You've helped them one at a time. The real understanding is how the ideas CONNECT — teach that next.
Arch (the Math-Art bridge — proportion, the golden ratio, symmetry) ×Cable (the Math-Music bridge — frequency ratios and rhythm)
A 3:2 proportion looks balanced in a painting, and a 3:2 frequency ratio sounds harmonious as a musical fifth. What does that reveal about Arch and Cable?
Arch then says: “The 3:2 in a painting and the 3:2 in music are unrelated accidents with no shared math.” — is that right?
The link: proportion and harmony are the same ratio, met by two different senses.
One ratio — seen as proportion, heard as harmony.
Girder (the Math-computing bridge — order of operations is the same as sequence in code) ×Splice (the Math-ELA bridge — sequence and structure in writing)
A program gives the wrong answer because two steps ran in the wrong order, and an essay confuses readers because its points are out of order. What connects Girder and Splice?
Girder then says: “The order of steps matters in code, but you can arrange a piece of writing in any order you like.” — is that right?
The link: getting the sequence right is the same discipline whether you run it or read it.
Right order to run, right order to read.
Capstone — build one cross-subject bridge together
Three ways math shows up elsewhere. Bring in the cast member for each.
Ratio you can SEE — proportion in art. Who?
Who do you bring in?
Ratio you can HEAR — frequency in music. Who?
Who do you bring in?
Order you can RUN — sequence in code. Who?
Who do you bring in?
The synthesis: ratio you see, ratio you hear, and order you run — the same math crossing three subjects.
