Mental Math for Kids
1. What is Mental Math?
It is doing calculations in your head without the help of pen and paper or
calculators.
2. Why should children do mental math?
Understanding simple math facts can offer students a tremendous advantage
in school. Children’s math fluency increases with the improvement of mental
math skills, which allows them to advance more easily to higher level
mathematics. More than anything, learning some basic, but useful mental
math strategies, can work to greatly improve your children’s self-confidence.
Students who succeed in mental math are…
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Focused. Because students aren’t distracted by large numbers, they
concentrate on the logic of the problem.
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Efficient. Easier problems are solved more quickly, which leaves more
time for difficult problems.
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Fearless. As students are able to do more math in their head, they are
more and more confident in their abilities.
It improves their ability to solve math problems.
3. What can parents do to help their children with mental
math?
Mental math should not be confused with the memorization of basic
mathematics facts— such as knowing the times-tables by heart. However,
memorizing basic facts makes mental math easier. Children must know their
multiplication tables and the number pairs adding up to 10. Mental math
requires continual practice of addition, subtraction, division, and
multiplication. The key is: Practice, practice, practice. Keep it light. Make it
fun. Vary the exercises. Use:
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Games
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Computer
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Drill
3.1 Games
3.1.1 Mental Mystery
Have your children count out five small objects such as coins, marbles, or candy (10
– 20 objects for older children) and close their eyes. Then hide some of the five
objects, while leaving the rest uncovered. Ask your children to calculate how many
objects they see and how many objects are covered. Practice this activity until your
children can quickly solve these simple equations. Add one additional object once
your children have mastered that level to increase difficulty.
3.1.2 The Number is Right
On a piece of paper, write a number between 1 – 100 and have your children take
turns guessing the number written. After each incorrect guess, you must tell the
players if the number guessed is higher or lower than the number written down. The
game continues until someone correctly guesses the number.
3.1.3 Dice
Using a standard die, each player will roll the die as many times as they like and
keep a running total of the numbers rolled. If the player rolls number 1, the player
loses his or her current total and another player takes turns rolling the die. Players
can hold their current score by passing on the die to their opponents. The game can
continue until each player has had five turns or reach a total sum of 25.
3.2 Computer
A great tool to improve a child’s math proficiency and speed is the computer. There
are lots of computer games that require a math fact to be solved within a given time.
You can usually increase the speed on these games as your child’s proficiency
improves. Children enjoy learning this way, and it is very effective. A good site to use
is https://www.mathsisfun.com/
3.3 Drill
Finally, good, old-fashioned drill and practice works well to improve speed and
proficiency of math facts. The key to basic fact progress is consistent practice for
short periods of time (five to seven minutes) frequently. So, if your child can practice
his/her math facts three times per day for five minutes each time, it will be more
effective than one 15- or 20- minute spurt.
4. Strategies and examples
*Attached (It is taken directly from the first two websites mentioned at the
end)
5. Final word
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.
6. Websites
http://cmc-math.org/family/PDF%20Documents/MentalMathPart1.pdf - very useful
http://www.dearteacher.com/mental-math - useful strategies and examples
https://www.mathsisfun.com/ - acts as a math dictionary and has an excellent times-table trainer
Strategies for Addition
Doing addition problems in your head is probably the best way to start doing mental math.
 Adding One
Adding one means hearing a number, then saying one number up—or counting up one number. The
best way to introduce this to your children is to say a number out loud and then, after allowing them
time to think, have them tell you the next higher number.
 Adding Two
Adding two means hearing a number, then saying the number that is two more. To do this, children
can either mentally add two or count up by two. If you first teach your children to count by twos: 2,
4, 6, 8, 10, . . . etc., it will be easier for them to add two mentally. However, remember that they will
also have to learn how to count by the odd numbers: 1, 3, 5, 7, 9, . . . Also, if children understand
that any odd number, plus 2, will always be another odd number, and that any even number, plus
two, will always be another even number, these mathematics concepts can help them check their
answers mentally.
 Counting-On
Counting-on is one of the simple but powerful mental math strategies children can learn and is the
easiest for most students—many children figure out this strategy naturally. Counting-on means a
child mentally says the biggest number to add, and then counts-up the second number, one (or two)
at a time. For example, in the equation 5 + 3, you start with the 5 in your head, and then count up: . .
. 6, 7, 8. You might suggest to your children that if they want to add 2 + 6 in their head, they should
start with the bigger number, in this case 6, and count up (. . . 7, 8) since, with addition, you can add
numbers in any order and get the same answer—order does not matter.
When mentally counting-on, children and adults often resort to using their fingers to count up (or
down), simultaneously counting on their fingers while they count in their heads. If your children use
this handy device, let them. It is not harmful if it helps to make counting-on a useful mental math
strategy.
