1. What is Mental Math?
Mental math is a group of skills that allow people to do math “in their head” without using pencil and paper or a calculator. It is often used as a way to calculate an estimate quickly through the use of math facts that have been committed to memory, such as multiplication, division, or double facts.
However, mental math should not be confused with the memorization of basic mathematics facts – such as knowing the times-tables by heart. While memorizing basic facts makes mental math easier, doing mathematics mentally requires both memorized facts and manipulating numbers and operations to solve problems that are much more complex than the simple number facts we can easily memorize.
The Manitoba Association of Mathematics Teachers defines mental math as “a combination of cognitive strategies that enhances flexible thinking and number sense. It is calculating mentally without the use of external memory aids. It improves computational fluency by developing efficiency, accuracy, and flexibility.”
2. Research-backed benefits of mental math
We all use mental math in our daily life: in the grocery store, on the street, at the end of each month when the bills come. Even outside of our professions, mental math is useful for ordinary tasks and help us answer questions like:
- What is the sale price for this item?
- Do I have enough cash to buy everything in my cart?
- Am I getting the correct amount of change from the cashier?
- When should I leave in order to arrive on time?
Even more important than adult use, kids should strengthen mental math skills to bolster their budding math skills since mental math comes in handy to solve math equations and problems easier and quicker.
Mental math can also help kids understand math concepts better. Using and practicing mental math regularly helps kids improve their number sense. For example, which is a better deal? Buying a box of 10 packs of gum for $18.00 or buying individual packs for $2.50 each? When kids develop mental math skills, they:
- Gain a deeper understanding of math beyond mere memorization
- Develop logical thinking and reasoning skills
- Learn skills that will improve math skills across all grade levels
- Master skills they’ll carry over for life no matter their profession!
Understanding simple math facts can offer students a tremendous advantage in school. By conducting basic addition and subtraction problems mentally, your child’s math fluency can improve, allowing her to advance more easily to higher level mathematics.
3. Fun strategies to get your child better at mental math
There are a number of ways to work mental math practice into everyday situations. For example, doubling a recipe, counting change, double-checking till receipts and scoring a game of Scrabble all involve using knowledge of basic maths operations to work out the answers. The following mental math strategies are arranged in general order from the easiest strategies children can learn to perform in their head to more difficult and challenging mental math gymnastics.
1. Skip counting
Skip counting should be one of the first mental math skills all children learn. It uses the fact that multiplication is simply repeated addition of the same number. To multiply 5×2, children could mentally “say:” 2, 4, 6, 8, 10, or five 2s. If your child knows the simple multiples, such as 2s, 3s, 5s, and 10s, then they can skip count by 2s, 3s, 5s, and 10s. If they are really good and know all their multiples up to 10, then this strategy is even more useful. Once again, if you are willing to allow your children to use their fingers, she can more easily skip count in her head while counting on her fingers to make sure she “skips” the right number of times.
2. Make friends with “Friendly Numbers”
There are certain number pairs that go together nicely and are easy to work within our heads; we call these friendly numbers. For example, 75 + 25 totals 100 – those kids who know how to use money can get this very quickly. Although we do not often get many problems as simple as 75 + 25, we can combine this friendly number strategy with other mental math strategies. For example, to add 78 + 25, we would instead think 75 + 25 + 3, changing it into two friendly numbers and one easily added number instead.
3. Balancing Strategy
Balancing numbers before adding them is a variation of the friendly number strategy. This strategy involves “borrowing” one or more from one number and “trading” it to the other number to make two numbers that are friendly. For example, 68 + 57 are not friendly numbers, but if we mentally borrow 2 from 57 and add it to the 68, the problem now becomes 70 + 55—a much easier problem to do mentally. For example, if the sum is 57 + 48, our thought process might be:
- I’ll round up those numbers to 60 + 50 because that’s easier to add.
- But I’ll keep in mind that I’ve given myself an extra 5 for the round up (3 to turn 57 into 60, and an extra 2 to turn 48 into 50). I’ll have to subtract that 5 from my final answer when I get there.
