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This is pretty challenging … a grade 6 example might be ordering numbers on a number line. I originally thought of negative numbers, but that got a bit too challenging for me —
So I’l start with just simply comparing 2 fractions, say 4/5 and 2/3
Direct comparison – looking at visual models of the fractions (bar models) to determine which is bigger
Indirect comparison – using something like a strip of paper or a string to measure the length of each fraction and then compare those strips (??? not sure about this one)
Direct measure – using unifix cubes to build equivalent models of the fractions (dividing into the same number of parts – 15) and then count the cubes to compare those quantities
Indirect measure – creating fractions that have common denominators and then comparing numerators
This does seem pretty complicated but there are some deep understandings that could be uncovered and critical connections to be made through this type of representation.