Just a Little Beautiful Math Thing
One of us, Maria, recently posted this on our Facebook page:
This is what I call “lap-ware”: a little beautiful thing you show a toddler who climbs into your lap as you work on your computer. Even someone who knows nothing about math can change, say, 2 to 3 in the formula and observe the (beautiful) results. Math experimentation for the w
And the other one of us, Yelena, tried it with her son. The results where exciting and unexpected.
The first thing that my almost 5-year old boy said when he saw the original graphics was “Wow! Can I see it again?!“. That sounded promising. So I told him that not only could he watch it, but he could control it and change it HIMSELF! Immediately he was eager to try his hand at manipulating the graphics. I showed him the formula and explained that it was a coded command, called a function, that he could control by changing one, two or three parameters and put his own numbers where the original 2, 2 and 0.7 were.
First, he replaced the first two numbers only and kept the third one, 0.7, the same. He tried 1, 3, then 7. Then, as he was about to try plugging in 4, I asked him what he thought the result was going to be. Was it going to be flat, similar to what he got when he put 1 into the equation. Or was it going to be all scrunched up and spiky like when he used 7. After a bit of thinking, he predicted that, although the result wouldn’t be flat, it wouldn’t be as “wrinkled” as the result he got with 7. Even though his prediction turned out to be accurate, he was more thrilled with the ability to check his prediction than with the accuracy of the prediction.
Next, he wanted to plug in more different numbers. So we tried ages of all the family members, including our cat. In the process, I noticed that some of us were squares and others – triangles (depending on whether our age was an odd or an even number). This led to lots of giggles as we were trying to figure out who was who in our family.
As we plugged the number 100 into the formula (the age of a tree outside), something wonderful happened. My son looked at the graphics and exclaimed “Look, Mom, it’s also symmetrical!” And sure thing, it was.
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Mini Math Quest #1 – Symmetry Seekers
Ask a child to be a line of symmetry for an object or an arrangement. Children are natural symmetry seekers whether they are building with blocks, drawing with crayons, or mimicking your gestures. Help your child explore the concept of symmetry this week.
Go on a quick (just a couple of minutes) symmetry scavenger hunt around the house or outdoors. Make your own symmetrical art. Arrange toys symmetrically. Identify and clearly mark lines of symmetry. Keep your camera ready because symmetry is beautiful. Take a picture and send it to us. Don’t forget to include your child’s name (or first initial) and age.
Note: If you have privacy concerns, don’t let them stop you from participating in this Challenge. Your child’s face does not have to be in the picture. In fact, why not take a picture of your child’s shadow or a bird’s eye view (so just the top of the head is visible). The possibilities are endless!
Submissions close January 22, 2012 at 10pm EST
Send submissions to yelena@moebiusnoodles.com
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Playing Math Every Day – December 12 – 18
Math games can be played any time anywhere. Here are some ideas for each day of the week. These games require very little, if any, advance prep. Give them and feel free to change them to make math more interesting for your children.
December 12 – More Evergreen Fun
Remember our Evergreen Fun gradients game from last week? If you don’t have a tree farm nearby, you can still play it. Simply cut isosceles triangles of various sizes out of green paper or felt and let your child create her own trees.
December 13 – Magnetic Pompoms and Patterns
Have you ever tried magnetic pompoms? These are just regular pompoms, but with little magnets hot-glued to them. There are countless games that can be played with these pompoms. One of the games is making patterns and designs with them on a fridge, a cookie sheet, etc. Another absorbing game is making little pompom sculptures and figuring out in the process the difference between odd and even numbers.
December 14 – South Pole Day
On this day in 1911 the Norwegian explorer Roald Amundsen and his dogsled expedition reached the South Pole. How can it help learn math? Remember the real multiplication tables game? If one of the Amundsen’s dogs were to need warm booties, how many would it need? What if two dogs needed warm booties? Three dogs?
