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## Are There Going to Be More Than 20? More Than 50?

Many of us were taught to “estimate” in elementary school. Maybe we were asked how many jellybeans there were in a jar. Or asked to round before finding the answer to a computation problem. But for many of us there was little connection between those activities and...

## Developing Mathematical Language is Hard Work

Using language to effectively communicate one’s mathematical thinking is an important skill—one that is a focus of Math Practice 6: Attend to Precision. Many of us know firsthand that clearly articulating mathematical ideas is challenging work, and that when students...

I was watching one of those legal shows on TV the other night. The prosecutor was asking the defendant a version of the same question for the third time. The defendant’s lawyer, getting annoyed, objected: “Asked and answered!” I’ve heard this phrase a hundred times in...

## What Happens When There Are More Than 10?

Imagine you are 6 years old. Or 7. You know you can use your fingers to model subtraction. For example, for a problem where there are 7 grapes and 2 get eaten, you can raise 7 fingers, put down 2, and count how many are left. But what do you do when the problem...

## The Lesson? Students Never Cease to Surprise Me

On a recent visit to a school in a small city in the Midwest, Karen and I joined a class of 5th graders as they learned a game in Unit 3 called Roll Around the Clock. In the previous session, students used a clock to find and name fractions and equivalent fractions....

## How Do We Support Students in Reflecting on Mathematics?

As I worked with teachers in classrooms this fall, the topic of how to help students reflect on their learning and the learning of others kept coming up. I’m still thinking about how to recognize, encourage, and promote student reflection about math ideas. What traits...