Circle 0

This virtual manipulative poses the problem:

Position the 14 numbers inside of the circles and intersections of circles in such a way that the three numbers in each of the circles sums (adds up) to zero.

Work on the problem by clicking on and dragging numbers to locations inside circles or intersections of circles.

When the three numbers in a circle add up to zero, the circle will change color.

Click on figure above to launch the Circle 0 virtual manipulative.

Teacher Information: Circle 0

This addition game encourages some logical analysis as well as addition skills. This particular "Circle" game uses positive and negative integers. Three others are variations on the same theme: "Circle 99" uses larger numbers, with a target sum of 99, "Circle 3" requires the addition of one-place decimals, and "Circle 21" combines positive whole numbers.

The blue numbers already in position when the manipulative loads are fixed. The remaining numbers (from -6 through 7) can be dragged into (or removed from) any empty space in the ring of circles. When the sum of the numbers in a circle is exactly 0, then the whole circle changes color. But it isn't enough to make a few circles in the ring add to 0. There may be several ways to make the first couple of circles sum to 0, but there is only one way to combine the given numbers so that every circle sums to 0.


One can drag numbers into a couple of target circles, but if a given choice appears to lead to a dead end, you can "back up" by removing any of the black numbers you've placed. Our experience suggests that it is a good idea to play freely at first, but pencil and paper are helpful to analyze what is needed to color the whole ring of circles.

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The New Game button provides another "seeding" of five blue numbers, so that a great deal of practice is available by repeated play. As students gain confidence and skill, it would be possible for two or more to race against each other or to record times.