Playing with Platonic Solids
There’s a lot of talk about how playing with building blocks helps children develop math skills. But what about children that are too young to even “tote and carry” blocks? Have you thought about introducing them to Platonic solids? Ok, here’s a little refresher about Platonic solids:
A Platonic solid is a 3D shape where each face is the same regular polygon and the same number of polygons meet at each corner.
If the idea of introducing this concept to a small child sounds a bit over the top, here’s a surprise – your infant might already be enjoying one. After all, a cube is a Platonic solid. But why leave out the other four – tetrahedron, octahedron, dodecahedron, and icosahedron? That’s exactly what British mathematician Richard Elwes and his wife Haruka have done. Here’s Richard’s story:
When some friends told us they were having a baby, Haruka set to work making a soft cubic toy to give the child, by sewing together square patches of colourful cotton cloth left over from other projects, and stuffing it with cushion-filler. Being a mathematician, Richard immediately suggested the set should be expanded to include all five Platonic solids. (One challenge was to make sure that no two adjoining faces were made of the same cloth.)
These toys are intended for very young children, so it cannot be expected that they will ‘learn geometry’ in the usual sense. Instead, what we hope is that they will begin to foster a geometrical aesthetic, enjoying the symmetries of the toys, and developing a familiarity with these five solids, which will remain throughout their lives.
As the children grow older, we hope they will keep revisiting the Platonic solids in other forms, perhaps as wooden or plastic toys, maybe as dice or puzzles, later making them themselves out of paper or card. But there is no need to stop with the Platonic solids! As soon as practical, why not introduce shapes like prisms, antisprisms, and Archimedean solids (along with their duals: bipyramids, trapezohedra, and Catalan solids)?
For a small child meeting the Platonic solids for the first time, there is is one potential problem: apart from the cube, the names of these shapes fail to reflect their elegant simplicity. For a toddler, the word “icosahedron” is surely a bridge too far. So why not reduce them to their initial syllables: tet, cube, ock, dode, & ike? This will allow the child to have fun identifying and comparing the shapes, without getting bogged down in unnecessary Greek verbiage.
Posted in Grow
Math Magic – Magic Transformations Game
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.
Key words
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?
If you haven’t yet, check out Art of Inquiry website, watch some math circle videos and try your hand at sample problems.
Posted in Make
Moebius Noodles Newsletter is Live
Have you seen our first newsletter? Then you are familiar with our mascot, Moby Snoodles, the math whale. If not, here is the link and don’t forget to sign up through the form in the side bar or here. You might be wondering why do we need a newsletter. Or you might be wondering why would you read it. So here are some answers:
1. Book Updates
Thanks to many of you, this project, a book of advanced math games for very young children, has become a reality. We are working on putting it all together and would like to keep you informed of our progress. Plus, we want to share with you not just the finished and polished book, but take you on behind-the-scenes tour of its development.
2. Stories
If math is indeed all around us, then why is it oftentimes so hard to notice? Maybe it’s exactly because math is all-pervasive, woven into the fabric of our daily lives. We think of math as numbers. Yet our daily life is not expressed in numbers, but rather a narrative, a story. Stories fascinate, surprise, delight us, adults and children alike. We think sharing math stories, ours and our friends, will help us get better at recognizing math in our daily experiences.
3. Beautiful Lapware
Do you know what else is fascinating, surprising and delightful? Toys! We can’t bring you regular toys, so instead we find free online activities and games that help your children create beautiful math in a matter of seconds. We call them lapware. We usually post links to them on our Facebook page. Once in a while we find a particularly engaging lapware which we will highlight in the newsletter.
Of course, we would love to hear your feedback. How can we improve our newsletter to make it even more interesting and helpful for you? Remember, you can always Reply to our newsletter via e-mail (Moby has his own e-mail box moby@moebiusnoodles.com), leave a comment on our Facebook page or on this blog. And don’t forget to subscribe to our newsletter if you haven’t done so yet.
Posted in Newsletter
Small Moments of Math
Today’s post comes from the wonderful Malke Rosenfeld of Map is Not the Territory blog. Malke combined her background as a percussive dancer with her love of math in a unique Math in Your Feet program. It is a fusion of math, dance, rhythm and the creative process that helps children build deeper understanding of mathematics.
Malke: On my blog I often write about the times when mathematical inspiration hits but, most of the time, our daily lives are made up of smaller, less dramatic math moments. It’s during these lovely transient events where I really get a good glimpse at how my daughter is thinking, mathematically speaking, and how she is applying her understanding in a number of different contexts.
