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#### Dressed Up (Equivalent) Fractions

##### (MathPickle, 2013)

Equivalent fractions should be explored first using the engaging Fractured Fraction puzzle. Only later is this structural video an option.

Engagement first, structure second.

This video introduces a challenge: how should we list all the fractions without repeating two that are the same (like 4/6 and 2/3.)

There is some beautiful and curricular algebra in proving the construction at the end of this video… That will definitely be the subject of another MathPickle video. For now, you can ask your students where a certain fraction – like 4/11 is on the tree. You can ask them if they are SURE it is only at one place on the tree. Is this true for all fractions? Do they appear once and only once? The proof is not too hard.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza’s God, it won’t love us in return.

Bertrand Russell

#### Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

##### MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

##### MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

##### MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.