`The Generation Of FractionsJune Muhammad                  Park Manor School                               7037 S. Rhodes                               Chicago IL 60637                               312-535-3070Objectives:      To use a unique multiplication grid to help students realize that simple    fractions (reduced fractions) may have many appearances, but have the same     value.    To help students learn how to factor each denominator completely.  Materials needed:    Group of four students      Four 5 x 8 1/2 white tag boards    Ruler                       Red construction paper for apples    Glue                        Green construction paper for trees    Masking tape                Brown construction paper for tree trunks       Black marker                Make grids for multiplication tablesStrategy:    Students will select fractions written on cut out apples from a bag.     To begin use only even number fractions.     Example:  The fraction 12/24 is selected by the students.  Students look    at the multiples of two column, and then count down to 12 grids in the    multiples of two.  The students stop on the sixth grid.  Ask students to    record where have counted.  The students' final fraction should be 1/2.    Remind the students that they must change multiples when the selected     fractions can be further reduced.    The fraction 3/6 requires that they leave the multiples of two.      Students can visualize reduced terms and the final simple term.  When odd     fractions are selected students can compare how each fraction is divided by     one and itself. Performance Assessment:    Students write five higher term fractions for one simplified fraction.      Teacher observes and records results.    All higher terms and reduced fractions are hung on the tree.    Odd fractions are hung on a crab apple tree.  Multicultural Aspect:    Fractions were invented by the Ancient Egyptians.Conclusions:        This activity may be used for small or large groups of students.`