Category Archives: Fractions

Fraction as function implicit in many lessons

After the natural numbers, 0, 1,2, etc. are introduced, the fractions are introduced.  What are they?  Did they already exist?  Or are they an operator on natural numbers? We can think of 1/2 as a function.  Its domain is the … Continue reading

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Fractions as mishmash

Fractions are taught as a mishmash of disparate ideas. These freely mix all types of concepts and applications of fractions a though they are on an equal logical plane. Fraction democracy is where every idea associated with fractions is taught … Continue reading

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Fractions as Operators and Transition to Proof

Fractions as operators are a good way to teach transition to proof.  First, because fractions are a key part of math education. Students stumble on fractions.  A big part of this is likely teachers don’t understand the abstraction or path … Continue reading

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Fractions as Operators Algorithm Approach

To teach fractions as operators, an algorithm approach can be used. If the denominator of the fraction is 2, we have to make sure the test number is even.  So 1/2 of 4 is 2. Dividing by 2 and factoring … Continue reading

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Fractions as functions on subsets of natural numbers

We can consider the fraction 1/2 to be a function with the domain of even natural numbers.  At this point we don’t do signs.  So the numbers are pure natural numbers.  We consider these a type of size. If we … Continue reading

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Fractions as operators to fractions as numbers

Steps from fractions as operators to fractions as numbers. Natural numbers are developed with all their logical structure including successor function and functions as ordered pairs.  Students are made familiar with proofs involving functions as ordered pairs including the recursion … Continue reading

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Fractions as an operator

Fractions can be introduced as an operator.  A fraction m/n can be applied to either 1) a multiple of n, or 2) to a number p such that p*m is a multiple of n. So formally, a fraction is defined … Continue reading

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