Why your child's math homework looks nothing like yours (and why it's fine)

The ten-frames, number bonds, open number lines and area models on your child's homework are not a new way to get the answer. They're the method you learned, taken apart so the reasons show. When you "carry the one," you are making a ten; when you do long multiplication, you are adding up the pieces of an area model; the homework just makes the child look at those steps before it lets them hide inside a shortcut. You can still say 7 + 5 is 12. The worksheet is asking for something different: how you know, in a form that will still work at 70 + 50, 0.7 + 0.5 and 7x + 5x.

Here's what the five most common pictures are for, in the order children meet them, with what to say when your child asks for help and you don't recognize the page.

Why can't I just say 7 + 5 is 12?

You can, and if your child knows it, they should. The standards most states use ask that first graders add within 20 "using strategies" and name them: counting on, making ten, using the link between addition and subtraction, and turning a fact into one you know (6 + 7 is 6 + 6 + 1). The point was never that 12 is hard to get. It's that a six-year-old who can only get 12 by recall or by counting has no way to get 70 + 50, or 7/10 + 5/10, and a child who has seen 7 + 5 as "7 and 3 is 10, and 2 more" does all three with the same move.

A mother's video asking exactly this question ("Why can't I just say 7 + 5 is 12?") went viral in December 2025, and her own conclusion after the teacher walked her through it was that she understood the reasoning and could see how it would help with algebra; she still thought it was early for a six-year-old. That is a fair place to land. The methods are not harder than the ones we learned. They are earlier.

Ten-frames (kindergarten to 2nd grade)

What it is: a two-by-five grid of boxes. Counters go in the boxes, filling the top row first.

What it's for: making ten visible. A child who sees 8 in a ten-frame sees two empty boxes, so 8 + 5 becomes "fill the two, then 3 left over: 13" without counting thirteen things. It's also how children learn that 13 is a ten and three, which is place value, which is the rest of elementary math.

What it replaces: nothing. You never had this one. You were handed "carry the one" and told to trust it; the ten-frame is the part that was left out.

Number bonds (kindergarten to 1st grade)

What it is: a number in a circle with two smaller circles under it: 10 at the top, 7 and 3 below. Sometimes drawn as a "part-part-whole" box.

What it's for: seeing that numbers are made of parts. A child who knows the bonds of 10 (1 and 9, 2 and 8, 3 and 7...) has the make-ten strategy, and subtraction stops being a separate thing: 10 − 7 is "7 and what makes 10?" The standards say exactly that: understand subtraction as an unknown-addend problem. Whether 7 goes in the left circle or the right doesn't matter; a journalist who snapped "just put the number in any circle" at her six-year-old turned out to be right about that and wrong to be annoyed.

What it replaces: the addition and subtraction fact tables, learned as two unrelated lists.

The open number line (1st to 3rd grade)

What it is: a line with no tick marks. The child writes a starting number and draws hops: for 47 + 36, a hop of 30 to 77, then 3 to 80, then 3 to 83.

What it's for: adding and subtracting in your head the way adults do. Nobody computes change at a store by stacking digits; they count up: "from 17 to 20 is 3, to 40 is 20, to 42 is 2, so 25." The open number line is that, written down, and it's the method that makes mental math possible. It's also the standards' preferred tool for fractions and for elapsed time, so a child who's fluent with it in second grade has a tool for fifth.

What it replaces: nothing again, but it sits next to the column method as a second route and a way to check it.

Decomposing and the "box" (2nd to 3rd grade)

What it is: 47 + 36 written as (40 + 30) + (7 + 6) = 70 + 13 = 83. Sometimes drawn as a box with tens and ones in separate cells.

What it's for: this is the column method, with the carry explained. In the column method, the 1 you carry is the ten from 7 + 6 = 13, moved to the tens column. Decomposing says so. The standards for second grade ask children to add and subtract within 1,000 using "strategies based on place value" and to explain why they work, and they don't ask for the standard written method to be fluent until fourth grade. The written method comes; it comes after the child knows what it's doing.

What it replaces: "carry the one," which most of us could do and few of us could explain.

The area model (3rd to 5th grade)

What it is: a rectangle split into parts. For 23 × 14, the sides are 20 + 3 and 10 + 4, and the four inner rectangles are 200, 80, 30 and 12; add them for 322.

What it's for: showing that multiplying two-digit numbers means multiplying every part by every part. The standards for fourth grade ask children to multiply using place value and to "illustrate and explain" with equations, arrays or area models. Long multiplication does the same four products in a particular order and lines them up in columns; the area model does them where you can see them. Five years later, the same rectangle multiplies (x + 3)(x + 4), which is why algebra teachers like children who've seen it.

What it replaces: long multiplication, temporarily. The written method is still taught; it's taught as a shorter way to write the rectangle.

What should I do when I don't recognize the method?

Four things, none of which require learning the method yourself first.

Ask the child to teach you. "Show me how your teacher does it." A teacher quoted on exactly this problem said the same: ask your child to teach you the method. Teaching it is the best practice they'll get, and you find out whether they understand it.

Don't trade methods mid-problem. Showing the way you learned is fine, with the words "here's another way," after they've done it the school's way. Swapping methods in the middle of a worksheet produces a child who half-knows two methods.

Don't review the method in front of the child. "I hate this new math" lands on the child, who has to do it tomorrow with the teacher who taught it. Keep the opinion for the adults, and ask the teacher for the parent guide most schools have.

Ask the teacher early. The journalist above waited months before asking what number bonds were. The teacher would have explained it in two minutes in September.

And if the homework ends in tears, the method is rarely the cause; what to say when your child cries over math homework covers that moment, and how to help when you're bad at math yourself covers the version where the parent is the one who's lost.

Is there evidence these methods work?

Some, and it's worth being precise about what it shows. The federal What Works Clearinghouse guide for elementary students who struggle with math gives a strong-evidence rating to two recommendations that are these methods by another name: use a well-chosen set of concrete and visual representations, and use the number line to teach concepts and procedures. What the evidence doesn't show is that the pictures work on their own; the same guide pairs them with explicit instruction and plenty of practice, and a child who draws ten-frames forever without ever moving to recall is as stuck as one who memorized without understanding. The pictures are scaffolding. The standards expect the written methods to arrive, by second grade for the facts and fourth for multi-digit arithmetic. Judge a classroom by whether the scaffolding comes down on schedule, not by whether it went up.

These models are also how Mathwell teaches: addition on ten-frames, carrying shown as ones gathering into a ten, multiplication as arrays, fractions as shares, with the Tutor reading each problem aloud and offering a smaller step rather than the answer when the child is stuck. Mathwell is a browser-based K–5 math tutor that reads every problem aloud and teaches with hints instead of answers; a parent who's never seen a ten-frame can sit beside the child and learn the method from the same lesson. Anyone can try the demo lesson without signing up; after that there's a 7-day free trial with a card on file, then $19 a month, $99 a year, or $169 for a three-year K–5 pass. It's for kindergarten through fifth grade only, and the child answers by tapping or typing, not by speaking.