Category

# Numerical Reasoning

Rebecca solved 7 – 3 by adding, demonstrating the important numerical reasoning strategy of applying the inverse relationship between addition and subtraction. Read about what happened when I used the video clip of Rebecca in a class lesson.
April 10, 2022
In a Listening to Learn interview, Nathan knew from memory that 6 x 5 equals 30. He explained to Rusty Bresser, "So, 6 divided by 2 equals 3, and you just add a zero behind it." Here's a suggestion for using that video clip in a lesson and what happened in two different classes.
February 22, 2022
I woke up early this morning, scanned Twitter, and was pulled in (as I always am) by Pam Harris’s Share Your Thinking problem. (Thanks, @pwharris!) Here’s how I responded and what I learned.
November 18, 2021
I love incorporating children’s books into math lessons. Since most of my teaching focuses on math, it’s a treat for me to read a book aloud to a class. After the students have a chance to enjoy the story and respond to the illustrations, then I use the book as a springboard for a math lesson.
August 31, 2021
Over the years, I’ve collaborated with Lynne Zolli and Patty Clark on a variety of math education projects. For this blog, we worked together to share our thinking about how Listening to Learn math interviews can serve teachers and students.
August 16, 2021
David Brooks wrote an opinion column in The New York Times on November 19, 2020, “Nine Nonobvious Ways to Have Deeper Conversations.” K–5 math wasn’t his focus or even hinted at in his message, but his suggestions jumped out at me as useful and important for connecting with students.
June 8, 2021
On Wednesday, May 5, 2021, I posted the sixth in my Wednesday Twitter series of video clips from Listening to Learn math interviews. The response to this Tweet amazed me―it received over 100,000 impressions! I was appreciative of the many supportive and insightful replies. Read more.
May 11, 2021
Asking students to solve problems mentally, without paper and pencil, is always revealing and often surprising. I thought that asking students to solve 100 ÷ 3 would be sort of a slam dunk. My, was I wrong!
April 8, 2021
I just learned about Factors and Multiples, a shelter-at-home game that’s engaging as solitaire and can be played as a two-person game either cooperatively or competitively. (I’ve played it both ways.) It’s intriguing for both adults and kids (as long as players know about factors and multiples of numbers up to 100). It’s a keeper.
April 3, 2020
Good Questions for Math Teaching is a Math Solutions book that has long been one of my favorites. It’s a resource that I dip into when I feel the need for something fresh. And it speaks directly to our current shelter-in-place coronavirus crisis as many of us look for ways to mathematically engage students online, children at home, or both. Here are samples to get you started. I’ll continue to post more ideas on Twitter (@mburnsmath).
March 17, 2020
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.
February 18, 2020
What am I doing on the floor? Teaching angles to fourth graders. Read about how instruction using Pattern Blocks and hinged mirrors, along with supporting number talks, can help students learn to understand and measure angles. Here I present a (sort of) photo essay to describe what actually occurred over the first three days of instruction. Ideas for continuing the instruction follow.
April 29, 2019
Last year, I agreed to meet with a friend’s sixth-grade son. Oscar’s math teacher had raised an alarm for my friend and her husband about Oscar’s math progress. They were shocked. Oscar did his homework and was proficient with paper-and-pencil math. What was the problem?
February 19, 2019
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?
October 1, 2018
When teaching students to add decimals, I wind up reminding students to “line up the decimal points.” This makes sense to some students while others follow the rule without understanding. How can we teach adding decimals to develop understanding and skill? Here’s a possible suggestion: Give the correct answer up front.
January 14, 2018
I believe strongly that mistakes are learning opportunities. At least that’s what I regularly tell students. But it sometimes feels different when the mistakes are mine . . . and especially when they are pedagogical mistakes that I make while teaching. That happened to me recently when teaching a lesson to fourth graders.
January 1, 2018
I love Twitter. On November 3, 2017, I saw this image in a Tweet posted by @MarkChubb3. The image stuck with me for several days. After talking about it over dinner with a teacher friend, and then again over lunch with another, I became curious to find out what students might think. I made arrangements to “borrow” three fifth-grade classes and made plans to teach the same lesson in each class.
December 19, 2017
A friend and I were talking recently about how much work we put into planning lessons. Even after all these years of teaching, I have to think through lessons as carefully as possible, both about the logistics and about the mathematical thinking I want to keep in mind and support. Here’s an example.

March 27, 2017
The card game Oh No! 99! is a keeper! It gives practice with mentally adding one- and two-digit numbers and with adding and subtracting 10 from two-digit numbers. The game encourages strategic thinking as students decide which cards to play and which to keep, and it’s also useful as an informal assessment. Read about how the game was used with second and fifth graders.
March 5, 2017
The children's book 17 Kings and 42 Elephants by Margaret Mahy is one of my long-time favorites. In this post I describe a division lesson that I’ve taught to third graders but recently revisited with fourth- and fifth-grade classes. With the older students, we tried extensions that differentiated the experience and put students in charge of deciding on problems for themselves. It was exciting to me to expand a lesson I've taught many times into a multi-day investigation.
January 30, 2017