New math methods explained for parents

The methods your child brings home are the column methods you learned, slowed down so that every step can be seen. Each one below has a small worked example, the reason schools teach it, and the line that connects it to the way you were taught.

9 minute read · Updated October 5, 2026

You may recognise this: your child is stuck on 23 × 14, so you set it out the way you were taught, two rows and a line. They watch for a moment and say, "That is not how we do it. We have to draw the box." You know the answer is 322. You have no idea what the box is. Here is each method you are likely to meet, with the numbers worked through.

Why is math taught differently now?

Math is taught with these methods so that children understand why a procedure works before they shorten it. England's Education Endowment Foundation puts it this way: "Pupils are able to apply procedures most effectively when they understand how the procedures work and in what circumstances they are useful." The standard column methods are still taught.

The same guidance says understanding lets pupils "reconstruct steps in a procedure that they may have forgotten". A child who knows that the little 1 above the tens column is a ten can rebuild a rule they have forgotten.

What are number bonds?

Number bonds are the pairs of numbers that make up another number: 6 and 4 make 10, and so do 7 and 3. Children learn the bonds to 10 first, then use them to add across ten by splitting one number, so that 8 + 5 becomes 8 + 2 + 3.

8 + 5
8 + 2 + 3       split the 5 into 2 and 3
10 + 3          8 and 2 make ten
13

Why schools teach it: it replaces counting on fingers with a step a child can do in their head. How it connects: carrying in column addition is a number bond. When 8 + 5 in the ones column gives 13, the ten that is carried is the ten your child has just made.

What is regrouping?

Regrouping is the same thing as carrying and borrowing. It means trading ten ones for one ten, or one ten for ten ones, so that a column can be added or subtracted. Schools in England often call it exchanging, and the working on paper is unchanged.

    4 12
    5  2
  - 2  7
  ------
    2  5

Why schools teach it: "borrow" suggests something is given back, and it never is. "Regroup" says what happens: 52 is still 52, written as 40 and 12. How it connects: nothing changes on the page.

You may also hear partitioning: splitting a number by place value, so 52 is 50 and 2. If this is where the slips happen, see carrying and borrowing mistakes.

What are partial sums?

Partial sums is a way of adding where each place value is added separately and written down in full, and the pieces are added at the end. For 47 + 38 a child adds the tens to get 70, adds the ones to get 15, and then adds 70 and 15 to get 85.

    4 7
  + 3 8
  -----
    7 0      40 + 30
    1 5       7 + 8
  -----
    8 5

Why schools teach it: nothing has to be held in the head, and the child can see that the 4 in 47 means 40. How it connects: look at the 15. In the column method you write its 5 under the ones and carry its 1 to the tens. That carried 1 is the ten inside the 15, and 7 tens plus that ten is the 8 in 85.

What are the area model and partial products?

The area model, also called the box or grid method, multiplies two numbers by splitting each into tens and ones and multiplying every pair of parts. The four answers are the partial products, and adding them gives the total. For 23 × 14 the parts are 200, 30, 80 and 12, which make 322.

          20      3
       +------+------+
   10  | 200  |  30  |
       +------+------+
    4  |  80  |  12  |
       +------+------+

   200 + 30 + 80 + 12 = 322

Written as a list instead of a box, the same four answers are the partial products method.

      2 3
    × 1 4
    -----
      1 2      4 × 3
      8 0      4 × 20
      3 0     10 × 3
    2 0 0     10 × 20
    -----
    3 2 2

Why schools teach it: no part can be forgotten, because every box must be filled, and the child sees that the 1 in 14 means 10. The US Common Core standards for Grade 4 describe multiplication as illustrated with "equations, rectangular arrays, and/or area models". How it connects: long multiplication has two rows where this has four. The first row, 23 × 4 = 92, is the 12 and the 80 added together. The second row, 23 × 10 = 230, is the 30 and the 200. And 92 + 230 = 322.

What are partial quotients?

Partial quotients is a way of dividing by taking away easy multiples of the divisor until nothing is left, then adding up how many were taken. In England it is often called chunking. For 156 ÷ 4 a child might take away 30 fours, then 9 fours, and add 30 and 9 to get 39.

  4 ) 1 5 6
    - 1 2 0      30 × 4
    -------
        3 6
    -   3 6       9 × 4
    -------
          0

  30 + 9 = 39

Why schools teach it: the child chooses multiples they are sure of, so a shaky 4 times table does not stop them, and every line is a real subtraction they can check. How it connects: long division is partial quotients with the largest possible chunk taken each time and the zeros left unwritten. The 3 written above the tens in long division is this method's 30.

What is the bus stop method?

The bus stop method is the name used in England for short division. The number being divided sits under a bracket that looks like a bus shelter, and the divisor waits outside. You divide one digit at a time from the left and carry each remainder to the next digit.

    0   3   9
    ---------
4 ) 1  ¹5  ³6

Why schools teach it: it is the quickest written way to divide by a single digit. England's national curriculum names "the formal written method of short division" in Year 5. How it connects: this is the division you were probably taught. Long division is the same idea with the subtractions written underneath, which is needed once the divisor has two digits. See long division step by step.

When do schools teach the column methods I learned?

Schools still teach the standard column methods, and the curriculum documents name the year for each. England's national curriculum names column addition and subtraction in Year 3 and long division in Year 6. The US Common Core standards name the standard algorithm in Grade 4 for addition and subtraction, Grade 5 for multiplication and Grade 6 for division.

In the US standards these are the grades where a child is expected to be fluent with the standard method, which is not the same as the first time they see it. A guide from the Massachusetts education department says nothing in the standards prohibits teaching the standard algorithm earlier. For the full list by grade and year, see math by grade.

Will showing my child my way confuse them?

You can show your child the column method: it is in the curriculum, so it is where the school's methods are heading. The timing matters, though. On a night when they are stuck, help with the method the school set, and show yours afterwards as a quicker way of writing the same answer.

Jason Zimba, a lead writer of the Common Core math standards, gave parents this advice in Education Week:

The most important rule as a parent is to make sure [homework] gets done. The math instruction on the part of parents should be low.

If your child is still stuck, write a note for the teacher instead of teaching a new method at nine at night: "We got stuck on the second row of the box. Which method should we practice at home?" More in how to end math homework fights.

Where Plusy fits

Plusy practices the column methods, the place these school methods lead to. A column question is drawn the way it is written on paper, with a box for each digit and carry or borrow boxes above for your child's own working.

When your child is stuck, Hint lights one column and asks a question. Show me fills in that single step and explains it, then hands the sum back. It never solves the whole question in one go. See hints and steps. Start free.

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