By Zack Hill The major work of grade 3 includes representing and solving problems that involve multiplication and division. Then, by the end of grade 3, students are expected to know from memory all products of two...
By William McCallum A world where all learners know, use, and enjoy mathematics. Perhaps the most mysterious verb in the IM vision—a world where all learners know, use, and enjoy mathematics—is the first one: know. Knowing...
By Kate Nowak How do we help our students build mathematical understandings that endure past the unit test? If we want students to construct strong, reliable bases of mathematical knowledge, our instruction needs to do more...
By William McCallum The number line is a seemingly simple object: a straight line with two points marked 0 and 1. Those two points are the seeds of great complexity, however. Whole numbers are located at positions marked...
By William McCallum In grade 3, as students start to learn about multiplication, they think about products like 6 x 7 in terms of equal groups. 6 x 7 is the number of things when you have 6 groups with 7 things in each...
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...
“I’m not sure this is working. Only five of my students are participating and commenting each day. The rest sit there and look at me.” By Tabitha Eutsler This was my conversation with our math coordinator after my first few...
We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So what can we do to support this other kind of thinking in class—the slow,...
The first thing you have to understand is that asking people to model with mathematics makes them mad. Not in all contexts, though! At a social gathering with a generally amiable and curious group of people, you might try...
This blog post is the third in a series of four blog posts exploring the student experience of problem-based learning. The first two posts are available here: “How Do Students Perceive Problem-Based Learning?” and “Inviting...
Q: What is the fastest way to get a heated debate going about some topic in the IM 6–-8 math curriculum? A: Show people this graph from Lesson 4 in Unit 8.5: By Kristin Umland Many of us learned that time is always the...
I asked my 15-year-old what she learned today at school. She paused for a moment and then answered, “What did you learn at school today?” It took me a while to think about what I had learned (which will make me more...
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...
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