Bridging in maths is a mental math strategy that involves using known number facts, particularly those related to 10, to simplify addition or subtraction problems. It avoids counting in ones, making calculations faster and more efficient.
Understanding Bridging
Bridging typically refers to "bridging to 10" (or other multiples of 10), but the underlying principle applies to other numbers as well. The goal is to decompose one number in the problem to create an easier-to-work-with intermediate step.
Bridging to 10 in Addition
Let's illustrate with an example: 8 + 5.
- Identify the larger number: In this case, it's 8.
- Determine how much is needed to reach 10: 8 needs 2 more to become 10.
- Decompose the smaller number: Break down 5 into 2 + 3.
- Bridge to 10: Add the 2 to the 8, making 10.
- Add the remaining amount: Add the remaining 3 to the 10, resulting in 13.
Therefore, 8 + 5 = (8 + 2) + 3 = 10 + 3 = 13.
Bridging to 10 in Subtraction
Bridging can also be used for subtraction. Example: 13 - 5.
- Think about bridging back to 10: How much do we need to subtract from 13 to get to 10?
- That amount is 3: 13 - 3 = 10.
- How much more do we need to subtract? We subtracted 3 from 5, so we need to take away another 2.
- Subtract the remaining amount: 10 - 2 = 8
Therefore, 13 - 5 = (13 - 3) - 2 = 10 - 2 = 8.
Benefits of Bridging
- Efficiency: It's faster than counting on fingers or using a number line.
- Mental Math Skill: Develops mental math skills and number sense.
- Conceptual Understanding: Reinforces understanding of number bonds and place value.
- Reduces Cognitive Load: Makes calculations simpler by breaking them down into smaller steps.
Examples
Here are more examples of bridging in action:
- 7 + 6 = (7 + 3) + 3 = 10 + 3 = 13
- 16 - 8 = (16 - 6) - 2 = 10 - 2 = 8
- 38 + 7 = (38 + 2) + 5 = 40 + 5 = 45
- 52 - 5 = (52 - 2) - 3 = 50 - 3 = 47
Bridging is a valuable strategy for developing fluency in basic arithmetic and a deeper understanding of number relationships.
