➕ Addition Hero: Add & Subtract Like a Pro ✨

In Grade 6, you need to add and subtract numbers up to millions using both mental strategies and the formal column method. A true Addition Hero can pick the fastest method, estimate first to check answers, and tackle multi-step word problems with confidence!

🧠 Mental: Partitioning
4,763 + 2,158→4000+2000=6000, 700+100=800, 63+58=121→6,921
📝 Column Addition
Line up digits, add right to left, carry to next column. Always estimate first!
🔄 Inverse Check
If 5,284 + 3,716 = 9,000 then 9,000 − 3,716 = 5,284 ✓

📏 Golden Rules

📐 Always estimate first: round each number to the nearest 100 or 1,000 before calculating. This gives you a "sense check."
📋 Column method: line up digits by place value (ones under ones, tens under tens, etc.). Always start from the ONES column.
⬆️ Carrying: if a column adds up to 10 or more, write the units digit and carry 1 to the next column.
⬇️ Borrowing (decomposition): if the top digit is smaller, borrow 10 from the next column. The next column's digit reduces by 1.
🔄 Inverse operations: use subtraction to check addition (and vice versa). The answer − one addend should give the other addend.
🧩 Multi-step problems: read carefully, identify what each step asks, work through one step at a time.

🎯 Ready to practise? Try the pages above!

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3 · Addition & Subtraction of Whole Numbers A & B

📚 Worked Examples

Example 1: Mental Addition (Partitioning)

Calculate 4,763 + 2,158 mentally.

Step 1 · Thousands: 4,000 + 2,000 = 6,000
Step 2 · Hundreds: 700 + 100 = 800
Step 3 · Tens and ones: 63 + 58 = 121
Step 4 · Combine: 6,000 + 800 + 121 = 6,921
✅ Estimate check: 4,800 + 2,200 = 7,000 ← close enough ✓

Example 2: Column Addition

Calculate 35,847 + 28,364

    1 1 1 1
 3 5, 8 4 7
+ 2 8, 3 6 4
 6 4, 2 1 1
Ones: 7 + 4 = 11 → write 1, carry 1
Tens: 4 + 6 + 1 (carry) = 11 → write 1, carry 1
Hundreds: 8 + 3 + 1 (carry) = 12 → write 2, carry 1
Thousands: 5 + 8 + 1 (carry) = 14 → write 4, carry 1
Ten-thousands: 3 + 2 + 1 (carry) = 6
✅ Answer: 64,211 · Estimate: 36,000 + 28,000 = 64,000 ✓

Example 3: Column Subtraction (with borrowing)

Calculate 72,305 − 46,817

Ones: 5 − 7? Can't do it! Borrow from tens. But tens is 0 — must borrow from hundreds. Hundreds becomes 2, tens becomes 10, then borrow 1 ten → tens = 9, ones = 15. 15 − 7 = 8
Tens: 9 − 1 = 8
Hundreds: 2 − 8? Can't do it! Borrow from thousands. Thousands becomes 1, hundreds becomes 12. 12 − 8 = 4
Thousands: 1 − 6? Can't do it! Borrow from ten-thousands. Ten-thousands becomes 6, thousands becomes 11. 11 − 6 = 5
Ten-thousands: 6 − 4 = 2
✅ Answer: 25,488 · Check: 25,488 + 46,817 = 72,305 ✓

Example 4: Multi-step Word Problem

A school library has 12,458 books. 3,672 are borrowed on Monday and 1,284 more on Tuesday. How many books are left?

Step 1 · Total borrowed: 3,672 + 1,284 = 4,956
Step 2 · Books left: 12,458 − 4,956 = 7,502
✅ Answer: 7,502 books remain.
 
Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🔬 Column Method Solver

Enter two whole numbers and choose + or −. Hit Solve It! to see the column working step by step.

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 1: Estimate First

Estimate 6,847 + 3,215 by rounding to the nearest 1,000. Which is the best estimate?

Hint: 6,847 ≈ 7,000 and 3,215 ≈ 3,000. What is 7,000 + 3,000?

9,000
10,000
11,000
8,000
Best Estimate:
?

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 2: Column Addition

Work out 24,573 + 38,264 using the column method.

Hint: Estimate: 25,000 + 38,000 = 63,000. Check your column working!

62,837
62,738
62,983
63,837
24,573 + 38,264 =
?

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 3: Column Subtraction

Calculate 80,000 − 34,567

Hint: This needs careful borrowing! Check: does your answer + 34,567 = 80,000?

44,433
45,433
45,333
46,433
80,000 − 34,567 =
?

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 4: Inverse Check

If 56,284 + 23,716 = 80,000, which calculation can you use to CHECK this?

Hint: Inverse of addition is subtraction. Subtract one addend from the total.

80,000−56,284
80,000+23,716
56,284+80,000
80,000÷23,716
Check calculation:
drag here

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 5: Multi-step Problem

A factory makes 45,600 items. 12,350 are sold on Monday and 8,720 on Tuesday. How many remain?

Hint: Total sold = 12,350 + 8,720 = 21,070. Then 45,600 − 21,070 = ?

