Episode 199 - The Many Ways to Show Numbers with Fingers

In this cross-posted episode from Math Chat, host Mona Iehl interviews Christina Tondevold about developing number sense in elementary students. Christina shares her journey from a "procedural" math student to becoming a math coach and founder of Build Math Minds. The conversation explores the eight components of number sense: four early numeracy concepts (subitizing, verbal counting, object counting, and cardinality) and four number relationships (spatial relationships, one/two more or less, benchmarks of 5 and 10, and part-part-whole). Christina explains how these concepts help move students beyond counting to more efficient math strategies. Practical classroom strategies discussed include using sticky notes to assess students' visual number understanding, implementing subitizing activities, and strategically choosing numbers in word problems to reinforce key number relationships. Both educators emphasize the importance of allowing students to solve problems in ways that make sense to them, rather than forcing procedural approaches. This episode provides valuable insights for teachers looking to build true mathematical understanding rather than just procedural knowledge in their students. Check out Mona’s podcast Math Chat Enroll in The Flexibility Formula Course

In Episode 202: Going Beyond the Task When Building Thinking Classrooms, we reveal the exciting lineup of special guests for our summer book study on 'Mathematics Tasks for the Thinking Classroom Grades K-5' by Peter Liljedahl and Maegan Giroux. Starting July 14th, each week will feature a video with reading prompts followed by live Q&A sessions with experts including first-grade teacher Tammy McMorrow, co-author of the book Maegan Giroux, and Official BTC Consultant Kim Rimbey. Join now at BuildMathMinds.com/bookstudy25 to receive a 20% discount code plus free shipping within the US, and participate in these valuable learning opportunities with educators who are transforming mathematics classrooms.

In Episode 201, I share two exciting summer learning opportunities for fellow Recovering Traditionalists as we prepare to pause the podcast until August. First, enroll in The Flexibility Formula online courses (K-2 or 3-5) to transform how you build math fluency with your students. BuildMathMinds.com/courses  Second, join our free summer book study on "Mathematics Tasks for the Thinking Classroom Grades K-5" by Peter Liljedahl and Maegan Giroux, starting July 14th. Register now at BuildMathMinds.com/bookstudy25 to receive a publisher discount (20% off with free US shipping) and access to exclusive weekly videos featuring insights from myself, Rosalba Serrano, and special guests. We'll explore Part 1 (BTC Practices in Review) and Part 4 (From Page to Practice), focusing on implementing thinking tasks and creating your own curriculum resources. This essential companion to Building Thinking Classrooms will help you prepare for next year's math instruction with practical strategies and ready-to-use templates.

In this milestone 200th episode of The Build Math Minds Podcast, I share the three essential math experiences every classroom needs: Number Routines, Word Problems, and Games. Drawing from research-backed practices in the IES/WWC guides, I explain why these activities are crucial for developing conceptual understanding, procedural fluency, and application in mathematics. Learn how Number Routines make implicit math concepts explicit, how Word Problems should help students understand mathematical structures beyond keywords, and how Games provide engaging practice that builds fluency. To celebrate this 200th episode milestone, I'm offering a free Google file with examples of all three experiences that you can download at BuildMathMinds.com/200. After 200 episodes, these core principles remain unchanged - Routines, Word Problems, and Games help Build Math Minds!

In this episode, I explore the fascinating world of finger use in math and specifically how we represent numbers differently. After noticing that Dan Finkel and I show the number 3 with completely different finger configurations, I dive into why these variations matter for children's mathematical understanding. Through personal stories about my own children's attempts to show the number 5, I highlight how fixed representations can limit children's number sense. Join me to discover why showing quantities in multiple ways—whether using fingers, ten frames, or rekenreks—helps develop deeper mathematical thinking and flexibility. A must-listen for teachers and parents wanting to build stronger number foundations with young learners.

In this episode, Christina Tondevold welcomes special guest Dan Finkel, founder of Math for Love and creator of popular games like Prime Climb and Tiny Polka Dot. Dan shares his three essential principles for effectively implementing mathematical games in the classroom: games should involve meaningful choices, math should be the engine driving the gameplay, and games should be simple to learn and quick to play. Through personal stories and classroom examples, Dan and Christina explore how games transform math from a dreaded chore into an engaging learning experience. The episode concludes with a demonstration of the "31 Game," a simple yet strategic counting game that exemplifies how mathematical play can build number sense, encourage strategic thinking, and create a classroom culture where students aren't afraid to show what they don't know. Perfect for educators looking to reinvigorate their math instruction between standardized testing periods! Join the Build Math Minds PD site to access the Mini Courses https://buildmathminds.com/bmm/  Dan’s website Math For Love https://mathforlove.com/  Dan’s game Prime Climb https://amzn.to/3Y3jN5y  Dan’s game Tiny Polka Dot https://amzn.to/44sfRiI 

In this final episode of our three-part series on upleveling missing part activities, I share ways to transform two popular math games: Salute and Number Sandwiches. Learn how to modify these traditional games to help your students build a deeper understanding of number relationships through missing part problems. These upleveled versions create opportunities for students to work with equivalent expressions while maintaining the fun and engagement of game-based learning. Perfect for elementary math teachers looking to enhance their daily math lessons with games that challenge students to think more deeply about mathematical relationships.

In this second installment of our three-part series on Missing Part Activities, we explore 'repackaging tasks' - a powerful approach to traditional missing part word problems. While educators are familiar with finding unknown parts in word problems like “Christina has $12, she spends some now she has $7.  How much did she spend?”, repackaging tasks push mathematical thinking further by having students redistribute quantities across equivalent expressions. Through practical examples in both multiplication and addition contexts, I demonstrate how these problems help students develop a deeper understanding of equality, number properties, and flexible thinking strategies. Learn how incorporating these enhanced word problems alongside your regular curriculum builds stronger mathematical minds. Part 1 is Episode 195 - https://www.youtube.com/watch?v=DZZKctj2pns  

In this episode, we explore how to elevate your 'Missing Part' math activities beyond the basic type like 5 + __ = 12' into more problems that help students develop a deeper understanding of mathematical equality and build foundational number properties. Get a quick way to implement these enhanced activities in your classroom. Perfect for elementary educators looking to strengthen their students' mathematical thinking without explicitly teaching formal properties. This is the first in a three-part series on upleveling Missing Part activities for more meaningful math instruction.

In this episode, we explore the common misconception about mental math in mathematics education. Featuring insights from Pam Harris' newly published book 'Developing Mathematical Reasoning: Avoiding the Trap of Algorithms,' we discuss why mental math isn't about doing calculations without paper—it's about developing quality thinking strategies.