Fun with Functions

httpv://www.youtube.com/watch?v=OlO8RvA3Jb4

If you’ve been burned on school math, like I have, you might cringe at the idea of introducing functions to your child. Children don’t start studying functions until later in school. But why wait? After all, children learn about functions very early on through toys as well as daily observations. Besides, functions can be way cool or at least familiar to all involved.

Think about your dishwasher – you put dirty dishes in (input) and, after a while, take the clean dishes out (output). As long as the input is consistent and your dishwasher doesn’t break, the output will be the same – clean and dry dishes. That’s an example of a function machine that even the youngest children are familiar with and curious about.

A vacuum cleaner is another example of a function machine. If you happen to have a model that allows certain adjustments, you can make your vacuum blow air out instead of sucking it in. In which case it is a machine with an inverse function.

So there you go, these are

BIG Math Concepts

• Function
• Input
• Output
• Inverse function
• Transformation
• Result

Take a look at your child’s toys. How many of these are function machines? In my house we have a couple of marble runs, several remote-controlled cars, a no-longer-used shape sorter that makes a sound with every correct match, and many others. All these toys are function machines. I bet you have quite a few of these on the shelves and in the toy boxes.

You can also invent a machine all of your own. Sketch or build a “function machine” that takes objects in and then transforms them. Make up a rule your child will be able to guess, but not immediately. Let the child put in objects or numbers a few times to see what happens to them and to guess the transformation rule. Take turns building more machines and guessing their rules!

Experiment with functions that find correspondences:

• input: age, output: age two years ago
• input: female animal, output: male animal (mate), for example, hen-rooster, doe-buck
• input: baby animal, output: adult animal (help babies find parents), for example, kitten-cat, puppy-dog

Infants  – Use qualitative functions, for example, a machine that adds a sticker to each toy the baby throws into it, or a machine that finds its mommy for each baby animal

Toddlers – Invite toddlers to change the first object and then repeat that same operation on other objects, for example, give each toy animal its favorite food (dog-bone, bird-seed, rabbit-carrot). Start using simple quantitative functions, such as the machine doubling whatever enters into it, or giving every character two raisins to eat (so, if several enter, you need to prepare enough raisins).

Older Children – Kids enjoy making up fancy machines that are hard to guess. Once you have the game going, you can play it in the car or on walks, for some oral computations. Kids may argue if the guess, “The machine doubles” is correct about their “Add the number to itself” function – help them figure out what’s going on!

Other ways to explore function machines

• Story ideas: Many fairy tales and science fiction stories have magical or mechanical objects that transform you or your stuff powerfully, for example, people turning into animals and back, cooking lots of porridge, or building palaces.
• Find function machines in everyday life. Some turn dirty clothes or dishes into clean ones, others turn cold things into hot things, or paint the object another color.
• Build the function machine that gives each animal its “house” or habitat; again, you will need pictures. A wonderful book for this activity is Mary Ann Hoberman’s “A House is a House for Me”.
• Play with the function machine that makes animal sounds for each animal that enters. You can use toys.
• The mirror machine: when the kid draws anything and inserts it into the machine, it makes the mirror image of it on the same paper.
• The upside-down machine turns everything that enters upside-down. Make sure to invite the kid to enter!
• The zero machine: a critter in the machine eats everything that comes in. Out of the machine always comes – nothing!