Addition of Whole Numbers with Regrouping

P6 Mathematics - Term I, Topic 3

Lesson 1 of 5

Learning Objectives:

• Add whole numbers with regrouping up to 7 digits
• Solve word problems involving addition
• Apply place value knowledge correctly

Mental Warm-Up!

Quick Addition

1. 40 + 50 = ?
2. 300 + 700 = ?
3. 5,000 + 3,000 = ?
4. 60,000 + 40,000 = ?

Think fast!

Mental Warm-Up: Answers

1. 40 + 50 = 90
2. 300 + 700 = 1,000
3. 5,000 + 3,000 = 8,000
4. 60,000 + 40,000 = 100,000

When Do We Add Large Numbers?

Real-Life Examples

• Money: School fees, business income, savings
• Population: Counting people in districts, sub-counties
• Distance: Total kilometers traveled
• Agriculture: Total bags of maize, kilograms of coffee
• School: Total number of learners in multiple schools

Place Value Review

Remember This Number?

2,345,678

Key Rule: When adding, we ALWAYS line up digits by place value!

Addition Without Regrouping

Example 1: Simple Addition

  234,321
+ 453,567
---------

Let's solve this step by step...

Example 1: Solution

  234,321
+ 453,567
---------
  687,888

Process:

• Ones: 1 + 7 = 8
• Tens: 2 + 6 = 8
• Hundreds: 3 + 5 = 8
• Thousands: 4 + 3 = 7
• Ten thousands: 3 + 5 = 8
• Hundred thousands: 2 + 4 = 6

No regrouping needed!

Addition WITH Regrouping

When Do We Regroup?

When the sum in any column is 10 or more!

• 9 + 4 = 13 → Write 3, carry 1
• 7 + 8 = 15 → Write 5, carry 1
• 6 + 6 = 12 → Write 2, carry 1

Remember: Carry the "1" to the next column on the left!

Example 2: Addition with Regrouping

  456,789
+ 287,654
---------

Let's work through this carefully...

Example 2: Step-by-Step

    ¹¹¹¹¹¹
  456,789
+ 287,654
---------
  744,443

Ones: 9 + 4 = 13 (write 3, carry 1)
Tens: 8 + 5 + 1 = 14 (write 4, carry 1)
Hundreds: 7 + 6 + 1 = 14 (write 4, carry 1)

Example 2: Continued

    ¹¹¹¹¹¹
  456,789
+ 287,654
---------
  744,443

Thousands: 6 + 7 + 1 = 14 (write 4, carry 1)
Ten thousands: 5 + 8 + 1 = 14 (write 4, carry 1)
Hundred thousands: 4 + 2 + 1 = 7

Final answer: 744,443

Let's Practice Together!

Example 3: Seven-Digit Addition

  1,876,543
+ 2,456,789
-----------

Work with me step by step!

Example 3: Solution

    ¹¹¹¹¹¹
  1,876,543
+ 2,456,789
-----------
  4,333,332

• Ones: 3 + 9 = 12 → 2, carry 1
• Tens: 4 + 8 + 1 = 13 → 3, carry 1
• Hundreds: 5 + 7 + 1 = 13 → 3, carry 1
• Thousands: 6 + 6 + 1 = 13 → 3, carry 1
• Ten thousands: 7 + 5 + 1 = 13 → 3, carry 1
• Hundred thousands: 8 + 4 + 1 = 13 → 3, carry 1
• Millions: 1 + 2 + 1 = 4

The Golden Rules of Addition

1. Line up numbers by place value
2. Start from the ones place (right side)
3. Add each column
4. Carry when sum is 10 or more
5. Check your answer by estimating

Word Problem Time!

Uganda's Maize Production

Problem: In 2022, Uganda's maize production was 3,456,780 kg. In 2023, production increased by 1,876,543 kg. What was the total production in 2023?

What do we need to do?

Word Problem: Solution

Step 1: Understand - We need to ADD
Step 2: Set up the problem
Step 3: Solve

  3,456,780
+ 1,876,543
-----------
  5,333,323 kg

Answer: 5,333,323 kilograms

Practice Problem 1

School Population

Add: 234,567 + 189,876

  234,567
+ 189,876
---------
    ?

Try this on your own!

Practice Problem 1: Answer

    ¹¹¹¹¹
  234,567
+ 189,876
---------
  424,443

Did you get it right?

Practice Problem 2

Large Number Addition

Add: 1,456,789 + 2,987,654

  1,456,789
+ 2,987,654
-----------
      ?

Practice Problem 2: Answer

    ¹¹¹¹¹¹¹
  1,456,789
+ 2,987,654
-----------
  4,444,443

Excellent work if you got this!

Practice Problem 3

Coffee Harvest

Add: 987,654 + 876,543

  987,654
+ 876,543
---------
    ?

Practice Problem 3: Answer

    ¹¹¹¹
  987,654
+ 876,543
---------
1,864,197

Notice we got an answer with 7 digits!

Word Problem Practice 1

School Learners

Problem: A school has 2,345 girls and 2,876 boys. How many learners are in the school altogether?

  2,345
+ 2,876
-------
  ?

Word Problem 1: Answer

   ¹¹¹
  2,345
+ 2,876
-------
  5,221 learners

The school has 5,221 learners in total.

Word Problem Practice 2

Coffee Harvest

Problem: A farmer harvested 345,678 kg of coffee from one plantation and 456,789 kg from another. What was the total harvest?

  345,678
+ 456,789
---------
    ?

Word Problem 2: Answer

    ¹¹¹¹¹¹
  345,678
+ 456,789
---------
  802,467 kg

Total harvest: 802,467 kilograms

Quick Assessment ✓

Answer these questions:

1. Add: 456,789 + 234,567 = ?

2. When adding, which place do we start from?

3. What do we do when the sum in a column is 10 or more?

Quick Assessment: Answers

1. 456,789 + 234,567 = 691,356

2. Start from the ones place (right side)

3. Carry to the next column on the left

Common Mistakes to Avoid!

Don't do this:

• Forgetting to line up by place value
• Forgetting to carry over
• Starting from the left
• Adding the carried number twice

Do this instead:

• Carefully align all digits
• Mark your carried numbers above
• Always start from the right
• Add carried number only once

Summary: What We Learned

Today we learned to:

• Add numbers up to 7 digits with regrouping
• Line up numbers by place value
• Carry when a column sum is 10 or more
• Solve real-life word problems
• Check our answers

Great job!

Homework

1. 567,890 + 345,678 = ?
2. 1,234,567 + 3,456,789 = ?
3. 876,543 + 987,654 = ?
4. 2,345,678 + 4,567,890 = ?
5. Word problem: A district has two sub-counties. The first has 234,567 people, the second has 456,789 people. What is the total population?

Show all your working!

Remember!

The 5 Steps:

1. Line up by place value
2. Start from the ones
3. Add each column
4. Carry if sum ≥ 10
5. Check your answer

Practice makes perfect!

Well Done!

You can now add large numbers with regrouping!

Next lesson: Subtraction with Regrouping

Keep practicing!