- My rounded-up sum: 60 + 40 = 110.
- Minus the 5 = 105.
4. Visualize a mental number line
The empty number line is a powerful model for children who need to see how numbers are logically arranged. If your child can close her eyes and visualize a mental number line, this too can be helpful in doing mental math. The best way to help students picture a number line is to post a paper number line in your home where your children can see it and use it regularly when they do mathematics. They will begin to notice all the wonderful number patterns, the twos, the fives, the tens – and many more. If they can then see the number line when they close their eyes, they can use these patterns to do mental math.
5. Rearrange Numbers and Operations
On paper, we tend to calculate with numbers in the order they are given. Doing mathematics mentally frees us to do calculations in the order we choose and can do more easily. For example, if we do 6 – 3 + 2 + 4 + 8 in our heads, we can rearrange it as (6 + 4) + (2 + 8) – 3—two combinations of 10, then subtract 3 last. However, to do this, a child must be able to remember the numbers and rearrange them mentally.
6. Use multiplication hacks
Memorizing multiplication tables is a mental math hurdle for most elementary learners, but it becomes a whole lot easier once they memorize the following ‘hacks’:
- Any number times 1 remains the same.
- Any number times 10 has a zero added to its end.
- Any number up to 9 times 11 is just the same digit repeated twice (e.g. 99).
Together, these hacks instantly give our students 60 multiplication facts that can be calculated automatically – without any need for memorizing
7. Round up when multiplying by 9
There are simple ways to alter difficult equations, making them easier to solve with mental math. Children can use existing rounding and fact fluency skills when multiplying by 9, 99, 999 and any number that follows this pattern. First, tell your child to round up the 9 to 10. Second, after solving the new equation, teach her to subtract the number they just multiplied by 10 from the answer. For example, 67 x 9 will lead to the same answer as 67 x 10 – 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 – 67. Despite more steps, altering the equation this way is usually faster and allows students to complete it in their heads.
8. Allow your child to make guesstimates
In everyday life, mental math rarely needs to be 100% accurate. If it does, we’ll usually reach for a calculator or piece of paper anyway. Therefore, tell your little learner that it’s totally OK to approach a more complex mental math problem by “guesstimating” the answer. This might mean just working with the highest place values in the sum and using this to calculate that the answer will be “around” a certain number. They can then check the answer via working out.
A bit of mental math advice by Everest Education
For some students, these above mental math strategies will be interesting and fun – and may even make them feel mathematically powerful. However, what appeals to one child may be uninteresting and hard to another. If there is one important bit of advice before you share any of these strategies with your children, it is: go slow and proceed only IF your children enjoy learning how to do mathematics in their head. A few minutes of playing with mental math are plenty – do not make it tedious. If learning mental math tricks is not fun for your children, it is best if you stop and look for other areas of mathematics, such as geometry or puzzles, that will appeal to your children more than mental math:
- Playing simple-but-fun math games is a fantastic way to not only stimulate your child’s mental math abilities but also an ideal way of improving number facts. If you’re looking for activities to help you learn how to teach mental math strategies to your child, let’s discover some playful Math activities in our older article here: https://blog.e2.com.vn/playful-math-activities-for-your-primary-kids/
- Don’t forget to utilize digital math applications and websites – which can offer your child an engaging environment to build a range of skills important for mental math. Try using tools like Quizlet – the favorite website that our teachers used very often in our Singapore math classes – to help your children improve their mental math.
- Work with a strategy until your child masters it before moving on to another strategy, but periodically come back to review the earlier strategy. When children have mastered several strategies, encourage them to think about which strategy is the most effective for solving a given problem.
Obviously, mental math matters, but in order for mental math lessons to work for your child, it needs to be done consistently each day or week. We hope that these strategies can boost your children’s calculation skills, help them comprehend those hard-to-grasp concepts and put an end to their math-related misery.
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