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Connecting math concepts across grades

by Sarah Tierney

How many times do we begin math class with the phrase, “Alright, kids, we’re starting something new today”? If I’m thinking about my own classroom, I used that line more than I’d like to admit.

It’s a way to hook students, to get them to perk up and get excited about what they’re learning that day. But how often should we really be starting something completely new in math, where concepts and ideas should feel like they’re part of a unified whole? When students fail to see connections to what they learned yesterday, this “new” thing turns out more confusing than exciting—for students and teachers.

The truth is, nothing students learn in math class is entirely new. Work with fractions in grades 3-5 builds on students’ experience partitioning shapes in earlier grades, and the introduction of integers in grades 6-8 is an extension of students’ work with whole number operations in grades K-5. Everything’s connected—the challenge is to make sure teachers and students experience math in that way, too.

The first step is for teachers and leaders to understand the connections—to see the standards as part of larger groups, or domains, that connect mathematical concepts and ideas from one grade to the next. Once we understand how the standards fit together, it’s important to make those connections explicit for students every chance we get. We should highlight how concepts are related and show them how what they’re learning today builds off of what they learned last week or last year.  

To help you do that, we’ve created guides for four domains within elementary and middle school mathematics. Because if teachers and leaders can see how the standards connect, our students are more likely to, as well.

Click the button below to learn how to use these documents as part of a professional learning experience or in a math planning meeting.


We’ve spent ten years learning from thousands of leaders and teachers across the country about the things that make a big difference for schools. Now, we want to give you the opportunity to do the same. This is the first in a series of tools, resources, and insights we are sharing from our work with school partners.

Sarah is a director of new partnerships and former coach at ANet. She’s leading the Lessons from the Field project.


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