in the limit | don steward

puntmat posted an interesting idea (7th August 2014) involving various functions and exploring their limit as n gets very large indeed (tends to infinity)

these resources have a similar intention
what fractions are shaded with a colour (out of the whole rectangle) at each stage?
what happens as the shape gets bigger and bigger?

all give rise to a common set (or subset) of fractions
with the same limit

the puntmat post helpfully included some animated gifs for two of these sequences:

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fractions of rectangles | don steward

this is practice in areas of shapes
with the question reversed – given the area, what could the shape look like?

students will hopefully seek suitable base and height dimensions
(possibly forgetting that in a triangle the area involves halving)

some questions have two solutions
this can create opportunities to discuss why e.g. triangles with the same base and between two parallels have the same area

it’s been suggested (thanks Tom) that you need blank grids on the back of each sheet

these could involve finding areas by dissecting a rectangle

the bottom left two can be justified…

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