Once students reach the point where counting on their fingers is no longer feasible but still need to do math in their heads, having good, reliable mental math strategies is essential. These skills, when properly developed, give us the ability to solve math problems quickly and efficiently.
If you’re on the hunt for good mental math strategies, beware: there are a lot of unhelpful gimmicks out there! They claim to be effective strategies but really, they’re anything but. In this article, we will explore what exactly mental math is, discuss how to take the stress out of mental math, and offer some truly helpful strategies to improve mental math calculations.
What is Mental Math?
Before we tackle the question of how to do mental math, let’s clarify what, exactly, we’re talking about! As the name implies, the term mental math refers to skills which allow a person to solve math problems in their head—without help from a calculator, or pen and paper. Mental math mastery helps students learn and understand a variety of math concepts quicker and easier.
Mental math is actually the mathematical skill we most frequently use in everyday situations. Think about when you add up prices while grocery shopping, or when you need to determine how long it will take to get from one point to another. As these examples suggest, mental math is the act of solving everyday problems in your head.
(That focus on the everyday is important—mental math strategies are not going to help you solve complex algebraic equations or master differential calculus in an instant.)
Starting in kindergarten, students learn the foundations of mental math by memorizing simple addition and subtraction problems. As they progress through the elementary grades and into middle school, a firm grasp of these foundations becomes increasingly important as their math coursework becomes more complicated.
Taking the Stress Out of Mental Math
As far as academic performance anxiety goes, math anxiety has consistently proven itself to be the most prominent among school-aged kids. Unfortunately, this anxiety leads many students to identify with the myth of “I suck at math.” The added stress can also make it much harder for students to adequately complete mental math in school and at home. That’s why it’s so important to be armed with strategies for overcoming math anxiety.
Next, we delve into six handy strategies, all accompanied by mental math examples.
Mental Math Tips and Tricks
1. The Trick With “9”
When adding nine to any number, you can find your answer by adding ten and then subtracting one. (After all, ten minus one is equal to nine!)
For example, let’s use this rule to solve 67 + 9.
First, you would change the equation to 67 + 10 = 77.
Now, subtract 1: 77 – 1 = 76.
So, the answer to 67 + 9 is 76.
Another way of approaching this, which combines the two steps above, is to turn the “9” in your problem to a “10” and subtract one from the other term (thus 67 + 9 becomes 66 + 10 = 76).
One final variant of this strategy involves rounding each term up to the nearest multiple of 10.
In our math problem above, we know that 67 + 3 = 70 and 9 + 1 = 10.
Then, we add the differences (3 + 1 = 4) and the rounded terms (70 + 10 = 80).
Finally, we subtract the differences from the rounded terms: 80 – 4 = 76.
2. Adding “Doubles Plus One”
Students typically memorize doubles (a.k.a. the “2 times table”) early in elementary school. Once they have mastered that, the “doubles plus one” trick is a great extension useful in solving a plethora of other math problems.
Doubles plus one is a practical math trick to remember any time you need to add a problem like 8 + 9 or 111 + 112.
It’s important that students have their doubles memorized before attempting this mental math strategy. If not, they might struggle to notice that 8 + 9 is simply one more than 8 + 8
8 + 9 = ?
8 + 8 = 16
16 + 1 = 17
Thus, 8 + 9 = 17
This holds true for any “doubles plus one” equation, even ones using very large numbers. Let’s explain further with our example of 111 + 112.
111 + 112 = ?
111 + 111 = 222
222 + 1 = 223
Thus, 111 + 112 = 223
3. Using “Fact Families” for Subtraction
The next of our mental math strategies relies on knowledge of “fact families,” a term which refers to a group of math facts which use the same numbers (e.g. 2, 3, 5). If a student has a solid understanding of simple addition facts, they can use this practical math strategy to solve related subtraction problems.
Consider our example above, using the [2, 3, 5] fact family.
We know that 2 + 3 = 5; thus we also know that 5 – 3 = 2 and 5 – 2 = 3.
While this strategy comes in handy with subtraction problems for lower numbers, it can also be applied to slightly more difficult problems, like 65 – 43 = ?. To break this more complicated question down, we should first ask ourselves “what number needs to be added to 43 in order to equal 65?”
We know that 40 + 20 = 60 and 3 + 2 = 5.
So, we add 20 + 2 to get our answer of 22.
If 43 + 22 = 65, then we know that 65 – 43 = 22.
(More advanced mathematicians will notice that this strategy is also useful if you want to introduce basic algebra to students!)
4. Finding Five Times a Number
Now that we’ve covered some addition and subtraction strategies, there are a few great mental math strategies for solving multiplication problems too. The first of these strategies is the trick for finding five times any number.
In order to do this, all you need to do is multiply the number by 10 and then divide your answer in half. For example, let’s say you need to solve 5 x 63 = ?.
To find this answer, first, we calculate 63 x 10 = 630.
(Remember that to multiply any whole number by 10, you simply add a “0” to the end.)
Then, we divide our answer in two: 630 / 2 = 315.
Thus, 5 x 63 = 315.
5. Finding Four and Eight Times a Number
Like our previous strategy, this one involves using simple multiplication to solve more complicated multiplication problems. Note that in order to use this strategy, you need to have a solid understanding of doubling numbers.
When trying to solve for four times any number, you can instead double the number two times. For example, let’s say you need to solve 4 x 53 = ?.
First, 53 x 2 = 106; then, 106 x 2 = 212.
Thus, 4 x 53 = 212.
Finding eight times any number is done in a similar way, except you will need to double the number three times instead of two. Let’s solve 8 x 53 = ? now.
As before, 53 x 2 = 106; then, 106 x 2 = 212.
Now, we double it yet again: 212 x 2 = 424
So, this means that 8 x 53 = 424.
6. Multiplying in Parts
Now, let’s say you have to solve a particularly tricky multiplication problem that looks like this: 7 x 453 = ?
This may look intimidating at first glance, but you can make it far less stressful by breaking it down a little bit. Instead of trying to solve the problem outright, multiply each place (1s, 10s, 100s) in 453 by 7 and then add each answer together.
We start with 7 x 400 = 2,800.
Then, 7 x 50 = 350.
Finally, 7 x 3 = 21.
Now, add them together: 2,800 + 350 + 21 = ?
Let’s begin with 2,800 + 350 = 3,150.
(Remember that in the 100s place, since 8 + 3 = 11, we will need to carry a 1 to the 1000s place).
Now let’s add 3,150 + 21 = 3,171.
After that mental work, we now see that 7 x 453 = 3,171.
Test Your Mental Math Skills With Piqosity!
Now that you’re equipped with these helpful mental math strategies, it’s time to practice using them! If you’re looking for math practice beyond what your teacher is assigning, Piqosity has you covered with math courses at a variety of different levels, full of practice problems that give you ample opportunity to test your knowledge.
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