Addition Strategies
Master mental and written strategies to add multi-digit numbers quickly and accurately.
Mental Addition Strategies
Mental strategies are clever tricks you can use to add numbers in your head. Choosing the right strategy makes addition faster and easier.
1. Jump Strategy (Counting On)
Start with the larger number and jump forward by the other number in easy steps.
Example: 467 + 230
2. Compensation Strategy
Round one number to make it easier, then adjust (compensate) at the end.
Example: 385 + 198
Think: 198 is close to 200.
3. Split Strategy (Partitioning)
Split each number into its place value parts, add each part, then combine.
Example: 356 + 423
Hundreds
300 + 400 = 700
Tens
50 + 20 = 70
Ones
6 + 3 = 9
700 + 70 + 9 = 779
Written Addition (Vertical Algorithm)
For larger numbers, we use the vertical addition method. Line up the digits by place value and add from right to left, carrying when a column totals 10 or more.
Example: 4,587 + 2,635
Ones: 7 + 5 = 12. Write 2, carry 1.
Tens: 8 + 3 + 1 = 12. Write 2, carry 1.
Hundreds: 5 + 6 + 1 = 12. Write 2, carry 1.
Thousands: 4 + 2 + 1 = 7.
Top tip: Always line up the ones, tens, hundreds and thousands columns carefully. Use grid paper to help keep digits in the right place!
Estimation: Checking Your Work
Before or after you add, estimate by rounding each number to the nearest hundred or thousand. This helps you check if your answer makes sense.
Example: Estimate 3,782 + 4,156
Exact answer: 7,938. Our estimate of 8,000 is close, so the answer looks correct!
Addition in Everyday Life
We use addition every day. Here are some real examples:
Shopping
$24.50 + $18.75 = ?
Road Trips
245 km + 378 km = ?
Sport Scores
1,280 + 965 points = ?
Key Vocabulary
Sum
The result of adding two or more numbers together.
Carry (Regroup)
When a column adds to 10 or more, move the extra ten to the next column on the left.
Estimate
A rough answer found by rounding numbers before calculating.
Compensation
Rounding a number to make calculation easier, then adjusting the answer afterwards.
Worked Examples
Use the compensation strategy to add 547 + 299.
Step 1: Round 299 up to 300 (that is 1 more).
Step 2: 547 + 300 = 847
Step 3: Subtract the extra 1: 847 − 1 = 846
Use the split strategy to add 1,245 + 3,632.
Step 1: Thousands: 1,000 + 3,000 = 4,000
Step 2: Hundreds: 200 + 600 = 800
Step 3: Tens: 40 + 30 = 70
Step 4: Ones: 5 + 2 = 7
Answer: 4,000 + 800 + 70 + 7 = 4,877
Use the vertical method to add 6,479 + 3,854.
Ones: 9 + 4 = 13. Write 3, carry 1.
Tens: 7 + 5 + 1 = 13. Write 3, carry 1.
Hundreds: 4 + 8 + 1 = 13. Write 3, carry 1.
Thousands: 6 + 3 + 1 = 10. Write 10.
Answer: 10,333
Knowledge Check
Select the correct answer for each question.
Question 1
What is 3,456 + 2,378?
Question 2
Using compensation, what is 645 + 397?
Question 3
What is the best estimate for 4,812 + 3,189?
Question 4
A school has 1,265 students. Another school has 987 students. How many students in total?
Question 5
Which mental strategy involves rounding one number to make the calculation easier?
Key Concepts Summary
- ●The jump strategy starts at one number and jumps forward in easy steps.
- ●The compensation strategy rounds a number, adds, then adjusts.
- ●The split strategy breaks numbers into place value parts before adding.
- ●The vertical method lines up digits and adds column by column from right to left.
- ●Always estimate first to check your answer makes sense.