Cardinal Math

Grades 1–2 (review in grade 3) · 1.NBT.4, 2.NBT.5, 2.NBT.7 · the long version

How do I help my child with carrying in addition?

Addition with regrouping (carrying)

Your child added 23 + 45 without a thought. Then the homework became 38 + 45 and the answers went strange: 73, or 713, or a 13 squeezed into one column. That's where addition starts needing the idea of a ten.

It's one idea: 8 ones and 5 ones are thirteen ones, a ten and three, and the ten goes with the other tens. Schools call that regrouping, composing a ten, or carrying. Stuck children aren't stuck on the small 1; they are not yet bundling ten ones.

What it looks like with blocks

Put out 38 and 45 in tens and ones and push the ones together: thirteen, too many for one column, so ten of them bundle and ride up to join the tens. Eight tens and three ones, 83. Later, each small 1 on paper should remind your child of that bundle.

The three ways it goes wrong

These mistakes aren't random. Nearly every wrong answer comes from one of three rules that almost work.

  1. Forgets the ten

    Adds each column and keeps only the ones digit of the total. The ten that should move left gets dropped.

    38 + 45 they write 73 it is 83

    Why children reach for it. The adding is right, and 3 is the digit that fits in the box. The child never saw the ten as a ten, only as a digit that wouldn't fit. The most common pattern by far.

    What replaces it. Build 38 and 45 in tens and ones and push the ones together: too many for one column, so bundle ten and ask where it goes. Then ask "where did the ten go?" on every written sum.

  2. Writes the whole column sum

    Writes each column's full total into the answer: 8 and 5 are 13, so 13 goes down; 3 and 4 are 7.

    38 + 45 they write 713 it is 83

    Why children reach for it. Adding correctly, recording honestly. What's missing is that a column holds one digit; the extra one is a ten that belongs next door.

    What replaces it. Ask how many ones are in 13 and how many tens, and whether a ten can live in the ones column. For a while, write it long: 38 + 45 is 70 and 13.

  3. Carries two columns over

    The carried ten skips a column and lands two places left, where it's worth a hundred.

    375 + 182 they write 1457 it is 557

    Why children reach for it. With three columns, "carry it over" has two destinations, and the child picked by habit rather than value. The carry has become a mark to move, not a ten to place.

    What replaces it. Say the carry's value out loud each time: "that's one ten, so it goes with the tens." Give three-digit problems with a carry in the ones only, then the tens only, before both.

The five-minute check

A short run of problems on a phone or tablet, chosen as your child answers. If one of the three patterns is behind their mistakes, the check names it. Nothing to install, nothing stored.

Hand the phone over, or play it here. When it says all done, take it back and tap see what we found.

Start the five-minute check

What the school is probably doing

Regrouping / composing a ten
The written method, through tens and ones first; the small 1 records a ten being made.
Expanded form
38 + 45 as 30 + 40 and 8 + 5: seventy and thirteen, then 83.
Friendly numbers
Take 2 from 45 to turn 38 into 40, then 40 + 43 = 83. No carrying at all, and the app plays it too.
Base-ten blocks and drawings
Sticks for tens, dots for ones. If your child draws these on homework, the lesson is working.

They're not the new way versus the right way, just one idea at different distances from the objects. Whichever way you learned, insist on knowing where the ten went.

Questions parents ask

What grade is this?

Two-digit plus one-digit with a carry is grade 1 in the US (1.NBT.4); two-digit plus two-digit is grade 2 (2.NBT.5), three-digit later that year (2.NBT.7).

Is carrying the same as regrouping?

Yes. The word changed because nothing is carried anywhere: ten ones are regrouped into one ten. If carrying works at your kitchen table, use it.

My child writes 13 under the line. Is that bad?

It's honest, and the easiest pattern to fix. The adding is right; the child just hasn't learned that a column holds one digit. Ask where a ten lives.

The answers are always ten too small.

That's the forgotten ten, the most common pattern. Back to blocks for a few days: thirteen ones have to bundle, and the bundle has to go somewhere.

Should I teach the little 1?

Teach the bundle first; the little 1 is just how we write it down. A child who only knows the notation loses it as soon as the sum looks unfamiliar.

How long should we practise?

Five to ten minutes most days beats an hour on Sunday. Three or four sums done slowly with blocks are worth more than a page.

Cardinal Math watches for all of these, every day.

Inside the app the same patterns are caught as your child plays, across the whole of K to grade 5, and explained to you in plain words. One price, no ads, no streaks. Coming to iPhone and iPad.

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