1. Counting on

‘Counting on’ is a mental math strategy that is used to add numbers. It is used to build number facts fluency.

You want your child to start with the larger number in the addition sentence, then count on the number added.

For example, 5 + 3 =?

Start with the larger number – 5 and count on 3 more 6, 7, 8. The answer is 8.

Your child can start using this strategy with the Number Line and then employ it mentally.

When your child is familiar with the ‘Count On’ Strategy, they can start counting on by 10 and solve addition calculations with larger numbers.

For example, 34 + 15 =?

· Teach your child to start with the larger number – 34.

· Count on by 10, which is 44.

· Continue to count 5 more, which are 45 46 47 48 49.

· The answer is 49.

You can use Number Line to show your child as well.

Image 2. Number Line Demonstration

2. Counting back

If we use ‘Counting on’ to solve addition sentences, we use ‘Counting back’ for subtraction. Subtraction means taking away the smaller number from the larger number. We use the ‘counting back’ strategy by counting backwards from the larger number.

Example: 9 – 4 =?

· Start from the larger number – 9.

· Count backward 4 more, which are 8 7 6 5.

· The answer is 5.

  Image 3. Demonstration of how counting back works.

3. Number Bond

The number bond strategy is a teaching and learning method used in mathematics education to help students understand the relationships between numbers and the components of various mathematical operations, such as addition and subtraction. Number bonds are a visual representation of a number and its parts, typically presented in the form of a diagram or a pair of linked equations. This strategy is often used in early elementary education to build a strong foundation for more advanced math concepts.

A number bond typically consists of a circle or rectangle that contains a number (the whole) and two or more smaller circles or rectangles (the parts).

The number in the whole represents the total number, while the numbers in the smaller circles or rectangles represent the parts that combine to make the whole.

In addition, a number bond helps students break down a number into its component parts. For example, if the whole number is 8, and the parts are 5 and 3, the number bond would look like this:

     Image 4: number bond 8 with the parts 5 and 3

Number bonds are also useful for subtraction. If the whole number is 9, and one of the parts is 5, you can represent it like this:

Image 5: Number bonds for subtraction

Number bonds help students understand how numbers relate to each other and that addition and subtraction are inverse operations. They provide a foundation for developing mental math skills, as students can quickly see number relationships and use them to solve math problems.

4. Bridge to 10

The “bridge to 10” mental math strategy is an exceptional technique that empowers young children to break down numbers into simple combinations that add up to 10. It unlocks the potential to become more efficient in addition and subtraction, especially for young learners who are working to master basic math facts.

· If you have an addition problem like 7 + 8, you can break down 7 into 2 and 5, making it easier to calculate: 8 + 2 + 5.

· Then, add 2 to 8 to get 10: 8 + 2 = 10.

· Finally, add 10 to 5 to get the result: 10 + 5 = 15.

· So, 7 + 8 = 15.

  Image 6: Example of Bridge to 10

The “Bridge to 10” strategy simplifies calculations by creating pairs of numbers that add up to 10 or multiples of 10, which are typically easier to work with mentally. This strategy can be extended to more complex addition and subtraction problems by breaking down numbers into combinations that bridge to the nearest multiple of 10.

Image 7: Bridge to 10 Example

5. Partitioning

Partitioning is a mental math strategy that involves breaking down a complex math problem into smaller, more manageable parts to make calculations easier. This technique is particularly useful for addition, subtraction, multiplication, and division. Here’s how it works:

For example, if you need to add 47 + 68, you can partition it as follows:

· 40 + 60 = 100

· 7 + 8 = 15

· Add the two results: 100 + 15 = 115

Image 8: Example of how to calculate addition using partitioning

If you need to subtract 386 – 254 =?

Image 9: Example of how to calculate subtraction using partitioning

6. Nearly Double

Nearly doubles in math is a proven and effective strategy that helps young students become more familiar with counting. A double is simply a number that is multiplied by 2, while a near double is a number that falls just short of being doubled, but only by a few. This strategy has been widely used to great success, particularly for students who are in the early stages of learning multiplication.

For example, 15 + 16 =?

· Use double fact to help with nearly double.

· Solve 15 + 16 by thinking of 15 + 15 + 1.

7. Compensation strategy

Compensation is an effective mental math strategy that involves adjusting one addend to a multiple of 10 and modifying the other addend to ensure the balance is maintained.

Example: 36 + 9 = ?

· Think of 36 + 10, then subtract 1.

Image 11: Compensation strategy for 36 + 9

Or 48 + 24 =?

· Think of 50 + 24, then subtract 2

Image 12: Compensation strategy for 48 + 24