Strategies that clarify the number line for every learner

Negative numbers are often taught through rules that don’t stick. In this episode, we return to meaning.

We explore how students have been reasoning about space, direction, and position on the number line since the earliest grades, and why negative numbers are an extension of that work—not a new concept. By grounding integer operations in movement and distance, this episode shows how students can reason about direction, magnitude, and value without relying on memorized rules.

You’ll hear classroom-tested routines that build understanding through visual models, rich conversation, and purposeful practice. We also connect this work forward into seventh-grade multiplication and division of integers and eighth-grade equations and expressions, showing how early sense-making supports long-term success.

This episode is designed to help teachers slow down instruction without lowering expectations and give students the tools they need to judge reasonableness, explain their thinking, and apply integer reasoning across domains.

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Thanks for tuning in to this episode of the Make Math Happen podcast! If you enjoyed today’s conversation, subscribe on your favorite listening platform, leave a review, and share this episode with your fellow educators.

You can also join the discussion and connect with me directly by clicking the link to join the Math Collective. Together, we’ll keep exploring practical strategies to transform classrooms and inspire students.

Remember, new episodes drop every Sunday at 9:00 am, so mark your calendars! Until next time, keep making math happen, and I’ll catch you in the next episode.

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When students struggle with fractions, decimals, and integers, it’s often assumed they’re missing skills. In reality, they’re missing understanding.

This episode opens our Understanding Math series by focusing on how students make sense of rational numbers as quantities that have value, direction, and position—not just symbols to manipulate. We explore how early experiences with counting, comparing, and representing numbers develop over time, why the number line is such a powerful organizer of thinking, and what students need to understand before operations make sense.

You’ll hear why rushing into procedures often leads to fragile learning, how a lack of magnitude and relational understanding impacts students’ ability to judge reasonableness, and what it looks like to slow down without lowering expectations. We also share concrete ways to help students reason about value, distance, and relationships across number systems—even when your current unit lives in another domain.

This episode is designed to spark meaningful PLC conversations and give you something you can use immediately in your classroom. It sets the foundation for the rest of the month and prepares students to connect quantities more confidently as we move toward ratios, proportions, and algebraic thinking.

Send us a text

Thanks for tuning in to this episode of the Make Math Happen podcast! If you enjoyed today’s conversation, subscribe on your favorite listening platform, leave a review, and share this episode with your fellow educators.

You can also join the discussion and connect with me directly by clicking the link to join the Math Collective. Together, we’ll keep exploring practical strategies to transform classrooms and inspire students.

Remember, new episodes drop every Sunday at 9:00 am, so mark your calendars! Until next time, keep making math happen, and I’ll catch you in the next episode.

If you like math videos, let's connect:

• YouTube
• TikTok

This episode closes our geometry focus by showing how similarity and scale serve as the bridge into ratios, proportions, and later functions. We explore what makes figures similar, how scale factor represents a preserved relationship rather than a formula, and why students need visual experiences with enlargement and reduction before working with numbers.

Along the way, we address real classroom challenges, including unfinished learning, limited instructional time, and the pressure to move students forward before connections are solid. We discuss how teaching concepts in isolation often deepens gaps, and why making relationships explicit is essential for sense-making and long-term understanding.

You’ll hear practical strategies for helping students reason about similarity using representations like tape diagrams, ways to anticipate common misconceptions, and ideas for re-engagement when timing or pacing doesn’t allow for a full instructional reset. We also connect these practices to research on high-impact strategies, including microteaching, reflection, and metacognition, and discuss how short video routines can activate learning both at home and in the classroom.

This episode is designed to spark meaningful PLC conversations, support thoughtful sequencing, and help teachers position students for success across domains. It closes the geometry chapter and opens the door to our next focus: ratios and proportions—same story, new chapter.

Send us a text

Thanks for tuning in to this episode of the Make Math Happen podcast! If you enjoyed today’s conversation, subscribe on your favorite listening platform, leave a review, and share this episode with your fellow educators.

You can also join the discussion and connect with me directly by clicking the link to join the Math Collective. Together, we’ll keep exploring practical strategies to transform classrooms and inspire students.

Remember, new episodes drop every Sunday at 9:00 am, so mark your calendars! Until next time, keep making math happen, and I’ll catch you in the next episode.

If you like math videos, let's connect:

• YouTube
• TikTok