The Language of Ratios: Theory and Scaling Walkthrough

Section role: supports the formalization section while the teacher leads the class in synthesizing group discoveries and introducing ratio notation. Slides: (1) Title — 'Making it Official: The Language of Ratios'; (2) Student Discoveries — bullets: highlights from the juice challenge, comparing how groups scaled 3 cups of orange juice to 2 cups of sparkling water; (3) Defining a Ratio — bullets: definition as a comparison by quotient, connecting back to the previous recipe problem; (4) Ratio Components — bullets: symbolic forms 'a : b' and 'a/b', clear labels for 'Antecedente' and 'Consecuente'; (5) Value of a Ratio — bullets: step-by-step calculation showing how 3 divided by 2 equals 1.5; (6) Scaling and Equivalence — bullets: showing how the 3:2 ratio maintains a value of 1.5 even when scaled to 30:20; (7) Part-to-Part vs Part-to-Whole — bullets: addressing misconceptions, explaining that ratios are not just fractions of a whole; Closing slide: 'How does our 1.5 value change if we add more water instead of juice?' — sets up the individual detective work in the final section.

Lara de Teachy