Numberless Word Problem 3: Data Exploration in 2nd Grade

I worked with a team of amazing 2nd grade teachers this week as a part of an ongoing lesson study. They were in the latter chapters of their curriculum where the Measurement and Data content is often stuffed away as an afterthought because they aren’t “Focus Standards.”

And it’s a drag too because there’s so many rich opportunities for meaningful student discourse about data. That is, if it’s done right. Most textbooks suck all the life out of the content. Students need to understand that data tells a story; it has contextual meaning that is both cohesive and incomplete. Students need to learn how to ask questions about data and to learn to identify information gaps. In other words, students need to learn to be active mathematical agents rather than passive mathematical consumers.

We’d like to share with you what we learned about using Numberless Data Problems and crafting an open investigation into bar graphs that is engaging for all students. As always, feedback welcome. Let’s get better together.

Seesaw 2: A 3-Act Lesson for 6th Grade Expressions and Equations

How do we invite 6th (and 7th) grade students to authentically engage with an equation in a way that invites students (1) to appreciate how the structure of an equation models a context and (2) to dive deeper in to the meaning of the relationships between variables?

Instead of teaching students how to use the properties of equality to solve “one-step” equations first (which is like using a bazooka to kill a cockroach by the way), I’m wondering if there’s a way to start the exploration of equation solving by inviting students to experience the dynamic relationship between variables first.

Here’s my thinking on one way to do that. I’d love to hear your thoughts so we can get better together.

Numberless Word Problem 2: Data Exploration in 1st Grade

Have you seen the amazing visuals over at Number Talk Images? These pictures are ideal for any teacher looking to get all students talking about numbers and mathematical reasoning, regardless of ability levels. We used this image as a number talk to launch a lesson that focused on first grade students making statements about a data display. Inspired by the work by Brian Bushart and Regina Payne, we used a numberless word problem approach to build and structure discourse about a data display.

I hope that there are other 1st (and 2nd) grade teachers out there that might find this analysis useful if they are looking for strategies to get students talking about their mathematical thinking. We wanted students to produce mathematical thinking, not just consume it. Here’s what we created.

The Objectives of Objectives, Part Three: Joy

One of the reasons why we teach is because we want our students to experience the JOY of mathematics. Mathematics should be about questioning, wondering, and the joy of discovery…and math classes should leave students wanting to know more math and do more math thinking. We cannot build an appreciation of math through content standards alone. Math classes should be filled with opportunities for students to have voice and a choice. At the very least, they need a voice in making meaning of problems and a choice in how they go about seeking a pathway to a solution.

But sometimes we (or our textbooks) squash all the joy out of a math lesson. We rob them of their right to notice math things, wonder about math ideas, or do messy math stuff. And lessons that focus on “measurable outcomes” with “explicitly defined objectives” often euthanize mathematical curiosity.