Mental math deepens students' understanding of fundamental math concepts. In addition, knowing that they can do mental math anywhere, without relying on pencils, paper, or manipulatives, gives students a sense of success and independence. Once students learn mental math tricks and techniques, they can often figure out the answer to a math problem in the amount of time it would take them to pull out a calculator.

### Did You Know?

In the early stages of learning math, the use of math manipulatives (such as beans or plastic counters) helps children visualize and understand one-to-one correspondence and other mathematical concepts. Once children grasp these concepts, they are ready to start learning mental math.

### Mental Math Tricks

Help students improve their mental math skills with these mental math tricks and strategies. With these tools in their mathematical toolkit, your students will be able to break down math problems into manageable—and solvable—pieces.

#### Decomposition

The first trick, decomposition, simply means breaking numbers down into an expanded form (e.g. tens and ones). This trick is useful when learning double-digit addition, as children can decompose the numbers and add like-numbers together. For example:

25 + 43 = (20 + 5) + (40 + 3) = (20 + 40) + (5 + 3).

It's easy for students to see that 20 + 40 = 60 and 5 + 3 = 8, resulting in an answer of 68.

Decomposing, or breaking apart, can be used for subtraction as well, except that the largest digit must always remain intact. For example:

57 – 24 = (57 – 20) – 4. So, 57 – 20 = 37, and 37 – 4 = 33.

#### Compensation

Sometimes, it’s helpful for students to round one or more of the numbers to a number that’s easier to work with. For example, if a student were adding 29 + 53, he might find it easier to round the 29 to 30, at which point he can easily see that 30 + 53 = 83. Then, he simply has to take away the "extra" 1 (which he got from rounding 29 up) to arrive at a final answer of 82.

Compensation can be used with subtraction, as well. For example, when subtracting 53 – 29, the student can round 29 up to 30: 53 – 30 = 23. Then, the student can add the 1 from rounding up to yield an answer of 24.

#### Adding Up

Another mental math strategy for subtraction is adding up. With this strategy, students add up to the next ten. They then count the tens until they reach the number from which they are subtracting. Finally, they figure the remaining ones.

Use the problem 87 – 36 as an example. The student is going to add up to 87 to mentally calculate the answer.

She can add 4 to 36 to reach 40. Then, she'll count by tens to reach 80. So far, the student has determined that there is a difference of 44 between 36 and 80. Now, she adds the remaining 7 ones from 87 (44 + 7 = 51) to figure out that 87 – 36 = 51.

#### Doubles

Once students learn doubles (2+2, 5+5, 8+8), they can build on that knowledge base for mental math. When they encounter a math problem that is near a known doubles fact, they can simply add the doubles and adjust.

For example, 6 + 7 is close to 6 + 6, which the student knows equals 12. Then, all he has to do is add the extra 1 to calculate an answer of 13.

### Mental Math Games

Show students that mental math can be fun with these five active games perfect for elementary-age students.

#### Find the Numbers

Write five numbers on the board (e.g. 10, 2, 6, 5, 13). Then, ask students to find the numbers that match the statements you will give, such as:

- The sum of these numbers is 16 (10, 6)
- The difference between these numbers is 3 (13, 10)
- The sum of these numbers is 13 (2, 6, 5)

Continue with new groups of numbers as needed.

#### Groups

Get the wiggles out of students in grades K-2 while practicing mental math and counting skills with this active game. Say, “Get in groups of…” followed by a math fact, such as 10 – 7 (groups of 3), 4 + 2 (groups of 6), or something more challenging such as 29-17 (groups of 12).

#### Stand Up/Sit Down

Before giving students a mental math problem, instruct them to stand up if the answer is greater than a specific number or sit down if the answer is less. For example, instruct students to stand up if the answer is greater than 25 and sit down if it’s less. Then, call out, “57-31.”

Repeat with more facts whose sums are greater than or less than your chosen number, or change the stand/sit number each time.

#### Number of the Day

Write a number on the board each morning. Ask students to suggest math facts that equal the number of the day. For example, if the number is 8, children might suggest 4 + 4, 5 + 3, 10 – 2, 18 – 10, or 6 + 2.

For older students, encourage them to come up with suggestions for addition, subtraction, multiplication, and division.

#### Baseball Math

Divide your students into two teams. You can draw a baseball diamond on the board or arrange the desks to form a diamond. Call out a sum to the first “batter.” The student advances one base for each number sentence she gives that equals that sum. Switch teams every three or four batters to give everyone a chance to play.