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## The Nuances of Understanding a Fraction as a Number

By Kristin Gray This was originally posted on Kristin Gray’s personal blog, Math Minds, on November 15, 2020. Student work is just the best. It is the one thing that will always motivate me to write! So, let’s kick this post off with a great work example from grade 3....

## The Story of Grade 5

by Sarah Caban From the start of the year, we want students to know they are capable of engaging in grade-level mathematics. In the Opportunity Myth (2018), data shows that there is an opportunity gap for historically marginalized students—often students of...

## Using Diagrams to Build and Extend Student Understanding

By Jenna Laib and Kristin Gray Take a moment to think about the value of each expression below.  $\frac{1}{4}\times \frac{1}{3}$ $\frac{1}{4}\times \frac{2}{3}$ $\frac{2}{4}\times \frac{2}{3}$ $\frac{3}{4}\times \frac{2}{3}$ What do you notice? How would you explain...

## Say What You Mean and Mean What You Say

By William McCallum In one of our professional development workshops, there is an activity in which the facilitator asks teachers to skip count by $\frac34$. The facilitator records the count, $\frac34$, $\frac64$, $\frac94$, . . . and then asks for patterns they...

## Fractions: Units and Equivalence

By William McCallum “I’m afraid I can’t explain myself, sir. Because I am not myself, you see?” Alice in Wonderland. The idea of equivalence in mathematics is tricky for learners, because when we talk about two things being equivalent, for example the...