Mental Math Strategies
In an addition equation, the addends are the two numbers that are being added together. The sum is the answer.
Addend + Addend = Sum
Counting On
When using the “counting on” strategy children begin with the largest number in the equation and count up by ones. For example, in the equation 6+4, the student should start at “6” and count up four numbers “7, 8, 9, 10” to get the sum of the two numbers.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 15+3, the student should start at “15” and count up three numbers “16, 17, 18” to get the sum of the two numbers.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 47+5, the student should start at “47” and count up five numbers “48, 49, 50, 51, 52” to get the sum of the two numbers.
Counting on is an efficient strategy when adding 1, 2, 3, 4 0r even 5 to a number. When adding larger numbers, for example, 9 + 8, counting on becomes less efficient because students can get mixed up and lose track of their counting.
Making Ten
This strategy encourages students to memorize the number combinations that add to ten. These include
10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, 4 and 6, 3 and 7, 2 and 8, 1 and 9, and 0 and 10.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
By breaking apart numbers to find the magic ten, students can quickly solve equations mentally. For example, in the equation 8+6= you can break the 6 apart into 2+4. By adding 8+2 you can create a magic ten. Then all you have to do is add 10 +4 to get 14.
In a subtraction equation, the minuend is the first (highest) number, the subtrahend is the number being taken away, and the difference is the answer.
Minuend – Subtrahend = Difference
Counting Back
When using the “counting back” strategy children begin with the minuend of the subtraction equation and counting back. For example, in the equation 9-3, the student should start at “9” and count back three numbers “8, 7, 6” to find the difference between the two numbers.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 18-4, the student should start at “18” and count back four numbers “18, 17, 16, 15, 14” to find the difference between the two numbers.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 64-3, the student should start at “64” and count back three numbers “64, 63, 62, 61” to find the difference between the two numbers.
Counting back is an efficient strategy when the subtrahend is a 1, 2, 3 or 4. If the subtrahend is any higher, students can get mixed up with their counting.
Counting Up
This strategy can help students see that there is a correlation between subtraction and addition. When using the “counting up” strategy children begin with the subtrahend of the subtraction equation and count up. For example, in the equation 7-3, the student will begin with the “3” and count up to the 7 saying, “4, 5, 6, 7” to find the difference between the two numbers, which in this case is 4.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 17-13, the student should start at “13” and count up “14, 15, 16, 17” to find the difference between the two numbers, which in this case is 4.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 72-68, the student should start at “68” and count up “69, 70, 71, 72” to find the difference between the two numbers, which in this case is 4.
This strategy is only efficient when the difference between the minuend and subtrahend is 1, 2, 3 or 4.
Thinking Addition
Since many students find subtraction difficult, this strategy teaches them to use fact families to solve related equations and to use addition equations to solve subtraction ones.
For example, in the equation 9-3, the student should ask themselves - What can I add to 3 to make 9? Then the student can list the facts 3+6=9 and 6+3=9 so 9-3=6 and 9-6=3.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 16-12, the student should ask - What can I add to 12 to make 16? Then the student can list the facts 12+4=16 and 4+12=16 so 16-12=4 and 16-4=12.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 87 - 82, the student should ask - What can I add to 82 to make 87? Then the student can list the facts 82+5=87 and 5+82=87 so 87-82=5 and 87-5=82
Using Ten
This strategy encourages students to memorize the number combinations for making ten and the corresponding subtraction equation. 10-0=, 10-1=, 10-2=, 10-3=, 10-4=, 10-5=, 10-6=, 10-7=, 10-8=, 10-9=, and 10-10=.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty. Now they would change a number to “10” and then adding on the remainder to solve a subtraction equation. For example, in the equation 14-9, a student would first perform the equation 10-9=1, and then add 4 more to make a total difference of 5.
Addend + Addend = Sum
Counting On
When using the “counting on” strategy children begin with the largest number in the equation and count up by ones. For example, in the equation 6+4, the student should start at “6” and count up four numbers “7, 8, 9, 10” to get the sum of the two numbers.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 15+3, the student should start at “15” and count up three numbers “16, 17, 18” to get the sum of the two numbers.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 47+5, the student should start at “47” and count up five numbers “48, 49, 50, 51, 52” to get the sum of the two numbers.
Counting on is an efficient strategy when adding 1, 2, 3, 4 0r even 5 to a number. When adding larger numbers, for example, 9 + 8, counting on becomes less efficient because students can get mixed up and lose track of their counting.
Making Ten
This strategy encourages students to memorize the number combinations that add to ten. These include
10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, 4 and 6, 3 and 7, 2 and 8, 1 and 9, and 0 and 10.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
By breaking apart numbers to find the magic ten, students can quickly solve equations mentally. For example, in the equation 8+6= you can break the 6 apart into 2+4. By adding 8+2 you can create a magic ten. Then all you have to do is add 10 +4 to get 14.
In a subtraction equation, the minuend is the first (highest) number, the subtrahend is the number being taken away, and the difference is the answer.
Minuend – Subtrahend = Difference
Counting Back
When using the “counting back” strategy children begin with the minuend of the subtraction equation and counting back. For example, in the equation 9-3, the student should start at “9” and count back three numbers “8, 7, 6” to find the difference between the two numbers.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 18-4, the student should start at “18” and count back four numbers “18, 17, 16, 15, 14” to find the difference between the two numbers.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 64-3, the student should start at “64” and count back three numbers “64, 63, 62, 61” to find the difference between the two numbers.
Counting back is an efficient strategy when the subtrahend is a 1, 2, 3 or 4. If the subtrahend is any higher, students can get mixed up with their counting.
Counting Up
This strategy can help students see that there is a correlation between subtraction and addition. When using the “counting up” strategy children begin with the subtrahend of the subtraction equation and count up. For example, in the equation 7-3, the student will begin with the “3” and count up to the 7 saying, “4, 5, 6, 7” to find the difference between the two numbers, which in this case is 4.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 17-13, the student should start at “13” and count up “14, 15, 16, 17” to find the difference between the two numbers, which in this case is 4.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 72-68, the student should start at “68” and count up “69, 70, 71, 72” to find the difference between the two numbers, which in this case is 4.
This strategy is only efficient when the difference between the minuend and subtrahend is 1, 2, 3 or 4.
Thinking Addition
Since many students find subtraction difficult, this strategy teaches them to use fact families to solve related equations and to use addition equations to solve subtraction ones.
For example, in the equation 9-3, the student should ask themselves - What can I add to 3 to make 9? Then the student can list the facts 3+6=9 and 6+3=9 so 9-3=6 and 9-6=3.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty.
For example, in the equation 16-12, the student should ask - What can I add to 12 to make 16? Then the student can list the facts 12+4=16 and 4+12=16 so 16-12=4 and 16-4=12.
As soon as students are comfortable working with numbers to twenty, they can use this strategy for numbers up to one hundred and beyond.
For example, in the equation 87 - 82, the student should ask - What can I add to 82 to make 87? Then the student can list the facts 82+5=87 and 5+82=87 so 87-82=5 and 87-5=82
Using Ten
This strategy encourages students to memorize the number combinations for making ten and the corresponding subtraction equation. 10-0=, 10-1=, 10-2=, 10-3=, 10-4=, 10-5=, 10-6=, 10-7=, 10-8=, 10-9=, and 10-10=.
Once students are comfortable working with numbers to ten, they can use this strategy for numbers up to twenty. Now they would change a number to “10” and then adding on the remainder to solve a subtraction equation. For example, in the equation 14-9, a student would first perform the equation 10-9=1, and then add 4 more to make a total difference of 5.