Addition to Multiples of 10

Understanding Multiples of Ten

Multiples of ten are special numbers that end in zero: 10, 20, 30, 40, 50, 60, 70, 80, 90. These numbers are called multiples of ten because they can each be made by multiplying ten by another number (1×10=10, 2×10=20, 3×10=30, and so on). Understanding how to add to multiples of ten is a crucial skill that makes mental math faster and builds your understanding of place value.

What Makes Multiples of Ten Special?

Multiples of ten have unique properties that make them easier to work with:

• They end in zero: This makes them easy to recognize
• They represent complete tens: No leftover ones to worry about
• They're benchmarks: We use them to estimate and anchor our thinking
• They're building blocks: All larger numbers are built from tens and ones

When you become fluent with multiples of ten, you gain a powerful tool for mental calculation.

The Pattern of Multiples of Ten

Let's look at the complete list up to 100: - 10 (1 ten, 0 ones) - 20 (2 tens, 0 ones) - 30 (3 tens, 0 ones) - 40 (4 tens, 0 ones) - 50 (5 tens, 0 ones) - 60 (6 tens, 0 ones) - 70 (7 tens, 0 ones) - 80 (8 tens, 0 ones) - 90 (9 tens, 0 ones) - 100 (10 tens, 0 ones)

Notice the pattern: the tens digit increases by one each time (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), while the ones digit always stays at zero.

Adding Single Digits to Multiples of Ten

One of the most useful skills is being able to quickly add a single-digit number (1-9) to a multiple of ten. This creates two-digit numbers in the next "decade."

The Basic Pattern

When you add a single digit to a multiple of ten: - The tens digit stays the same - The ones digit becomes the number you added

Examples: - 20 + 3 = 23 (the 2 tens stay, you add 3 ones) - 40 + 7 = 47 (the 4 tens stay, you add 7 ones) - 60 + 5 = 65 (the 6 tens stay, you add 5 ones)

Why This Works: Place Value

Understanding place value makes this clear: - 20 means 2 tens and 0 ones - When you add 3, you're adding 3 ones - Result: 2 tens and 3 ones = 23

The tens stay constant because you're only adding ones!

Visual Representation with Base-Ten Blocks

Imagine using base-ten blocks: - For 30: You have 3 tens rods - Adding 4: You add 4 unit cubes - Result: 3 tens rods + 4 unit cubes = 34

The tens rods don't change—you're just adding ones alongside them.

Adding Multiples of Ten Together

Another important skill is adding two multiples of ten together. This is like counting by tens!

The Simple Strategy

When adding multiples of ten: 1. Look at the tens digits 2. Add those digits together 3. Put a zero at the end

Examples: - 20 + 30 = 50 (2 tens + 3 tens = 5 tens = 50) - 40 + 20 = 60 (4 tens + 2 tens = 6 tens = 60) - 30 + 50 = 80 (3 tens + 5 tens = 8 tens = 80)

Why This Works

Each multiple of ten represents a certain number of tens: - 20 = 2 tens - 30 = 3 tens - 2 tens + 3 tens = 5 tens = 50

You're essentially counting tens instead of ones!

Connection to Basic Addition

If you know 2 + 3 = 5, then you know 20 + 30 = 50. The basic fact doesn't change—you just add a zero because you're working with tens instead of ones.

Mental Math Strategies

Developing strong mental math with multiples of ten makes you a more confident mathematician.

Strategy 1: Skip Counting

Skip counting by tens is one of the easiest ways to add multiples of ten:

30 + 40: - Start at 30 - Count by tens four times: "40, 50, 60, 70" - Answer: 70

Strategy 2: Number Line Jumps

Visualize a number line: - Mark your starting multiple of ten - Make jumps of ten for each ten you're adding - Count where you land

For 20 + 30: - Start at 20 - Jump three tens: 20 → 30 → 40 → 50 - Land on 50

Strategy 3: Think "Tens + Ones"

Break numbers into tens and ones:

50 + 7: - Think: "5 tens and 0 ones plus 0 tens and 7 ones" - Keep the tens together: 5 tens - Keep the ones together: 7 ones - Result: 5 tens and 7 ones = 57

Strategy 4: Benchmark Thinking

Use 50 as a benchmark (halfway to 100):

30 + 40: - "30 is 20 away from 50" - "I'm adding 40, which is more than 20" - "So I'll go past 50... 30 + 20 = 50, then 50 + 20 = 70"

Real-World Applications

Multiples of ten appear constantly in everyday life:

Money

• Counting ten-dollar bills: $10, $20, $30, $40, $50
• "I have $20 and earn $30 more = $50 total"
• "Something costs $40, I pay with $50, I get $10 change"

Time

• Counting minutes: 10 minutes, 20 minutes, 30 minutes
• "Class is 20 minutes, then recess is 30 minutes = 50 minutes total"

Measurement

• "The room is 40 inches wide, the table is 30 inches = 70 inches if I put them together"

Age and Years

• "My dad was born 40 years ago, my mom was born 30 years ago, that's 70 years of birth dates to remember!"

