In every subject, there are common errors students make. Mathematics is no different. Here I’ve listed 10 common mistakes students make when solving mathematics problems.
(1) Incorrect order of operations
Example
Calculate 5 + 3×2
Correct is 11 as multiplication must be done before addition.
Common error
would be to add 5 and 3 first then multiply by 2.
If that error is made then the wrong answer is 16.
(2) Forgetting what power notation means
Example
Calculate 23 + 7
Correct
23 = 2×2×2 = 8
8 + 7 = 15
Common error
Not knowing what 23 means and either thinking it is 23 or 2×3 = 6.
If these errors were made the answers would be 30 or 13.
(3) Forgetting that two brackets side by side should be multiplied.
Example
(5 + 4)(2 + 7)
Correct
(5 + 4)(2 + 7) = (5 + 4)×(2 + 7) = 9×9 = 81.
Common error
Use =, – or ÷ to connect the brackets so the calculation becomes
(5 + 4)+(2 + 7) = 18
(5 + 4)-(2 + 7) = 0
(5 + 4)÷(2 + 7) = 1
(4) Adding and subtracting fractions incorrectly
Example
Do this calculation
Correct
Incorrect
Common error is to just add or subtract the numerators and denominators.
This would be incorrect.
(5) Thinking 1 is prime
A prime number has exactly two factors. 1 has only one factor.
(6) Finding the original price from a sale price
Example
In a sale all prices were reduced by 10%. What was the pre-sale price of something that sold for $90 in the sale?
Correct
Let the pre-sale price be p.
p – 10%p = 90
0.9p = 90
p = 90÷0.9
p = 100
Pre-sale price was $100.
Incorrect
Pre-sale was 90 + 10%90 = 99
Common error
Adding instead of dividing
(7) Cancelling incorrectly
Example
Calculate
Correct
Incorrect
Common error
Splitting the fraction prematurely
Cancelling should only be done when there is multiplication
Example
As in the above example
(8) Confusing multiples with factors
Example
Write down the factors of 14 and the first 4 multiples of it.
Correct
The factors of 14 are those whole numbers which divide into it without a remainder. They are 1,2, 7, 14.
Multiples of 14 are numbers which arise by multiplying other whole numbers apart from 0 by 14. The first 4 multiples of 14 are 1×14 = 14, 2×14 = 28, 3×14 = 42 and 4×14 = 56.
(9) Interpreting the algebraic expression xy wrongly.
Correct
xy = x × y
xy ≠ x + y
xy ≠ x – y
xy ≠ x ÷ y
(10) Using the √ in trying to solve a quadratic equation
Example
Solve x2 = 3x + 4
Correct
x2 = 3x + 4
hence x2 – 3x – 4 = 0
hence (x – 4)(x + 1) = 0
x = 4 or x = -1
Incorrect
x2 = 3x + 4
hence x = √(3x + 4)
All sorts of errors then follow.
How to avoid these errors? Practice, practice and more practice!! There may be some tricks to help such as remembering the order of mathematical operations by the mnemonic (word) BEDMAS
which means Brackets first, Exponents(powers) next, Division and Multiplication next then Addition and Subtraction. However in the end basic mistakes are avoided by a lot of practice.
Great set of tips! This article is bound to help lots of budding mathematicians!
I appreciate you creating Student Shed. I am looking forward to assisting my son prepare for his B.J.C exams come 2019. I just hope and pray he stays the cause. Your explanation of common errors that students make is meaningful. Our kids need to pay attention to what the question is asking them to solve, look carefully at how the numbers are written and pay attention to how they prepare their step by step explanation for their answers. I would appreciate you explaining the quadratic equation a little more. Break it down or give several examples please. Thank you so much for your kind assistance.
Patricia