# Marilyn Burns’s Math Blog: A Tour

Marilyn Burns’s math blog has been around since 2015. Her posts cover a wide range of topics, including math games (some of which appeal to kids and adults alike), teacher resources, math and children’s literature, and more. Please join me on a tour of just a few interesting posts on her blog that might be fun or useful to engage with, especially while staying at home during these unprecedented times.

“What’s the Longest Number String Possible?”

Burns explains how to play the “Factors and Multiples” game. It’s supposedly for kids ages 7 to 16, but I found it fun enough to play several rounds myself. It’s designed for two players, but I found the online, interactive version enjoyable even when I was playing against myself. Players are given bubbles with positive integers between 1 and 100 written on them. The first player chooses an even number less than 50 from the group to start the string. The next player must then choose a number that is either a factor or a multiple of the first number to continue the string. Play continues in this manner until one of the players is unable to find a number that can be used to continue the string. That player loses.

The game is hosted on the University of Cambridge’s NRICH website. The NRICH project “aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice,” according to its website, which contains other games, projects and resources (for teachers and students) sorted by age/academic level.

“What Are Good Math Questions to Ask Students?”

I often think about how the quality of math questions impacts students — for better or worse. In this post, Burns reviews three components of good math questions presented in the book “Good Questions for Math Teaching: Why Ask Them and What to Ask, K–6″ by Peter Sullivan and Pat Lilburn.

“These features sing to me. Good questions require more than remembering a fact or reproducing a skill. It’s possible for students to learn by answering the question. There may be several acceptable answers,” Burns wrote.

She then shares some of the sample questions from the book, along with the rationale behind them and tips for tweaking them to meet different students’ needs. She also points out that there is a companion book focused on questions for middle school students.

“Race for 20―A Counting Game for All Ages”

In this post, Burns presents a simple game (along with variations) that can engage people of all ages. “Race for 20” seems like a great game to play with family, especially since many of us are now spending extended time periods at home. There are only three rules in the basic version.

1. Choose who will start and then take turns.
2. Starting at 0, when it’s someone’s turn, they can add 1 or 2 positive numbers to the string of numbers. For instance, if the first players says “1,” the second player would say either “1, 2” or “1, 2, 3.”
3. Whichever player gets to the number 20 wins.

Burns presents options for making the game more accessible to kids who are still learning how to count to 20, ways to make the game more concrete and more. At the end of her post, she shares connections between the game and game theory.

Race for 20 fits into the category of the game of Nim. For more information, there’s lots online. Here’s a definition of Game Theory that I’ve cobbled together from a slew of online choices: Game theory is the study of how and why people make decisions. It is the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants. Game theory has been applied to contexts in economics, business, and biology,” she wrote.

“Using Math Menus: Some Nuts & Bolts”

In an Educational Leadership piece on the “Math Solutions” website, Burns explains what math menus are and how they can be used in classrooms. “A math menu is a list of math options posted for all to see. The options can include problems, investigations, games, and other activities that promote students’ understanding, support their reasoning, or provide practice with the content and skills they’ve been learning,” Burns wrote in the Educational Leadership piece. The approach also seems like it would be helpful to parents who are currently educating their kids at home due to the pandemic and are looking for additional ways to supplement their instruction.

She explains that these menus can be used to respond to three big questions from teachers: “What can I do with students who finish their math assignments more quickly?” “How can I free up time to work with students who need extra help?” and “How can I differentiate experiences to support struggling learners while also meeting the needs of students who need additional challenges?”

In her blog post, Burns describes how she responded to some questions about the approach posed by Jill Downing, a Title 1 Educator with the Helena Public Schools in Montana. Burns also shares some of the written responses students have shared about their experiences with math menus.

Want to share an idea with us? Reach out in the comments below or on Twitter (@writesRCrowell)!

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