 Making-Ten(s)
Since ten is the basis of our number system, students who know all the single-digit combinations
that equal 10 can make good use of them in doing mental math. The makingten strategy involves
memorizing the number combinations that add to ten: 7 + 3, 8 + 2, 5 + 5, etc.—they are not as useful
if children need to think hard to remember these combinations. Once students memorize these,
counting-on or other strategies become easier. For example, 6 + 4 = 10 may be a trivial problem, but
if you know your combinations of ten, this strategy can then be extended to harder problems, such
as 76 + 4, since 76 + 4 = 70 + 6 + 4 = 70 + 10 = 80—easy!
 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.
 Visualizing A Mental Number Line
Number lines, such as those found on the wall in many classrooms, are a visual model of our number
system and can be very helpful for children who need to see how numbers are logically arranged. If
children can close their 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.
 Adding Ten
The number line can teach students that adding ten is easy because ten is an easy “jump” up the
number line. No matter what number you start with, the one’s digit stays the same but the ten’s
digit increases by one. For example: 5 + 10 = 15, 12 + 10 = 22, 23 + 10 = 33, etc.
 Adding Nine
Once adding ten is easy to do, adding nine is the next strategy to learn. To add nine, a student just
adds ten, and then counts down by one. A child would mentally say 5 + 9 = 5 + 10 – 1 = 15 – 1. Once
understood, this mental math strategy is almost as simple as adding ten.
 Double Numbers
Making use of doubles—5 + 5, 7 + 7, etc.—is a bit harder, but can be very useful for mental math.
Doubles come up often in calculations, so if all the single-digit doubles are memorized, students can
combine these known facts with the mental math strategies already mentioned. For example, when
faced with the problem 76 + 6, students can think of it as 70 + 6 + 6. If they remember that 6 + 6 =
12, then they can rearrange the problem as 70 + 12, and then again rearrange the problem as 70 +
10 + 2 = 82—making it an easy mental math problem.
 Near-Doubles
Once students have memorized their doubles, the use of near-doubles in mental math follows easily.
For example, in the expression 5 + 6, if students first remember the double, 5 + 5 = 10, then it is easy
to add one more, getting an answer of 11. Children actually do not have to memorize the neardoubles if they know their doubles. For example, in the equation 37 + 8, when children use the neardoubles strategy, it follows that 30 + 7 + 7 + 1 = 30 + 14 + 1 = 44 + 1 = 45.
 Front-end Addition
We frequently do mathematics differently in our heads than we do with paper and pencil. The
typical way to add a pair of two-digit numbers is to add the digits in the ones place first, carry ten if
necessary, add the digits in the tens place next, and finish by combining the tens and ones results.
However, many people can keep track of these calculations more easily in their minds if they reverse
this order—adding the tens first, remembering that number, then adding the ones, and only then
combining the tens and ones. For example, in the problem 65 + 26, if students first mentally
calculate 60 + 20 = 80, the number 80 is pretty easy to remember—to store away mentally for a few
moments. If they then add the ones, 5 + 6 = 11, they can recall the easily remembered number, and
compute 80 + 11 = 91.
 “Friendly Numbers” Strategy
Certain number pairs go together nicely and are easy to work with in our heads; we call these
friendly numbers. For example, 75 + 25 totals 100—we know this well from using money. 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 students would instead
think 75 + 25 + 3, changing it into two friendly numbers and one easily added number instead.
 Balancing Strategy
Balancing numbers before you add 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 you mentally
borrow 2 from 57 and add it to the 68, the problem now becomes 70 + 55—a much easier problem
to do mentally.
Examples
To become experts at mental math, children need considerable practice because mental
computation is not done in the same way as pencil-and-paper procedures. There are many ways
to add, subtract, multiply, and divide using mental math. As there is no one clear-cut method to
use in solving a problem, children need to choose the method that works best for them.
Addition
It is easy to add tens and hundreds if place-value words are used.
Example: 200 + 300 + 40
Think or say: 2 hundred and 3 hundred is 5 hundred and 40 more is 540.
It can be easier to add hundreds and thousands if the thousands are thought of as hundreds.
Example: 4200 + 500
Think or say: 42 hundred and 5 hundred is 47 hundred.
Begin on the left when using mental math to add numbers.
Example: 24 + 32
Think or say: 20 and 30 is 50. 4 and 2 is 6. 50 and 6 is 56.
Example: 37 + 45
Think or say: 30 and 40 is 70. 7 and 5 is 12. 70 and 12 is 82. OR
37 and 40 is 77. 77 and 5 is 82.
It is easy to add by making one of the numbers a multiple of ten and then compensating. This
method works especially well when adding numbers ending in an 8 or 9.
Example: 69 + 18
Think or say: 69 and 1 is 70. 70 and 18 is 88. 88 take off 1 is 87. OR
18 and 2 is 20. 69 and 20 is 89. 89 take off 2 is 87.
Numbers are easier to add when both numbers end in 5.
Example: 65 + 28
Think or say: 28 is 25 and 3. 65 and 25 is 90. 90 and 3 is 93.
Compatible numbers are numbers that go together to make tens or hundreds.
Example: 70 + 20 + 80
Think or say: 20 and 80 is 100. 100 and 70 is 170.