How we play:
My approach to math exploration at home has been hands-off, necessitated by a child who likes to captain her own ship. Math generally happens in bite-sized pieces around here. While I do influence the process, I hardly ever make formal plans. Instead, I am always looking for new games, thinking about what she might need or want to learn next and also how to introduce new things in a way that has the appearance of being at least 50% her idea. I also leave stuff lying around to be ‘discovered’ or engage in my own pursuits, which inevitably leads to some curious inquiries from the wee bystander.
Here are some examples of the small moments of math that have been happening around our house lately, all symmetry related.
This originally started as a whole lunch, but when the kid saw the design with a whole tomato in the center she insisted in cutting it in half before eating:
I am a big fan of the Reggio Emilia approach, particularly, of a belief that the child’s environment can and does influence children’s learning in very powerful ways. This includes meal time! I like to arrange meals in a pleasing manner and this plate lent itself wonderfully to creating a rotation design of four pieces of a whole, round chicken patty alternating with the tomatoes.
You can also use any items that interest your child to make spontaneous symmetry designs, anywhere you are. One morning I noticed my daughter creating a reflection design after breakfast, utilizing her rock and mineral collection.
This kind of activity can be initiated by anyone, though, as long as it’s done with a playful spirit. The main point is that balance and symmetry are pleasing to look at but also a joy to create. As a parent, you are in the best position to model the spirit of discovery through these playful moments. Often, all I have to do is start an inquiry with blocks, tangrams or other shapes and the kid takes over within minutes. Little jewels of math are all around us just waiting to be discovered at unexpected moments!
Key words that you can introduce during such activities are
- Whole
- Half
- Opposite
- Center
- Turn
- Reflect
- Balance/Balanced
Additionally, you can offer these activities, suggestions or make observations during and after play time:
- “Look! I can turn your lunch on this plate and it looks the same no matter how far it turns around!”
- “We’ve got five on one side and only four on the other – let’s balance out our design by making them the same on both sides. How can we do that?”
Symmetry is something that even the very young children can joyfully explore as long as you modify the activities to match your child’s age and developmental stage.
Baby: Cut out large symmetrical shapes to hang above the baby’s changing table or crib. Add a mirror (safe non-breakable) to your baby’s selection of toys and place objects in front of the mirror forming simple designs.
Toddler: Use larger items, model making simpler designs while offering child a chance to help you.
Young Child: Observe child as they play and find those ‘small moments’ as they happen. Initiate reflection and rotation designs at a playful moment – sidewalk chalk at the park (make a chalk outline of your child, have them draw a line down the center of their body) or be on the lookout for examples of symmetry as you go about your day. Take a look at the ‘symmetry finder’ game on Yelena’s blog which is easy to do anywhere and anytime you notice reflection symmetry happening.
Some more ideas for exploring symmetry through playful activities and art include
Butterfly designs using cut paper (Adult narrates while folding and cutting):
“Let’s make a butterfly! What color paper should we use?”
“I’m going to fold this paper in half. I’m cutting out the butterfly shape.”
“Here is what it looks like when the wings are folded. Let’s open it up and see the whole butterfly!”
“Let’s decorate our butterfly! I’ll color a spot on one wing and you draw the same spot in the same place on the opposite wing.” [Or, you could pre-cut some paper shapes – circles, stripes – and glue them on with gluestick.]
Line Designs (Adult says, drawing a line down the center of a piece of paper):
“Let’s make a design on either side of this line using our Cuisenaire rods (or pattern blocks, or legos…)”
“When I put down a blue rod next to the line on my side, you put your blue rod next to the line on your side.”
Adult leads for a while then asks child to lead. You can alternate turns. Try to keep all block placements in relation to the line or other blocks already placed. For older kids, you could use graph paper to position your blocks. (“How many squares is this block from the line?”)
Be My Mirror
Even toddlers would love a chance to be your mirror! Notice your reflections in the mirror with your child. Give your reflection a (gentle) ‘high five’. Notice how your reflection’s thumb and fingers match your own. Use this idea at other times to initiate a Mirror Game with your child. Start by saying, “Can I be your reflection? Let’s face each other and you make a slow movement and I’ll try to copy it.” If your child is ready, see if they can mirror/reflect your movements as well. Use all parts of your body, including your tongue (!), eyes, eyebrows, elbows, knees, etc.
If you haven’t had a chance to check out Malke’s blog, you are going to love it. Not only does it have lots of ideas for exploring math all around us, but also wonderful stories that, like “Small Moments of Math” and “Small Moments of Geometry” help us, parents, notice the rich mathematical opportunities in our children’s lives.
Posted in Grow
