I’m often surprised by what I learn when I interview students. Watch this 46-second video clip of Jonah solving 100 ÷ 3. Then read how I used the clip in a lesson with a class of fifth graders, and also read the letters the students wrote to Jonah.

Have you ever asked students to solve 12.6 x 10, and they respond that the answer is 12.60? I have, many times. Students who do this apply a pattern that works when they multiply whole numbers by 10—they tack on a zero to the end of the number they’re multiplying. But then they apply the same pattern when working with decimals. What can we do?

Over a year ago, I blogged about The 1–10 Card Investigation. I didn't provide a solution to the problem and no one who commented asked for one. But a newly posted comment requested the solution. That pushed me into a conversation with myself about how I should respond, and about giving answers in general.

Here's one of my favorite oldies. (No, not the photo—the border problem.) I was so pleased to see this math investigation included in Jo Boaler’s latest paper. This blog post presents a detailed lesson plan for using the border problem with students and also includes a five-minute video clip to give you a sense of how the instruction went with one class.

Place value is one of the most important foundational concepts about our number system. Watch my assessment interviews of second graders and learn how you can find out what your students understand about place value.

I’ve taught students in grade 2 through middle school how to solve KenKen puzzles. If you’ve never solved KenKen puzzles yourself, or haven't engaged your students with them, read about how I’ve introduced them in the classroom. But be warned: KenKen puzzles can be addictive.

I began a back-to-school session for elementary teachers by asking everyone to write an opening sentence for Goldilocks and the Three Bears. The teachers were surprised by the request—the session was supposed to focus on teaching math. What was the connection?

The 1-10 Card Investigation has a big payoff with students. It engages their interest, involves them with making sense of a problem and persevering to solve it, and gives them experience with evaluating their progress and changing course as necessary. Plus it has a playful aspect that too often is lost in math class.

I asked a class of fourth graders to figure out the answer to 99 + 17 in their heads. In this post, I describe why I chose that problem, include a video of how the lesson unfolded, describe a teaching error I made in a subsequent lesson, and more.

A long-standing instructional practice has been to teach students how to multiply (or add, subtract, or divide) and then, after the students have learned to compute, give them word problems to solve. In this post I present a lesson with a different approach, where word problems become the lead and reason for learning to compute.

After I told Steven, the man seated next to me on an airplane, that I was a math teacher, he described the Dealing in Horses problem that he was given at a corporate management training session. The problem has been one of my teaching staples ever since.

When a workshop participant raised his hand to offer how he was taught to subtract when he was in elementary school, I was surprised by the process he described. He called it the “trouble-coming method” of subtraction. I hadn’t ever seen it before, and I’ve never seen it since.

Here’s another post about subtraction. I’ve long been a fan of having students invent and use their own methods for computing, as long as they can explain why their strategies make sense. Here’s what I learned from Jesús, a fifth grader.

Word problems have long been difficult and frustrating for students to solve and for teachers to teach. A colleague recently forwarded an email from a woman looking for resources to help her fourth-grade granddaughter with word problems. I thought for several days about how to offer positive support to both the grandmother and her granddaughter.

How much is 12.6 × 10? This is a question from the Math Reasoning Inventory (MRI) decimal assessment. What do you think were the most common incorrect answers given by the more than 7,800 students who figured out the answer in their heads? And what about the boy who answered, “One hundred twenty and thirty-fifths?”