When students notice structure, they stop doing math and start seeing it. They might decompose 49 + 52 into 50 + 51 because the five tens are easier to hold onto. They may look at 7 × 8 and see five groups of eight with two more eights left over.

Students Noticed! is a place for teachers to share these moments. Every so often, the best of these sightings get featured here and in my newsletter, with the teacher’s permission and full credit.

What Counts?

Student thinking.

A student’s written or drawn strategy that reveals structure (place value, properties of operations, equivalence — or something you think we haven’t named yet)
A “What if…?” question a student asked, and where it led
A photo of student work, a short clip description, or just the moment in words

It doesn’t have to be pretty. It doesn’t even have to be correct. Half-finished thinking often shows more what a student understands about the structure.

Before You Upload – Privacy First

Please crop, cover, or blur student names, faces, and any identifying details before uploading photos of student work.

Share only what your school or district policy allows. If you’re unsure, describe the moment in words instead.

Students Noticing Structure

Equivalence (E), Place Value (PV), and Properties of Operations (PO)

PV- Grade 4

Students trying to determine how many cards in a card house that used 13 decks of cards. Using place value and properties within the open array. How could you make these structures visible to these students?

E, PV, & PO – Grade 2

This group counted a collection of counters. They counted them into units of tens, ones, and hundreds, then counted them as 100, 200, 300, 400, 500, 510, 511, 512, 513, 514, 515, 516, 517. How might these students benefit from seeing the place-value structure? How could you make these structures visible to them?

E & PO – Grade 9

This student used equivalence and properties of operations to show that 2x – 1 and x + (x – 1) are the same – “We said the same thing… just differently.”

The Form

* required

Your name (first name is fine) *

Email *

School / District

Grade band *

What happened? Tell the story — what did the student notice, say, or do? *

Which structure is hiding in there?

Before you upload: please crop, cover, or blur student names,
faces, and any identifying details. Share only what your school/district policy
allows — or skip the photos and describe the moment in words above.

Student work — photo 1 (jpg, png, or webp, max 8 MB)

Photo 2 (optional)

I confirm this submission contains no student-identifying information, and I've followed my school/district policy for sharing student work. *

Feature permission
Please check with me before it's featured anywhereGo ahead and feature it (first name and grade band only)

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