24,530
25,430
24,630
25,530
Items remaining =
?

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🎯 Drag Exercise 6: Missing Number

Find the missing number: __ + 34,862 = 100,000

Hint: Use the inverse operation: 100,000 − 34,862 = ?

65,138
65,238
64,138
65,148
?
+ 34,862 = 100,000

Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

📝 Practice Questions

Work through all 20 questions. Try each one before revealing the answers!

  1. 5,347 + 2,618 = ?
  2. 8,924 − 3,461 = ?
  3. Estimate 7,832 + 4,219 to the nearest 1,000.
  4. 46,285 + 33,714 = ?
  5. 72,000 − 48,657 = ?
  6. 123,456 + 87,654 = ?
  7. 500,000 − 267,483 = ?
  8. What is 84,000 + 16,000?
  9. Estimate 29,461 − 12,783 (to the nearest 1,000).
  10. 63,847 + 27,165 = ?
  11. Missing number: 45,000 + ___ = 100,000
  12. 1,000,000 − 1 = ?
  13. 347,218 + 152,782 = ?
  14. 800,000 − 345,621 = ?
  15. A school raised £34,750 in Term 1 and £27,860 in Term 2. What is the total raised?
  16. Check using inverse: if 56,321 + 33,679 = 90,000, what is 90,000 − 33,679?
  17. 4,005 − 3,978 = ?
  18. 99,999 + 1 = ?
  19. A city has 234,500 people. 56,750 move away. How many remain?
  20. What number is 100,000 less than 1,456,789?

✅ Answers

  1. 5,347 + 2,618 = 7,965
  2. 8,924 − 3,461 = 5,463
  3. Estimate: 8,000 + 4,000 = 12,000
  4. 46,285 + 33,714 = 79,999
  5. 72,000 − 48,657 = 23,343
  6. 123,456 + 87,654 = 211,110
  7. 500,000 − 267,483 = 232,517
  8. 84,000 + 16,000 = 100,000
  9. Estimate: 29,000 − 13,000 = 17,000 (approximately)
  10. 63,847 + 27,165 = 91,012
  11. 45,000 + 55,000 = 100,000
  12. 1,000,000 − 1 = 999,999
  13. 347,218 + 152,782 = 500,000
  14. 800,000 − 345,621 = 454,379
  15. £34,750 + £27,860 = £62,610
  16. 90,000 − 33,679 = 56,321
  17. 4,005 − 3,978 = 27
  18. 99,999 + 1 = 100,000
  19. 234,500 − 56,750 = 177,750
  20. 1,456,789 − 100,000 = 1,356,789
Collins Stage 6 Cambridge Primary Maths · Units 2 & 3

🏆 Challenge Problems

These multi-step word problems will test your Addition Hero skills. Show all working!

  1. A stadium holds 85,460 people. On Saturday 67,284 attend and on Sunday 71,903 attend. How many more people attended Sunday than Saturday?
  2. Mount Everest is 8,849 m high. The Mariana Trench is 11,034 m deep. What is the total difference in elevation from the bottom of the trench to the top of the mountain?
  3. A country's population is 4,567,823. In one year 87,450 people are born and 61,234 die. What is the new population?
  4. A business earns £345,670 in January and £287,940 in February. Their target was £650,000. By how much did they miss (or beat) the target?
  5. Three runners complete a relay race. Runner A takes 4,325 steps, Runner B takes 3,867 steps, Runner C takes 4,108 steps. What is the total number of steps?
  6. A book has 524 pages. Sam reads 187 pages on Monday and 143 pages on Tuesday. How many pages are left to read?
  7. Country A has a land area of 678,900 km². Country B has 234,500 km² and Country C has 456,300 km². How much larger is the combined area of B and C compared to A?
  8. A shop sells 23,456 items in week 1 and 31,782 items in week 2. Returns are 1,245 and 987 respectively. What are the net sales?
  9. The distance from London to Sydney is 16,993 km. A plane has already flown 7,846 km. How far is still remaining?
  10. A number is 345,678 more than 654,322. What is the number?

✅ Challenge Answers

  1. 71,903 − 67,284 = 4,619 more people attended on Sunday.
  2. 8,849 + 11,034 = 19,883 m total difference in elevation.
  3. 4,567,823 + 87,450 − 61,234 = 4,594,039 new population.
  4. £345,670 + £287,940 = £633,610; £650,000 − £633,610 = £16,390 below target.
  5. 4,325 + 3,867 + 4,108 = 12,300 steps in total.
  6. 187 + 143 = 330 pages read; 524 − 330 = 194 pages remaining.
  7. 234,500 + 456,300 = 690,800; 690,800 − 678,900 = 11,900 km² larger.
  8. (23,456 − 1,245) + (31,782 − 987) = 22,211 + 30,795 = 53,006 net sales.
  9. 16,993 − 7,846 = 9,147 km remaining.
  10. 654,322 + 345,678 = 1,000,000.
Collins Stage 6 Cambridge Primary Maths · Units 2 & 3 · Addition & Subtraction of Whole Numbers A & B