Number and Operations Archives - Page 5 of 5

General Interest Number and Operations Numerical Reasoning Problem Solving

A Number Line Exploration

Here’s an idea that I was first introduced to about ten years ago by Nicholas Branca, a math educator who contributed profoundly to my thinking about math and teaching. I’ve tried presenting it as a math-in-three-acts investigation.

Marilyn BurnsAugust 13, 2015

General Interest Number and Operations Numerical Reasoning

A Mental Math Lesson, Part 2

In my June 2 post, I described how students solved 99 + 17. Actually I described only part of the lesson. Now, in response to a tweet, I explain how I also had students think about one of the important mathematical practices.

Marilyn BurnsAugust 11, 2015

Assessment General Interest Number and Operations Numerical Reasoning Videos

A Mental Math Lesson

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.

Marilyn BurnsJune 2, 2015

Number and Operations Numerical Reasoning Real-World Problems Videos Word Problems

Word Problems: Don’t Put the Cart Before the Horse

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.

Marilyn BurnsMay 20, 2015

General Interest Number and Operations Problem Solving Real-World Problems Word Problems

Where’s the Math?

Students’ ideas often amaze me, and Lydia’s is one of the most suprising examples. She used 7 x 3 = 21 to figure out that 8 x 4 = 32. She reasoned that since the factors in 7 x 3 were each 1 less than the factors in 8 x 4, she’d just increase each digit in the answer, changing 21 to 32. She was correct! Read about Lydia's discovery, what I did, and what I learned.

Marilyn BurnsMay 11, 2015

General Interest Number and Operations Numerical Reasoning Problem Solving Real-World Problems Videos Word Problems

An Unusual Word Problem: “Dealing in Horses”

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.

Marilyn BurnsApril 28, 2015

General Interest Number and Operations Subtraction Videos

Yet Another Way to Subtract

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.

Marilyn BurnsApril 14, 2015

General Interest Number and Operations Numerical Reasoning Subtraction Videos

Another Way to Subtract

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.

Marilyn BurnsMarch 30, 2015

Number and Operations Numerical Reasoning Word Problems

A Problem with a Word Problem

A word problem on a third-grade standardized math test didn’t call for a numerical answer, but instead asked students to decide if the problem should be solved by adding, subtracting, multiplying, or dividing. One third grader complained to his teacher, frustrated because he thought there was more than one correct possibility.

Marilyn BurnsMarch 19, 2015

General Interest Number and Operations Numerical Reasoning Subtraction

Why I Like Using Open Number Lines (Though I Don’t Like the Name)

This post is about subtraction, which is typically difficult for students to learn and for teachers to teach. Think about 503 – 398, for example. To estimate the answer, I can change the problem to 500 – 400 (rounding 503 to 500 and 398 to 400). That gives me an estimate of 100, which I know is close. But how can I know if the actual answer to 503 – 398 is greater or less than 100? I raised this question with third graders.

Marilyn BurnsFebruary 25, 2015

Number and Operations