December 15 – Puzzles Day
Do you have a Pentomino puzzle? If not, it’s easy to make out of craft foam, cardboard or construction paper. If you have building blocks to spare, then you can use those too, just hot glue them together. Younger children might be more interesting in creating their own designs than solving actual puzzles. Still, Pentomino teachs such important mathematical concepts as rotational and reflection symmetry, chirality, and tessellation or tiling.
December 16 – Math That Is Hands (and Feet) On
Let’s continue learning about chirality by turning it into a mix of a scavenger hunt and an art project. First, let’s make some hand and foot prints. Are these symmetrical? Are these chiral? If your child needs a bit more help figuring out the answer, you can help by cutting out one of the hand prints and suggesting he superimposes it over the other print. Repeat it with foot prints. What about other objects around the house, such as blocks, LEGO pieces, sliced fruits and veggies, letters of the alphabet…
December 17 – Live Sculptures Fun
Let’s make live sculptures. The trick is your sculpture must be symmetrical to your child’s creation. But guess what… live sculptures sometimes move. Can you keep up and maintain the symmetry?
December 18 – Crazy Gumball Machine
How would your child like having a gumball machine in the family room? Well, what if this gumball machine had a mind of its own? A regular well-functioning gumball machine follows a simple rule: one quarter goes in, one gumball comes out. This machine is different. What kind of crazy wacky rule can it follow? Would it give 2 gumballs at a time? Red gumballs only? How about red gumballs for a quarter and green ones for a dime? Let your child figure out the gumball machine’s rule. Then let him take a turn controlling the machine.
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Playing Math Every Day – December 5 – 11
Math games can be played any time anywhere. Here are some ideas for each day of the week. These games require very little, if any, advance prep. Give them and feel free to change them to make math more interesting for your children.
December 5 – Rhythm is Math
Does your child love drumming? Have a drum circle and come up with simple drumming sequences for him to repeat. No drums? No problem. Pots and kitchen utensils will do nicely or, for a quieter version, cardboard boxes and paint stirrers.
December 6 – Mathematical Poetry
You can find some mathematical rhymes, but why not write your own math-y poems? Does it sound intimidating? Then start with a cinquain. It has a prescribed form, but does not require you to count syllables which can be confusing to younger children. But cinquain’s structure allows even very young children be involved in the writing process, not to mention illustrating the completed poem.
December 7 – Winter Weather Day
Sure, you can play a game of matching mittens and socks. Or you can explore geometry with some mini-marshmallows and toothpicks.
December 8 – Evergreens are Everywhere
By now there’s a Christmas tree bazaar on every corner. Why not use this opportunity to practice some measuring? What can a tree be measured with? Can it be measured with a paper clip? How about a mitten and arm length? Find the smallest tree on the lot and measure its height, say, with a mitten. Now find a tree a bit taller and see if your child can estimate how tall this tree is in mittens?
If there is a Christmas tree farm nearby that you can visit, you can play a game of gradients, finding taller and taller (or shorter and shorter) trees and taking pictures of your child next to them. Then print the pictures and ask your child to arrange the trees from shortest to tallest.
December 9 – Pinecone Fibonacci
Go on a walk and collect some pine cones of different sizes. Let your child explore the pine cones. How are the pine cones alike? Show the whirls on the bottom of the pine cones. Your child might be interested in painting the whirls different colors or making pine cone prints with them.
December 10 – Start a Collection
Does your child have a collection? What does she collect? What other people collect? Can you have a collection with one item? Two items? Play a scavenger hunt in the house looking for items that can be grouped together into collections. Photograph or otherwise record your finds.
December 11 – Dicewalk
The idea is simple – walk around the neighborhood and every time you get to an intersection, throw a dice to decide which way to go. For detailed instructions, including how to make the dice, check out The Artful Parent Dicewalking blog post. If your kids are too young to walk a lot or you don’t live in a walkable neighborhood, you can play this game in the yard or even indoors. How about making a very simple map of your neighborhood (or your living room) and mapping the route while you’re at it?
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