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>we played a game in which you had to be able to envision the impact of different numbers in the numerator and denominator of the divisor in order to create a winning strategy.

Would you describe the game?!

This is great, thank you!

The game is similar to many that Marilyn Burns describes in her Extending Fractions book but the kids were excited that it was one that I made up specifically to help them feel more secure (we've talked a lot about the role of games and strategy in helping their brains really make sense of a concept.)

The game: Draw a box followed by a division sign followed by a fraction with a box in the numerator and denominator. Draw two boxes below that for your throw away numbers. Your opponent does the same thing. One rolls a die (we used 10 sided) and decides which box to put the digit in (choices are the whole number dividend, the numerator or denominator of the divisor, or trash). An extension was to make the dividend a fraction as well (but that can give you a fractional quotient which really pushed on their still fragile understanding).

Another new game we made up together was to roll the die to create a target fraction (we only allowed proper fractions) then each person draws a decimal point and three boxes for place value to the thousandths. Like before, there are two boxes for trash. This time, one has to use a 10 sided die because you try to get the decimal closest to the target fraction (WITHOUT USING A CALCULATOR to figure it out). Then students compared decimals and decided who was closest (using a calculator to check if necessary).

With these and all games, the discussion of strategies yielded rich insights for how the numbers interacted and successful ways to use estimation and mathematical logic.

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