenario to Mr. Potato Head has to wear a disguise as he moves around the grid). Even if you only have 1 Potato Head and not enough accessories, you can still play this game by drawing the grid and the elements on paper.
A few days ago my 5-year old and I were busy picking peas in our vegetable garden. The 30 or so pea pods looked so delicious, that we decided to eat them right away. And since shelling pea pods takes some time, we had a moment or two for the all-about-peas math:
- Each pod snaps into two halves length-wise. Let’s count how many peas are in each half?
- How many peas are altogether in each pea pod? Let’s count them to make sure.
- Can you see without counting how many peas are in each half?
- Can you tell how many peas are in a pod without counting? (this can be done either with subitizing or by adding peas from the two halves)
- Which half has more peas in it?
- Does this pea pod have more peas in it than the one before?
- Can you divide peas from this pod between the two of us so we both get the same number of peas? Why? Why not?
- How many peas do you think will be in this pod? (keep track of this data; we found out that most of the time we had pea pods with 7 peas in it; 5 was also pretty common; only a few pods had 3 peas in them; just one had 8 peas; there were several pods that appeared to have 6 peas, but on closer examination we would always fine the 7th tiny pea at the tip of the pod)
- Do you think we will get a pea pod with no peas in it? With 100 peas in it?
- What do we find more often – pea pods with odd or even number of peas?
Now summer carrots are almost ready for picking. I’m thinking we might explore gradients (length, thickness, weight, taste), fractals (carrot leaves), measurements (including how tall are you measured in carrots).
Have you tried garden math? Share your story in the comments or link to your blog post.
As we are getting ready for the Moebius Noodles display, we continue to be on high alert for great ideas that introduce grids to children. So I was really excited to see an art through math activity for young children on one of my favorite blogs, The Educators’ Spin On It.
The idea is to use grids to help make a copy of a picture. Inspired by a local chalk art festival, Amanda of the Educators’ blog decided to create chalk art with her children. The results are beautiful and Amanda documents the entire process with wonderful photographs (which she so generously allowed me to use in this post).
Amanda notes that even toddlers can participate in this activity. And the idea lends itself easily to customization based on your child’s interests. Amanda chose a picture of the beautiful St. Basil’s Cathedral in Moscow to reproduce. Your child might be more interested in something else (I’m pretty sure that mine is going to ask for either WALL-E or a Star Wars clone trooper).
You can also choose a different art medium – paints, crayons, markers, even thumb prints (hey, that would be a fun idea to try). Or, if your child has a favorite picture that’s very large (say, poster-size), you can try making a smaller version of it.
Thank you, Amanda!
If you haven’t yet, do read Amanda’s entire post, get inspired and try it this weekend! When you do this activity with your children, take pictures. You can upload them to Facebook and share them on our page. Or you can post them to your blog and link to the post on our Facebook page or in the comments.