Rod Fractions

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


What fraction is the yellow rod of the orange rod? 

 


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Rod Fractions


Use this picture to help you. Note that it only uses orange and yellow rods.

 
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Rod Fractions


You might like to use the interactivity further down this page to help you answer the following problems:

Using as many brown and red rods as you like, but no rods of any other colours, work out what fraction the red rod is of the brown one.

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Rod Fractions


Using as many red and orange rods as you like, but no rods of any other colours, work out what fraction the red rod is of the orange one.

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Rod Fractions
 

 


Can you find any other pairs of rods so that the length of the shorter rod compared with the longer rod is a fraction with 1 as its numerator? 




Given an unlimited supply of any two differently coloured rods, can you find a general rule to work out what fraction the shorter rod is of the longer one?

You may like to explore this by using the pairs of colours suggested below as starting points.

Dark green and blue:

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Rod Fractions
 

Pink and orange:

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Rod Fractions
 

Light green and orange:

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Rod Fractions
 

Why does your rule work?

Now, looking back at the different pairs of rods you have explored, can you find a way to express the longer rod as a fraction of the shorter rod?