In an associated file, I show PRESCHOOL KIDS how to contruct a PECKING ORDER ON 3 PEEWEES. For ELEMENTARY SCHOOL KIDS this becomes a lattice (L₃₀) on factors of 30 = 2 x 3 x 5, 3 primes.

                                      30 ("SUPERCHICK")
                                      /\
                                     /  \
                                    /  | \
                                   /   |  \
                                  /    |   \<---- FACTOR-MULTIPLE-LINES ("PECKLINES)
                                 /     |    \
                                /      |     \
                               /       |      \
                              /        |       \
                             /         |        \
                ("MIDDIE")  6         10 (MD)    15 ("MIDDIE")
                            |\        / \       /|
                            | \      /   \     / |
                            |  \    /     \   /  |
                            |   \  /       \ /   |
                            |     /         \    |
                            |    / \       / \   |
                            |   /   \     /   \  |
                            |  /     \   /     \ |
                ("PEEWEE"}  2          3(PW)    5 ("PEEWEE")
                             \         |       /
                              \        |      /
                               \       |     /
                                \      |    /
                                 \     |   / 
                                  \    |  /
                                   \   | /
                                       1 ("YARDBIRD")

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In a PLAIN PECKING ORDER, NO PEEWEE PECKS A PEEWEE. This corresponds to a FACTOR LATTICE IN WHICH NO SQUARE OCCURS. In a MIXED PECKING ORDER, A PEEWEE CAN PECK ANOTHER PEEWEE. This corresponds to a FACTOR LATTICE CONTAINING A SQUARE, as below.

	   SUPERCHICK(12)
                /\
               /  \
              /    \
        PEEWEE(4)  MIDDIE(6)
             |     /|
             |    / |
             |   /  |
             |  /   |
             | /    |
             |/     |
        PEEWEE(2) PEEWEE(3)
              \    /
               \  /        
                \/
           YARDBIRD(1)

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By working with PECKING ORDERS IN PRESCHOOL, KIDS PREPARE FOR THE CORRESPONDING FACTOR LATTICES IN ELEMENTARY SCHOOL, AND LOGIC LATTICES IN HIGH SCHOOL. These become other fields of MATH if pursued far enough.