Careless mistakes are perhaps the most painful of any Math mistakes…
Careless mistakes don’t discriminate if you’ve spent many hours studying and practicing.
When it happens, you lose the marks regardless of the hard work you’ve put in before test, and regardless of your level of competence and understanding of the subject.
And losing such precious marks could be the difference between a pass and a fail, or an A or a B grade.
So before we start solving the problem of careless mistakes, we need to first understand the various types of mistakes.
We’ve produced a list of the most common careless mistakes done in Primary School Math.
We call them the ‘7 Deadly Math Sins’…
Be careful when reading your Problem Sum questions, especially the long questions.
Don’t rush to interpret them and make sure your answer is what they are looking for.
How To Avoid Deadly Math Sin #1:
A tip to avoid this is to highlight/ underline/ circle the keywords and objective of the question.
A Process that we like to teach our students is our F.O.C.U.S process (explained below).
Although this might seem like a rather silly mistake to make, it does happen under timed, or exam stress conditions.
The “copy-wrongly” mistake is caused by a transfer error – or when the brain reacts ahead of the eye and the hand, and assumes a number incorrectly.
This causes students to transfer the number wrongly or to write the number in a wrong sequence.
The error could be when transferring the number from question to workings. Or from one step of the workings to the next one.
The question states:
“Johnny had 69 apples and 98 pears.”
“Johnny had 96 apples”
3 units → 69 apples
1 unit → 96 ÷ 3 = 32 apples
How To Avoid Deadly Math Sin #2:
Highlight or circle the relevant numbers before copying them over.
Also, if you know that you have done this error before, you can take a little more time to be extra careful when transferring numbers, and transfer each digit, one at a time.
This is the error of forgetting to write the units in the answer of a problem sum
Using the wrong units while doing your workings.
How To Avoid Deadly Math Sin #3:
Type #1: Forgetting to write the units in your answer
This can be avoided by doing a quick check after you’ve done the entire paper.
Just flip through all your solutions, and ensure that there is a unit at the end of each answer.
Just assume that EVERY answer requires a unit, and if the answer really doesn’t, you can indicate in your working column (or in pencil) that no unit is required.
Type #2: Using wrong units in your workings
To avoid this, before even starting on your workings, check that you convert the figures to the same units FIRST.
You can even write it in pencil beside the questions right after reading the question for the first time.
Be EXTRA careful when more than 2 conversions are required.
For example, convert all m (meter), to cm (centimeter), and back again to m (meter).
Also, it’s a good habit to write the units in each step of your workings.
So it can remind you what the units are, and that the answer at the end should include the units.
You’d be surprised – this mistake actually happens more often to students who are used to scoring high marks in their exam papers.
Yes – even students who can score really high marks do make careless mistakes.
And this happens when you get a little overconfident, assume that the answers that you write are usually correct, and get slightly complacent in writing down all the steps.
Some students might think that “skipping” steps would help them complete the questions faster.
However, skipping steps can result in errors.
It’s worse when the errors are in the early part of the solution, thereby affecting all the following steps in the solution.
For example, this is one scenario where an error often occurs:
2(u + 4) = 24
2u + 4 = 24
2u = 20, therefore u = 10. Wrong
In the above, multiplication was not applied to the ‘4’ in the brackets – a common mistake.
How To Avoid Deadly Math Sin #4:
One way of avoiding this is to insert a step to remind you to apply the multiplication to all items in the brackets, i.e.
2(u + 4) = 24
(2*u + 2*4) = 24
2u + 8 = 24
2u = 16, therefore u = 8. Correct!
Skipping steps also makes it more difficult to find out where the error is when you come around to check your answers.
On the flip side, while writing down each step clearly may take a few more seconds, it would lower the chance of a careless mistake significantly.
What’s more, you’d get method marks (even if you do have a wrong final answer), and it will be much easier to check your solution.
So for students who are used to scoring high marks, or students who like to finish their math paper much faster than the allotted time, one key thing to remember is:
You do not get extra marks for finishing first.
You get your full marks from getting your solution steps (i.e. your working), and your answers correct.
So take the time to write down all the steps clearly.
It will be worth the time.
This is the opposite of the above mistake (Deadly math Sin #4)
Sometimes a complicated or difficult question appears in the earlier part of the paper.
Some students feel the need to solve that question before moving on to the next question.
However, this might take up too much time and leave very little time for the student to finish the other questions – which could be much easier to solve!
How To Avoid Deadly Math Sin #5:
A good tip to remember is:
If the question is 3 marks, you should only be spending 3 minutes on it.
If you’ve exceeded 3 minutes, move on to the next question.
You can come back to this question again once you’ve done all the easier questions that you can solve.
Similar to Math Sin #4: The Skipping Steps mistake, this happens more often to kids who like to do their work very fast, and typically get higher scores than their peers.
This mistakes stems from being too overconfident, and therefore complacent when it comes to checking.
You do not get extra marks for finishing first.
