Being an expert at addition and subtraction means having a flexible approach to problem-solving. By mastering multiple strategies, you can confidently tackle problems even when a preferred method slips your mind or when tools like calculators aren’t available. Different techniques, such as breaking numbers apart, using number lines, or applying mental math shortcuts, allow for greater accuracy and efficiency. Understanding these methods also strengthens number sense, making complex calculations easier to manage. This lesson will explore various ways to approach addition and subtraction, helping you build confidence and adaptability in solving mathematical problems.
Moving beyond the standard algorithm (see images below) opens the door to a deeper understanding of numbers and greater flexibility in problem-solving. While traditional column addition and subtraction are reliable methods, alternative strategies such as breaking numbers apart (decomposition), using number lines, and applying mental math techniques can make calculations more intuitive and efficient. These approaches help develop number sense, allowing for quicker estimations and creative solutions, especially when working with large numbers or solving real-world problems. By exploring different methods, learners gain a well-rounded mathematical foundation that extends beyond rote memorization and fosters true numerical fluency.
 |
 |
Breaking numbers into parts can make addition and subtraction easier.
Example: \(3467 + 2859\)
Break it into place values:
\[(3000+2000) + (400+800) + (60+50) + ( 7+9)\]
\[5000 + 1200 +110 + 16\]
\[(5000 + 1000) + (200+100) + (10 + 10) + 6\]
\[6000 + 300 +20 +6 =6326\]
Example: \(7532 - 4268\)
Break it down:
\[(7000-4000) + (500-200) + (30-60) + (2-8)\]
We can use negative numbers.
\[3000 + 300 - 30 - 6\]
\[3000 + 270 - 6 \]
\[3000 + 264 =3264\]
Try It: Solve \(6743 + 3185\) and \(8301 - 4527\)
Using a number line helps visualize additions and subtratctions
Example: \(2375 +1648\)
Example: \(5623-2487\)
Try It: Solve \(7235+ 4528\) and \(9801- 5643\)
This method makes numbers easier to work with by adjusting them slightly.
Example: \(4998 + 3276\)
Instead of adding directly, round 4998 to 5000 (adding 2) and adjust at the end:
\[5000+ 3276=8276\]
Now subtract the extra 2. (The inverse operation of adding 2 from above):
\[8276-2=8274\]
Example: \(8012- 4991\)
Instead of subtracting directly, round 4991 up to 5000 (a difference of 9) and adjust at the end. (Note: Why did we adjust the second number, but not the first?)
\[8012- 5000=3012\]
Now add back the extra 9 (Going from 5000 back to 4991):
\[3012+ 9=3021\]
Try It: Solve \(7999+ 3482\) and \(9004- 4998\)
To check subtraction, use addition. To check addition, use subtraction.
Example: \(6315- 2478=3837\)
Check by adding:
\(3837+ 2478=6315 \checkmark\)
Example: \(4329+ 5672=10,001\)
Check by subtracting:
\(10,001- 5672=4329 \checkmark\)
Try It: Solve \(8675- 3492\) and check with addition.
Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.