How would you explain to a 4th grade student why subtraction and division
of fraction is so difficult for J. Here is a dialog I wrote to review all
the big ideas students should remember from third grade. Tables show how
some verbs like + and times are commutative and * and % are not. If the verb
is commutative you need only "master" a little more than half of the table.
+/~i.5
0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
-/~i.5
0 _1 _2 _3 _4
1 0 _1 _2 _3
2 1 0 _1 _2
3 2 1 0 _1
4 3 2 1 0
*/~i.5
0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12
0 4 8 12 16
%/~i.5
0 0 0 0 0
_ 1 0.5 0.333333 0.25
_ 2 1 0.666667 0.5
_ 3 1.5 1 0.75
_ 4 2 1.33333 1
1r3%i.5
_ 1r3 1r6 1r9 1r12
+/~ 1r3%i.5
_ _ _ _ _
_ 2r3 1r2 4r9 5r12
_ 1r2 1r3 5r18 1r4
_ 4r9 5r18 2r9 7r36
_ 5r12 1r4 7r36 1r6
-/~ 1r3%i.5
|NaN error
| -/~1r3%i.5
*/~ 1r3%i.5
_ _ _ _ _
_ 1r9 1r18 1r27 1r36
_ 1r18 1r36 1r54 1r72
_ 1r27 1r54 1r81 1r108
_ 1r36 1r72 1r108 1r144
%/~ 1r3%i.5
|NaN error
| %/~1r3%i.5
t=: 13 :'>:/~i.y'
t 5
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
1 1 1 1 1
(t 5)*+/~i.5
0 0 0 0 0
1 2 0 0 0
2 3 4 0 0
3 4 5 6 0
4 5 6 7 8
(t 5)**/~i.5
0 0 0 0 0
0 1 0 0 0
0 2 4 0 0
0 3 6 9 0
0 4 8 12 16
(t 5)*+/~ 1r3%i.5
_ 0 0 0 0
_ 2r3 0 0 0
_ 1r2 1r3 0 0
_ 4r9 5r18 2r9 0
_ 5r12 1r4 7r36 1r6
(t 5)**/~ 1r3%i.5
_ 0 0 0 0
_ 1r9 0 0 0
_ 1r18 1r36 0 0
_ 1r27 1r54 1r81 0
_ 1r36 1r72 1r108 1r144
Linda I
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