Sports and Games

• Scoring by tens: "Team A has 30 points, scores 40 more = 70 points total"

Shopping

• "Bananas cost $20, apples cost $30 = $50 for fruit"

Practice Activities

Make learning interactive and engaging:

Activity 1: Multiple of Ten Dominoes

Materials: Index cards

How to play: 1. Create cards with multiples of ten (20, 30, 40, etc.) 2. Create cards with addition problems (30 + 20) 3. Match each problem to its answer 4. Time yourself and try to beat your record!

Activity 2: Multiple of Ten Bingo

Materials: Bingo cards with multiples of ten

How to play: 1. Create bingo cards with numbers like 20, 30, 40, 50, 60, 70, 80, 90 2. Call out addition problems like "20 + 30" 3. Players mark the answer (50) 4. First to get bingo wins!

Activity 3: Build the Numbers

Materials: Base-ten blocks or drawings

Activity: 1. Choose a multiple of ten (like 40) 2. Build it with tens rods 3. Add some ones cubes (like 5) 4. Write the equation: 40 + 5 = 45 5. Try different combinations!

Activity 4: Multiple of Ten War

Materials: Deck of cards (remove face cards, use only 1-9)

How to play: 1. Each player flips two cards 2. Multiply the first card by 10 (if you flip 4, that's 40) 3. Add the second card (if you flip 3, that's 40 + 3 = 43) 4. Highest number wins the round!

Activity 5: Real-World Hunt

Activity: - Look for multiples of ten in your environment - Prices, measurements, addresses, page numbers - When you find two, add them mentally - Example: "Address is 40, room number is 30, together that's 70"

Building Fluency

Fluency means quick, accurate recall without hesitation. Here's how to build it:

Daily Practice Routine

3-Minute Morning Drill: - Practice 10 problems adding single digits to multiples of ten - Example: 30+4, 50+7, 20+9, 80+3, etc.

3-Minute Afternoon Drill: - Practice 10 problems adding multiples of ten together - Example: 20+30, 40+50, 10+60, 30+40, etc.

Progressive Challenge

Week 1: Focus on 10, 20, 30, 40 Week 2: Add 50, 60 Week 3: Add 70, 80, 90 Week 4: Mix everything together Week 5: Time yourself and track improvement

Multiple Formats

Practice in various ways: - Written: Write equations on paper - Verbal: Say problems and answers out loud - Visual: Draw number lines or use blocks - Digital: Use apps or online games - Physical: Move around a floor number line

Common Challenges and Solutions

Challenge: "I forget the pattern"

Solution: Remember this simple rule: - Adding ones to tens: The tens stay, the ones appear - Adding tens to tens: Add the tens digits, put a zero at the end

Challenge: "I still count by ones"

Solution: Practice skip counting by tens first: - 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 - Do this until it's automatic - Then apply it to addition problems

Challenge: "I get confused with larger numbers"

Solution: Start small! - Master 10 + ones first - Then 20 + ones - Then 30 + ones - Gradually work up to 90 + ones

Challenge: "I can't do it in my head"

Solution: Use tools at first: - Number lines - Hundred charts - Fingers (each finger = 10) - Gradually reduce tool use as confidence builds

Connecting to Other Concepts

Two-Digit Addition

Understanding multiples of ten helps with all two-digit addition: - 25 + 34: Think "20 + 30 = 50, then 5 + 4 = 9, so 50 + 9 = 59"

Subtraction

If you know 40 + 30 = 70, you also know: - 70 - 30 = 40 - 70 - 40 = 30

Skip Counting

Adding multiples of ten is the same as skip counting by tens: - 20 + 10 + 10 + 10 = 50 is like counting 20, 30, 40, 50

Multiplication Preview

Adding multiples of ten previews multiplication: - 20 + 20 + 20 = 60 is the same as 3 × 20 = 60

Place Value Understanding

Working with multiples of ten reinforces that: - The digit in the tens place tells how many tens - The digit in the ones place tells how many ones - They work independently!

Assessment Checkpoints

You've mastered this concept when you can: - ✓ Quickly add any single digit to any multiple of ten (like 70 + 8) - ✓ Quickly add two multiples of ten together (like 30 + 50) - ✓ Explain using place value why 40 + 6 = 46 - ✓ Count by tens starting from any multiple of ten - ✓ Use these skills to solve real-world problems - ✓ Work mentally without counting by ones

Looking Ahead

This foundation prepares you for:

Adding to Larger Numbers

• 120 + 5 = 125
• 300 + 40 = 340
• The same patterns continue!

Three-Digit Addition

• Understanding that 200 + 300 = 500
• Same pattern, just with hundreds instead of tens

Mental Math with Money

• Quickly adding dollars: $30 + $40 = $70
• Making change: "I paid $50, it costs $37, I get $13 back"

Estimation Skills

• Rounding to multiples of ten helps estimate answers
• "32 is close to 30, 48 is close to 50, so about 80 total"

Conclusion

Mastering addition with multiples of ten is a powerful skill that combines understanding of place value with practical mental math. These skills make you faster and more confident with numbers. Remember that multiples of ten are your friends—they're the scaffolding that supports all two-digit and larger numbers. Practice regularly, use visual tools when helpful, and celebrate your growing speed and accuracy. You're building mathematical foundations that will serve you well throughout your education and life!