The teacher will coordinate and record this activity.
Preparation: Teacher draws 11 slots on the
board, and writes "0" in the first and "10" in the
last.
0 10.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
Teacher draws a number-line with the points 0,1,..., 10
labeled.
--+---+---+---+---+---+---+---+---+---+---+--
0 1 2 3 4 5 6 7 8 9 10
Teacher reminds the class of the three conditions:Producing the next number. "What do I put in this first slot?" Students will figure out that it has to be odd. Hold out for a fairly large one, like 7 or 9 (makes maze more interesting). When the number is decided on, write it in the slot and draw the corresponding segment in the appropriate place above the number-line. Go on to the next number, which will be even. When it is chosen, write it in its slot and draw the corresponding segment below the number-line. Suppose the first choice is 9, and the second choice is 4. then the number-line diagram will show
_____________________________________
--+---+---+---+---+---+---+---+---+---+---+--
0 1 2 3 4 5 6 7 8 9 10
_____________________
Continue until all the slots are filled. For example,
if the sequence chosen is 0 9 4 7 6 5 8 1 2 3 10,then the number-line picture will be
____
____________________________
____
_____________
_____________________________________
--+---+---+---+---+---+---+---+---+---+---+--
0 1 2 3 4 5 6 7 8 9 10
_____ _____________________
_____
_____________
______________________________
Getting stuck. Fairly often, there is no way to
choose another number that is compatible with the rules.
What has happened is that the class has found a smaller
maze. If you want to keep it, you should
renumber
the entries to "count around" the unused numbers. Otherwise
start over, or look at the number-line picture to see
where a different choice would solve the problem. With
a little experience, the teacher can see these problems
coming and can "guide" the choices to avoid them.
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