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Teachers appreciate that children understand mathematical concepts best when the children are given an authentic problem to solve and time to invent their own mathematical strategies. In this videative, kindergarten children have an authentic need to know the total number of pumpkin seeds that come from four Halloween pumpkins. And on another day, they need to know how many checkers they have yet to make for the checkerboards they are giving as gifts. These two experiences illustrate the children's cleverness as well as the teacher's willingness to allow the children to apply a strategy to see how it does not work.

During one segment of the video, Jensen and two friends decide to count a large pile of pumpkin seeds. The girls divide the supply of seeds into three piles to individually count and then add their subtotals together. But this task soon becomes overwhelming. So in another segment of the video, during which Jensen is faced with another counting task involving checkers, she places two checkers on each plate so that she can count by twos. This way she does not have to add several large sums as with the pumpkin seeds and it is easy for her to see that there are exactly two checkers on each plate. While this checker counting strategy represents an improvement on her pumpkin seed counting strategy, a few problems still remain.

Keywords: Fives, Counters, Children-Teacher, Counting, Sets, Base Ten, videative

Length of videative: 6 text pages, 11 video subclips

Length of stand-alone master video clip: 8 minutes, 18 seconds