Untangling fractions, ratios, and quotients

Untangling fractions, ratios, and quotients

By William McCallum In everyday language, $\frac{a}{b}$, $a\div b$, and $a : b$ are all different manifestations of a single fused notion. Here, for example are the mathematical definitions of fraction, quotient, and ratio from Merriam-Webster online: Fraction: a...
Why We Don’t Cross Multiply

Why We Don’t Cross Multiply

By Kate Nowak (co-authored with Kristin Gray) “Ultimately, the goal of this unit is to prepare students to make sense of situations involving equivalent ratios and solve problems flexibly and strategically, rather than to rely on a procedure (such as “set up a...
Fraction & Decimal Number Lines

Fraction & Decimal Number Lines

By Kristin Gray Recently, our 3rd, 4th, and 5th grade teachers had the opportunity to chat math for 2 hours during a Learning Lab held on a professional development day. It was the first time we had done a vertical lab and it felt like perfect timing as 3rd and 4th...