Carrying tens with marble runs

A made-up example built from a parent's description. A way, never the way.

Guide: Nora · Learner: Eli · Age band: 7–9 · Subject: Math

Where the learner was stuck

Eli could add the digits in each column of a two-digit addition problem, but wrote the two column results side by side rather than grouping them. Asked to add 27 and 15, Eli produced 312: the tens total (3) and the ones total (12) placed next to each other, with no carrying. Eli also froze before trying when a column of numbers appeared, saying "I can't" before making any attempt.

The approach (built through what they love)

Marble runs already model overflow: when too many marbles pile up in one spot, extras roll to the next track. The session starts with Eli teaching Nora how to set up an overflow track, then Nora names the connection — the ones spot holds up to nine, and when you reach ten, one marble rolls up to the tens track. That is carrying. Every example in the session is framed this way: count the ones, check for overflow, roll the extra ten up. The game uses the same language, and Eli can hear the "roll" happening in each question.

For the guide: the shape of a session

A session has three parts. First, Eli teaches — Nora asks how the overflow track works and genuinely does not know how Eli has set it up. Second, Nora names the math connection in one sentence, using Eli's own words. Third, Eli tries the game at the learner's own pace, with Nora beside them. The guide's job during the game is to notice the face, not the score. If Eli goes quiet after a wrong answer, Nora does not wait or ask why — she gives Eli something to do in the first two seconds: "let's count the ones together" and starts counting herself. Keeping the page to one question at a time, or folding a printed page, prevents the overwhelm that a full column of numbers triggers.

What only a person can do

Nora can see the moment before the freeze — the held breath, the looking away — and interrupt it before it sets in. She can connect the marble run to one Eli actually built, not a generic one. She can tell when Eli is guessing versus thinking. She can read the room: if the session starts to feel like a test, she can stop the game, return to the marble run, and let Eli be the guide again. A page cannot do any of this. The decision to stop early, to shift tone, to follow an unexpected question — those belong entirely to Nora.

Where the learner leads

The session opens with Eli as the guide. Eli knows more about building a marble run that works than Nora does. Eli sets up the overflow track and explains why the marbles go where they go. Nora listens and asks one question: what happens if the extras have nowhere to go? That question is real — Nora wants to know. Eli's answer contains the whole idea of carrying; Nora's job is to name it afterward.

The game on the learner's side

The game presents two-digit addition problems one at a time, each with a visual showing the column structure. There are three levels, each with four questions. After three correct answers in a row, the numbers get a bit bigger. After a miss, the next question is a bit easier. Wrong answers name the specific mistake — side-by-side writing, forgetting the carry, or dropping the ones — so Nora's note after the session can say exactly what came up. Nothing bad happens on a wrong answer. The game says: wrong answers help us know what to work on next.

When to seek an evaluation

Most children find carrying awkward at first and get it with practice. But if a child consistently cannot hold two things in mind at the same time — a partial result and what to do with it next — even after many patient tries, or if numbers seem to slip and rearrange in ways the child cannot explain or notice, or if the frustration is sharp and persistent across many subjects and types of work, it may be worth talking to someone whose work is understanding how children learn. A professional who observes children and learning can watch, ask questions, and tell you what they see. You do not need a label to have that conversation, and the information you get is yours to use however you choose.

A way, never the way

The marble run is one way to think about carrying. Another child might reach for a different picture — a full row of LEGO bricks moving up to the next layer, a score counter that rolls over, anything. If the learner reaches for their own model, follow it. The goal is that the learner can carry tens reliably. How they get there is open.