Regrouping and Borrowing: Why It Falls Apart

By Laura Lurns · Reviewed by Philip Weaver · Last reviewed 2026-10-23

Why does regrouping fall apart?

A US federal guide on extra math help came out in 2021 (Fuchs and colleagues). It covers children who struggle with math, from kindergarten to sixth grade. It is about help in small groups or one to one, at school. The guide we hold does not say why regrouping goes wrong for one child. It gives three steps for teaching it. The guide lists these three for place value and regrouping.

The 2021 guide is not a guide to dyscalculia. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success.

Each study tested a whole package of help. So the guide cannot say what one step adds on its own.

The guide's first step: base 10 blocks, linked to the written sum

The guide's first step: use base 10 blocks, and link them to the written sum. Ten ones match one ten, so the blocks show the trade. The guide shows the model and the written sum together.

The guide rates the evidence for hands-on and drawn models, linked to the numbers, as strong. Strong means its studies kept finding gains, across different groups of children. That grade is for the advice as a whole, not for each step in it. Which model suits which topic is the panel's advice.

The guide says to fade out objects and drawings only as a child becomes accurate without them.

The guide's second step: say "regrouping"

Say "regrouping." The guide prefers "regrouping" to "borrowing" or "carrying." The guide rates the evidence for teaching clear math words as strong. That grade is for the advice as a whole, not for each step in it.

The same advice has children explain their thinking out loud. The guide suggests sentence starters to help. One we might use is "I traded one ten for…" That sentence starter is ours.

In our view, the word "borrowing" can confuse, because nothing is given back.

The guide's third step: mix in sums that need no regrouping

Mix in sums that need no regrouping. The guide says this keeps regrouping from being overused. The guide rates the evidence for step-by-step teaching as strong. That grade is for the advice as a whole, not for each step in it. The same advice says to start new ideas with easy numbers.

Regrouping with blocks at home

The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it. The worked examples below are ours too.

No blocks? In our view, you can use bundles of ten straws instead. Tie ten straws with a band to make one ten. Loose straws are ones.

Taking away: 42 − 17. Put out 4 tens and 2 ones. You cannot take 7 ones from 2. So trade one ten for ten ones. Now there are 3 tens and 12 ones. Take away 7 ones, which leaves 5. Take away 1 ten, which leaves 2 tens. That is 25. Write each step beside the blocks as you go.

Adding: 38 + 25. Put out 3 tens and 8 ones. Add 2 tens and 5 ones. Now there are 13 ones. Trade ten of them for one ten. Now there are 6 tens and 3 ones. That is 63.

A mixed pair. Give 47 − 23 next to 42 − 17. Ask which one needs a trade. 47 − 23 does not, so it is 24.

One mistake to look for. For 42 − 17, a child writes 35. They took 2 from 7 in the ones place. Lay out the blocks. There are only 2 ones, so a trade has to come first.

In our view, go back to the blocks whenever a sum gets hard.

Place value in a list of signs

A German medical guideline summary lists signs of dyscalculia with no age (Haberstroh and Schulte-Körne, 2019). Here is one of them.

• Place value, and writing numbers down.

By the summary's account, one mistake is not a sign. The summary judges mistakes by how varied, lasting and frequent they are. In our view, tell the teacher what you see. In our view, you do not need to wait for a pattern.

When to ask for help

Each of these is a reason to ask for help on its own.

• Little change, even with steady practice and good teaching.
• Math well below your child's other schoolwork.
• A teacher who raises a concern about math.
• Extreme upset about math.
• Complete avoidance of math.
• Worry about math that spreads into the rest of learning.
• Sadness or worry that lasts.
• A skill that was there and has gone. Our position is that a lost skill goes to a doctor first, not a tutor.

If no skill has gone, start with the teacher. Say what you are seeing at home, and what you have tried. Beyond the teacher, the right person depends on what it turns out to be about. If the work is too hard, someone who works on that school skill. If worry or mood is the thing, someone who works with children's mental health. In our view, if you are worried enough to ask, a professional evaluation is worth asking about.

Any talk of hurting themselves is a same-day call to your doctor or a crisis line.