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Look at the multiplication table and find your favorite cell or fact. Some people like full squares, such as 5*5=25, some like doubling, such as 2*7=14, and some like facts that are the hardest to remember: 6*7=42, 7*8=56, and so on.
Having selected a fact, find as many ways as you can to represent it. What IS multiplication? I am selecting 4*5=20 for my example: what is four times five? I double dare you (Double! Get it?) to find or to build a good definition for multiplication. It's very hard. Bring an army. - See if you can find some examples around you. 4*5 is fingers and toes on our four limbs!
Maybe you can make this multiplication out of some objects in the house. Cookies? Legos? Letters of your name? MMMMM MMMMM MMMMM MMMMM If four ladies want to kiss five frogs, each lady trying every single frog to see if it will turn into a prince for her... Is multiplication about love and kisses?
How much is four nickels? Many countries have coins worth five, like the American nickel, but did any country in the world ever made a coin or a banknote worth four? I don't know of any - do you?
I can probably represent 4*5 in more than a hundred ways, each different from the rest. Five measures of music with four notes per measure. A fragment of a dance to go with that music. Four exotic fruits, each experienced by our five senses. The number of outfits made with four skirts and five shirts. I have collected ways to represent multiplication for years, and it's been an adventure. This poster shows a few of the most common representations. I vividly recall a roomfull of researchers at an international conference in Hawaii, coming by my multiplication board to contribute to the collection of representations: the mundane, the bizarre, the incomprehensible. Researchers like to show off. It is fun to do this activity in groups of interested people - kids, teachers, parents, mathematicians. You can even do it competitively, as researchers did, I suppose - seeing who can find the most interesting representation, or who can find more of them, or whose representations are the easiest to understand for young children, or the hardest to understand for anybody. A kid starting to work with multiplication can usually find two or three different ways to represent each fact. My challenge of the day: find at least ten ways to represent your favorite fact. It is, after all, the favorite. Honor it well. More detailed description of how to support the two activities offered here: Definition Wars . Two or more people can play this fast-paced, emotional game. It does not require any materials, so it's great for car trips. Representation collections <link coming soon>. This can be a solitaire activity, a face-to-face group game, or an extended distributed project, for example, in a blog or a forum.
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