Teachers learn Fraction Multiplication using a grid

work it out!
I find that most of the teachers do not understand the logic behind fraction multiplication. They know it as a rule because they were taught it as a rule and because the teacher's teacher also was taught it as a rule. However, somewhere along the line, someone got to ask "but why". Students of course ask, but the teachers also should wish to know the WHY!
So I make them do this simple activity on paper or graph paper.
To multiply 1/7  and 1/5, draw a 7 by 5 rectangle and sill it with lines as shown. Shade 1/7th of it and then shade 1/5th of it. How many rectangles are shaded twice?...that is the answer.
This is what leads to really the meaning of 1/5th of 1/7th. That we first find 1/7th and then 1/5th of 1/7th.
One can take this forward using pictures or stories...up to us!
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