Subtraction
When children are doing subtraction, they will find it helpful to think addition.
Example: 15 - 7
Think or say: 7 + what equals 15. 8.
Making the number to be subtracted a multiple of ten and then keeping track of how much is
added on to that number to get the total is one method of mental math subtraction. Two other
methods to solve the same problem will follow.
Example: 53 - 47
Think or say: 47 and 3 is 50 and 3 more is 53. 3 and 3 is 6.
As in addition, you can begin on the left when using mental math to subtract numbers.
Example: 53 - 47
Think or say: 50 - 40 is 10. 10 and 3 is 13. 13 - 7 is 6.
It is easy to subtract by making tens with the number to be subtracted and then compensating.
Example: 53 - 47
Think or say: 53 - 40 is 13. 13 - 7 is 6.
Use compensation when you subtract numbers ending in 8 or 9.
Example: 53 - 19
Think or say: 19 + 1 is 20. 53 - 20 is 33. 33 + 1 is 34.
Larger numbers can be handled easier by dropping common zeros. Caution: These zeros must be
added back on to get the right place value in the answer.
Example: 800 - 400
Think or say: 8 - 4 is 4. Then add back the zeros to get 400.
Example: 840 - 400
Think or say: 84 - 40 is 44. Then add back the missing zero to get 440. OR
8 - 4 is 4. Add back the missing zeros to get 400 then add 40 more. 440.
You can drop the ending digits if they are the same in both numbers just like in dropping
common zeros. However, you must remember to add zeros to get the correct place value.
Example: 846 - 446
Think or say: 8 - 4 is 4. Add two zeros to get the correct place value 400.
Multiplication
Numbers that have many zeros are easy to multiply. You multiply the nonzero numbers first
and then add on the zeros. Caution: You must understand the relationship between the zeros
and place value. One zero represents tens, two zeros represents hundreds, three zeros represents
thousands, and so on.
Example: 7 x 300
Think or say: 7 x 3 is 21. Add on two zeros. 2100. OR
7 x 3 is 21. Use place value. 21 hundred. 2100.
Go from left to right when multiplying large numbers. Multiply the large number first and then
add in the little parts.
Example: 74 x 8
Think or say: 8 x 70 is 560. 8 x 4 is 32. 560 and 32 is 592.
When multiplying very large numbers, break the number into parts that are easy to handle.
Example: 524 x 3
Think or say: 3 x 500 is 1500. 3 x 24 is 72. 1500 and 72 is 1572. OR
3 x 500 is 1500. 3 x 20 is 60. 3 x 4 is 12. 1500 and 60 and 12 is 1572.
To multiply numbers ending in 8 or 9, use the next higher multiple of 10 and then compensate.
This is especially helpful when dealing with money.
Example: 6 x 49
Think or say: 6 x 50 is 300. 6 x 1 is 6. 300 take back 6 is 294.
Example: 6 x $4.98
Think or say: 6 x $5.00 is $30.00 less 6 x 2 cents. $30.00 less $.12 is $29.88.
Some numbers are easier to multiply if you halve one number and double the other.
Example: 8 x 15
Think or say: Half of 8 is 4 and double 15 is 30. 4 x 30 is 120.
Example: 8 x 16
Think or say: Halve and double more than once. 4 x 32. Then 2 x 64 is 128.
Rearrange one or both numbers to make mental multiplication easier.
Example: 16 x 25
Think or say: 16 x 25 is 4 x 4 x 25. 4 x 25 is 100. 100 x 4 is 400.
Division
When using mental math to do division, think multiplication just as in pencil-and-paper
problems.
Example: 56 ÷ 8
Think or say: What times 8 is 56. 7.
When the number to be divided has zeros, cut off the zeros, divide, and then put the zeros back.
Example: 2400 ÷ 8
Think or say: Cut off the zeros. 8 times what is 24. 3. Then add back the zeros to get 300. OR
Cut off the zeros. 24 divided by 8 is 3. Then add back the zeros to get 300.
When both the number to be divided and the divisor have zeros, cancel the common zeros.
Example: 600 ÷ 300
Think or say: 3 times what is 6. 2. OR 6 divided by 3 is 2.
Example: 600 ÷ 30
Think or say: 3 times what is 60. 20. OR 60 divided by 3 is 20.
Start at the left. Break the number to be divided into parts to make division easier.
Example: 240 ÷ 4
Think or say: 240 is 200 and 40. 200 ÷ 4 is 50. 40 ÷ 4 is 10. 50 and 10 is 60.
Change the number to be divided so it is rearranged into multiples of the divisor.
Example: 136 ÷ 8
Think or say: 136 can be changed to 80 plus 56. 80  8 is 10. 56  8 is 7. 10 and 7 is 17.
Change both the number to be divided and the divisor in the same way.
Example: 700 ÷ 25
Think or say: Multiply both numbers by 4. 700 x 4 is 2800. 25 x 4 is 100. 2800 ÷ 100 is 28.