You get your full marks from getting your solution steps (i.e. your working), and your answers correctly, without any errors.
How To Avoid Deadly Math Sin #6:
To help ensure you don’t make any mistakes, always do a reverse-check
(Refer to Deadly Math Sin #7: Check Using The Same Method Mistake, below)
It’s great that you’re checking your answers.
However, checking your answers using the same method may cause you to repeat the careless mistake.
How To Avoid Deadly Math Sin #7:
To make the most of your “checking” time, always check your working using the Reverse-Check method.
With this, put your answer back into the equation to check.
Many don’t do this when they are rushed for time, but this is often faster than going through the working again.
Based on the previous example above:
2(u + 4) = 24
Let’s say you did the “Skipping Steps” mistake and got the answer: u = 10.
You can easily check by replacing u with 10 in the equation:
2(10 + 4) = 2 14 = 28 ≠ 24
So using the reverse check method, you know for sure that the answer u = 10 is wrong.
If you have gotten the answer u = 8, then…
Applying the reverse-check method:
2(8 + 4) = 24
And you find that the answer is correct!
F – Find Keyword & Numbers
O – Objective (what is the objective of the question?)
C – Concept (what concept is this question based on?)
U – Units (remember to circle and convert all to the same units, and write the units in the working and answers)
S – Solve and Check
|Months before PSLE/ SA2||Action Steps|
Practice on the Concepts that you’re weaker at, and make sure you totally understand them. Refer to the Math Concept map of the 11 Concepts that will be tested in PSLE Paper 2 below this table.
Seek help from teacher/parent/coaches if you do not understand some concepts.
|3-2 Months||Practice on Concepts that you’re good at, and make sure you can get it all correct within the time limit.|
|3-2 Months||Do practice/ mock exams. Practice questions from past Prelim and PSLE papers within a timed condition. It’s best if you have a parent/coach with you to ensure you stick to the timing, and to review with you how you could have done better during the mock exam.
(to find out about Math Scholars’ Mock Exams, click here)
Look through the mistakes that you’ve done in the past and in your mock exam. Go through the corrections, and ensure that you can solve them correctly this time!
Get adequate rest, and stay in tip top health!
It is a good idea to keep a notepad or clipboard where you keep track of the common mistakes you make – whether in Maths, Science, English etc. For English, this is especially useful if there are some common errors that you have a tendency to repeat e.g. using It instead of It’s, complement instead of compliment or every day instead of everyday.
Very often, a good way to double-check is to see if your answer makes sense. If not, double check your problem-solving procedure. However, don’t panic if you think your answer doesn’t make sense. If you are sure of the method you have used, stick with the answer.
Here’s a checklist that you can download and print:
(For a printable version, click HERE)
|7 Deadly Math Sins
(Math Careless Mistakes that I can Conquer!)
|I need to overcome this!||I never do this|
|Deadly Math Sin #1: The “Misread the Question” Mistake|
|Deadly Math Sin #2: The “Copy-Wrongly” Mistake|
|Deadly Math Sin #3: The “Missing/Wrong Units” Mistake|
|Deadly Math Sin #4: The “Skipping Steps” Mistake|
|Deadly Math Sin #5: The “Stuck On One Question For Too Long” Mistake|
|Deadly Math Sin #6: The “Do Too Fast and Don’t Check” Mistake|
|Deadly Math Sin #7: The “Check Using The Same Method” Mistake|
Want to know where your child struggles in math…and how to fix it?
Who Makes Careless Mistakes?
The answer is – simply, EVERYONE.
It is not just the Primary school students.
We adults do it all the time, too.
Interestingly, our propensity to succumb to careless errors actually increase with our level of understanding of the subject matter!
The reason is due to over-confidence.
Studies have proven that smarter children are more prone to careless mistakes, simply because they make computations based on approximation to what they already know.
For example, for the following equation:
4 + X = 6
the common made mistake is X = 10, because our minds is trained to immediately associate the numerical operators with the operation that we need to conduct.
If we want to help our children, we must be able to distinguish the exact stage where the error occurred, instead of simply labelling everything as CARELESS MISTAKES.
While it is true that Reading and Comprehension errors could also be due to carelessness arising from anxiety or time pressure, we must give our children the benefit of doubt that they really did not understand the words or question, and work on ways to help them improve in these areas.
Generally, only encoding errors should be classified as “careless”, but even that depends on whether the child has been properly instructed to present his/her answer in the acceptable manner.
All other kinds of errors show a lack of understanding of the problem-solving concept, which has nothing to do with carelessness.
When that occurs, we have to do what we can to enlighten the child instead of simply dismissing it as a careless mistake, which might have the child thinking that he/she might really be “stupid” after all, leading to loss of confidence and even dislike for the subject or topic.
All the best!
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Helping kids love learning,
Math Scholars Program Manager
Has your child been making these careless mistakes? Do you have other useful tips you’d like to share?
Let us know in the comments below!