The backpack is on the floor, the pencil is already being dramatic, and your 2nd grader says, "For 8 plus 5, I took 2 from the 5 to make 10, and then I had 3 left." Your adult brain wants to say: sweetie, just add it and carry the one. I get it. "Carry the one" still lives rent-free in my head too, and I do this for a living.
Why the homework doesn't say "carry the one" anymore
Most elementary math now starts with number sense and gets to the standard algorithm later. Kids spend real time on what numbers are made of: tens, ones, near-tens, doubles, all the little shortcuts adults use without ever naming them.
The algorithm still comes. In most schools kids meet it formally somewhere around 3rd or 4th grade, depending on the district. Nobody took "carry the one" out back and buried it behind the soccer field.
But when your child is halfway through a mental strategy, "just carry the one" scrambles it. If they're solving 47 + 35 by thinking "47 needs 3 to get to 50" and you jump in with columns, you've switched languages mid-sentence. They're reading a recipe and you've started giving GPS directions. Both useful. Not at the same time.
And here's the trick nobody tells you: the 1 you "carry" isn't a floating magic 1. It's one ten. Kids who know that can fix their own mistakes later. Kids who don't stare at the worksheet like it personally betrayed them. If the whole homework page looks like a foreign language, the new math homework translator covers the vocabulary; this piece is about the four strategies you'll see most.
Make a ten (and its cousin, make a hundred)
"Make a ten" is usually the first strategy kids can explain out loud, even if it comes out sounding like a tiny accountant having a rough day.
Take 8 + 5. Your child sees 8 is close to 10 and needs 2 more. So they break 5 into 2 and 3: 8 + 2 is 10, plus 3 is 13. That's what "I took 2 from the 5" means. Nothing was stolen. The 5 got split into useful parts.
The ten-frame is what they're picturing: a little grid of ten spaces, two rows of five. Eight filled, two empty and waiting. Add 2, the frame fills, the rest is easy. Some kids see it so clearly they'll draw it in the air with a finger.
The same move grows up into "make a hundred," or "get to a friendly ten." For 47 + 35: 47 needs 3 to reach 50, so break 35 into 3 and 32. 50 + 32 = 82. No carrying, no columns, just place value doing its job.
The parent line that works: "What number were you trying to make?" If they say 10 or 50 or 100, you're in make-a-ten territory and you know how to listen.
Compensation: change the problem, then fix it
Compensation is the one that makes adults say "oh, I do that." Yes. You do. You've just never had to write a paragraph about it under a cartoon pencil.
You change one number to make the problem easier, then fix the change. 39 + 26: 39 is annoying, 40 is friendly. So 40 + 26 = 66, then take back the 1 you added. 65.
Subtraction too, and this is where the grown-up shopping brain kicks in. Something costs $19, you think "basically $20" and adjust. 52 − 19: subtract 20 to get 32, then add 1 back because you took one too many. 33.
Kids love compensation once it clicks, because it feels like cheating in the best possible way. The place they forget is the fix. They make 39 into 40, get 66, and proudly stop. Or they subtract 20 instead of 19 and never add the 1 back. My own 4th grader did this for about three weeks straight.
When it happens, skip "no, that's wrong." Try: "What did you change? How do you fix it?" Those two questions do more than a page of arrows. If your kid is also wobbly on what tens and ones actually mean, compensation will feel like a magic trick rather than math, and place value explained is the piece to read first.
Friendly numbers and decomposing
"Friendly numbers" are the ones that are easy in your head. Tens, fives, hundreds. Anything ending in zero is the golden retriever of elementary math.
"Decomposing" means breaking a number apart. It sounds fancy because curriculum writers can't help themselves, but it's place value said out loud. 48 + 27: split both into tens and ones. 40 + 20 = 60, 8 + 7 = 15, 60 + 15 = 75. Not new math. Not suspicious math. The number showing its bones.
Multiplication uses the exact same idea. A kid who knows 6 × 5 but not 6 × 7 yet can break the 7 into 5 and 2: 30 + 12 = 42. That's the distributive property, which sounds like it should come with a filing cabinet. At this age it's just "break the hard fact into facts you know."
A short glossary for the homework directions, which are sometimes allergic to plain English:
- Decompose: break apart. Compose: put together.
- Friendly number or benchmark number: an easier number to work with, usually a ten.
- Partial sums: add the pieces, then combine.
- Use place value: think tens and ones, not just digits.
If the worksheet has boxes labeled tens and ones, it's asking your child to show this thinking. Is that necessary once they can do it in their head? No. Some worksheets are like asking a kid to explain how they chew toast. But for a stretch, writing the parts down is what makes the idea stick, and the strategies are also what turn slow counting into real math-fact fluency later.
The one question that beats "here's how I'd do it"
The best question is boring and powerful: "How did you think about it?"
Not "why did you do it that way," which sounds like cross-examination to a kid who's one eraser tear from collapse. Ask it like you're curious, because you are: you're trying to find the road they took.
Then stop talking. Truly. Ten full seconds. I say this as someone who has filled that silence too early more times than I'd like to admit.
If the answer is right but the method is odd, let them finish. "I did 40 + 30, then 7 + 5, then 70 + 12." Great, that works. You can say, "So you broke both numbers into tens and ones." You just gave their method a name, and named things are easier to use again.
If the answer is wrong, don't replace their thinking with yours. Find the step that slipped. For 39 + 26 a kid might say, "I made 39 into 40, and 40 + 26 is 66." You: "Good friendly number. What did you change to get 40?" Them: "I added 1." You: "So what happens to the 66?" They'll often land on 65 by themselves, and that moment is worth more than your neat twelve-second explanation. There's more on staying in the helper seat in math homework help without taking over.
Sometimes their method is faster than yours. This is mildly rude of them, but we survive it. If your kid does 98 + 37 as "100 + 37 is 137, minus 2 is 135" while you're still lining up digits in your head, say "that was efficient" and go stir the pasta with your dignity intact.
The one time to step in harder: if the assigned strategy is causing real tears for several nights running, send the teacher a short note. Not a manifesto. "We're practicing make-a-ten at home and it's causing a lot of frustration. Do you want them to keep showing that method right now, or is another strategy okay while it develops?" That's rare, but it's real. Some kids need more time with one strategy. Some need permission to use the method that makes sense to them while they keep learning the school's language for it.
