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

A Mental Math Warm-Up to Start

Quick Addition

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

Think fast!

Checking Your Warm-Up Answers Now

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
• Agriculture: Total bags of maize, kilograms of coffee
• School: Total number of learners in multiple schools

Reviewing Place Value Before We Start

Remember This Number?

2,345,678

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

Addition That Needs No Regrouping

Example 1: Simple Addition

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

Let's solve this step by step...

Solving Example 1 Step by Step

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

Process: Ones 1+7=8, Tens 2+6=8, Hundreds 3+5=8

When Do We Need to Regroup?

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

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

Setting Up Addition with Regrouping

Example 2: Addition with Regrouping

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

Let's work through this carefully...

Working Through Example 2's First Steps

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

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

Finishing Example 2's Remaining Columns

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

Thousands: 6+7+1=14, Ten thousands: 5+8+1=14

Final answer: 744,443

A Seven-Digit Addition to Try Together

Example 3: Seven-Digit Addition

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

Work with me step by step!

Solving the Full Seven-Digit Addition

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

Every column from ones through hundred thousands carries a 1.

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

A Word Problem About Maize Production

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?

Solving the Maize Production Problem

Step 1: Understand - We need to ADD

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

Answer: 5,333,323 kilograms

Practice: Adding the School Population

School Population

Add: 234,567 + 189,876

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

Try this on your own!

Checking the School Population Answer

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

Did you get it right?

Practice Problem: Large Number Addition

Large Number Addition

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

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

Checking the Large Number Answer

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

Excellent work if you got this!

Practice Problem: Coffee Harvest Totals

Coffee Harvest

Add: 987,654 + 876,543

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

Checking the Coffee Harvest Answer

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

Notice we got an answer with 7 digits!

Word Problem: Counting All Learners

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
-------
  ?

Checking the School Learners Answer

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

The school has 5,221 learners in total.

Word Problem: Combining Two Harvests

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
---------
    ?

Checking the Combined Harvest Answer

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

Total harvest: 802,467 kilograms

Quick Assessment on Today's Addition Skills

Answer these questions:

1. Add: 456,789 + 234,567 = ?
2. When adding, which place do we start from?
3. What do we do when a column sum is 10 or more?

Checking Your 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 Worth Avoiding Today

Don't do this:

• Forgetting to line up by place value
• Forgetting to carry over
• Starting from the left

Do this instead:

• Carefully align all digits
• Mark carried numbers above
• Always start from the right

Summary of Today's Addition Lesson

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

Great job!

Tonight's Homework on Whole Number Addition

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: Two sub-counties have 234,567 and 456,789 people. Find the total population.

Show all your working!

Remember These Five Steps Always

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 on Today's Lesson!

You can now add large numbers with regrouping!

Next lesson: Subtraction with Regrouping

Keep practicing!