52 minus 37 equals 25? The “smaller from larger” subtraction error
Why children subtract the smaller digit from the larger in each place, how teachers can spot this subtraction error and what helps in maths lessons.
In brief: If a child works out 52 − 37 = 25, they have subtracted the smaller digit from the larger one in each place: 5 − 3 = 2 in the tens and 7 − 2 = 5 in the ones. The error only occurs in calculations that cross a ten, and it follows a fixed rule the child has made up for themselves. Exchanging with concrete materials, the jump strategy and checking with the inverse operation can help. Mazio Math recognises this pattern during practice and, if it becomes frequent in the class, shows you a class flag with a support card once a week.
This error is common in grades 2 and 3 and easy to overlook. The answer looks reasonable, and the child calculates correctly when no ten is crossed. This article shows teachers how to recognise the error reliably, where it comes from and how to address it in lessons.
What the error looks like
The child treats each place separately and always subtracts the smaller digit from the larger one, whether it is at the top or the bottom. In calculations that do not cross a ten this goes unnoticed, because the larger digit is at the top anyway.
| Calculation | Child’s working | Child’s answer | Correct |
|---|---|---|---|
| 43 − 7 | 7 − 3 = 4, the 4 tens stay | 44 | 36 |
| 52 − 37 | 5 − 3 = 2, 7 − 2 = 5 | 25 | 15 |
| 81 − 46 | 8 − 4 = 4, 6 − 1 = 5 | 45 | 35 |
| 524 − 168 | 5 − 1 = 4, 6 − 2 = 4, 8 − 4 = 4 | 444 | 356 |
| 65 − 23 | 6 − 2 = 4, 5 − 3 = 2 | 42 | 42 |
The last row shows why the error can go undetected for so long. When no ten is crossed, the wrong rule produces the correct answer. An answer to 43 − 7 that is larger than 43 is a sure sign.
The error occurs in informal written methods and in column methods. The handout for the PIKAS diagnostic assessment on informal written subtraction to 1000 (in German) states that crossing a ten can lead to errors with the jump strategy and above all with the split strategy, where tens and ones are calculated separately. The KIRA interview guide on column subtraction (in German) lists “always larger digit minus smaller digit” as a typical error.
Where the error comes from
- Calculating place by place with no plan for crossing the ten. A child who works out 52 − 37 as 50 − 30 and 2 − 7 faces a calculation in the ones that they think cannot be solved. Turning it round to 7 − 2 looks like a way out.
- Carrying over swapping from addition. In addition you can swap the numbers. Some children assume the same applies to subtraction.
- Digits instead of numbers. The child sees 5 and 2 instead of 50 and 2. Without an idea that a ten can be exchanged for ten ones, the only option left is to turn the calculation round.
- “You can’t do that.” The sentence “You can’t take 7 away from 2” from earlier lessons sticks, without it being clear what to do instead.
How to probe diagnostically
- Set pairs of calculations. Give calculations with and without crossing a ten, such as 65 − 23 and 62 − 25. If only the second one is wrong, this pattern is very likely.
- Ask the child to think aloud. “Work out 52 − 37 for me and say every step.” Listen for whether the child says “7 minus 2” in the ones.
- Check with the inverse operation. “Work out 25 + 37.” The child gets 62 and notices that something is wrong. Then ask where the mistake is.
- Estimate. “Roughly how much is 52 − 37?” A child who estimates 50 − 40 = 10 sees that 25 is too large.
- Model it with materials. “Make 52 with tens rods and ones and take 37 away.” This shows whether the child thinks of exchanging a ten.
What helps in lessons
- Exchanging with materials. With tens rods and ones cubes or in a place value chart, exchange one ten for ten ones before subtracting. Only then add the written digits.
- Jump strategy. 52 − 30 = 22, then 22 − 7 = 15, with an intermediate step via 20. The jumps can be drawn on an empty number line.
- Counting up. From 37 to 40 is 3, from 40 to 52 is 12, making 15 altogether. When the numbers are close together, this is often the easier way.
- Spotting errors. Children check other people’s calculations such as 81 − 46 = 45 and explain what went wrong. This sharpens their eye for their own working.
- Checking as a habit. After every subtraction that crosses a ten, do the addition as a check.
The jump strategy for calculations that cross a ten is not the right approach for every child. The aim is for children to know several methods and to choose the one that suits the calculation.
How Mazio Math makes the error visible
Mazio Math is a learning platform for maths lessons in primary school. While the children practise, Mazio Math evaluates every answer. Mazio Math assigns wrong answers to known error patterns using fixed rules. Subtracting the smaller digit from the larger in subtraction that crosses a ten is one of the patterns for which you can receive a class flag.
The class flag. Once a week, Mazio Math checks for each class whether a common misconception shows up in the wrong answers. On the dashboard home page, “Misconceptions” collects the flags from all your classes. “Matching suggestion” moves the content that fits the error to the top of the shelf, and “In results” takes you to the detailed evaluation.
The support card. It explains the misconception with an example and background, lists steps for the class under “In the classroom” and suggests units and Knobelbox tasks under “Matching content for the board”. You choose which content to put on the class board. Whether you act on the flag is your decision.
For the child. When a child makes a mistake, the learning assistant Mazio helps directly in the task, with a question, with highlights in the picture and, if needed, with a given partial step. He does not give the solution.
Practice in the Basiscamp. For grade 2, the Basiscamp practises in the world “Addition and subtraction to 100”, with the section “Bridging ten”. For grades 3 and 4 there is “Addition and subtraction to 1000” and separate sections on column methods. An exercise only counts as completed when several tasks in a row are solved at the first attempt and without help.
An example from the classroom. A grade 3 class has been working with numbers up to 1000 for two weeks. One morning the home page shows a flag that the smaller digit is being subtracted from the larger in subtraction that crosses a ten. The teacher opens the support card, starts the lesson with three calculations on the classroom whiteboard for the children to check, and has them exchange tens with materials at their desks. The teacher then places the suggested content and an exercise from the Basiscamp world “Addition and subtraction to 1000” on the class board as compulsory, with the note “Do a check for every calculation”. The difficulty adapts to each child’s previous work.
More on calculation methods can be found on the topic page on informal written methods (in German) and the topic page on bridging ten (in German). The article on errors with exchanging and zero in column methods describes what the same error looks like in methods with carrying and exchanging. Mazio Math is free for teachers: create a free account. Using it with a class is currently available to schools in Germany; if your school is in another country, registration records your interest.
Frequently asked questions
Why does a child get answers that are too large in subtraction?
Often the child subtracts the smaller digit from the larger one in each place. In calculations that cross a ten, this gives an answer that is too large. Put calculations with and without crossing a ten side by side and have the child check with the addition.
Which method helps with the “smaller from larger” error?
The jump strategy and counting up avoid the problem in the ones. In the long term, however, the child needs to understand that a ten can be exchanged for ten ones. Materials in a place value chart help with this.
Is the error a sign of dyscalculia?
Not in itself. It is common and can usually be resolved with targeted support. If it persists despite support and other difficulties appear as well, for instance with place value, a specialist assessment makes sense.