Make the Next Ten

Understanding "The Next Ten"

Every number has a "next ten" waiting for it—the next multiple of ten that comes after the number. For example, if you're at 23, the next ten is 30. If you're at 47, the next ten is 50. Learning to quickly identify the next ten and figure out how many ones are needed to reach it is a fundamental skill that strengthens your number sense and prepares you for advanced mental math strategies.

What is "The Next Ten"?

The next ten is simply the next multiple of ten that comes after your current number. Multiples of ten are numbers that end in zero: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and so on.

Examples: - For 23: the next ten is 30 (need 7 more) - For 47: the next ten is 50 (need 3 more) - For 68: the next ten is 70 (need 2 more) - For 91: the next ten is 100 (need 9 more)

Why This Skill Matters

Understanding how to make the next ten is important because: - It builds number sense: You develop an intuitive feel for where numbers sit on the number line - It prepares you for mental math: Many addition strategies involve making ten first - It helps with estimation: Knowing how close you are to the next ten helps with rounding - It strengthens place value understanding: You see clearly how ones fill up to make a new ten - It's foundational for regrouping: Making a new ten is what happens when we "carry" in addition

Identifying The Next Ten

The first step is being able to quickly identify what the next ten is for any given number.

The Pattern

Look at the tens digit of your number: - For 23: Tens digit is 2, so the next ten is 30 (2 + 1 = 3, add a zero) - For 47: Tens digit is 4, so the next ten is 50 (4 + 1 = 5, add a zero) - For 68: Tens digit is 6, so the next ten is 70 (6 + 1 = 7, add a zero) - For 95: Tens digit is 9, so the next ten is 100 (9 + 1 = 10)

Quick Rule

To find the next ten: 1. Look at your tens digit 2. Add 1 to it 3. Put a 0 in the ones place 4. That's your next ten!

Example: For 56 - Tens digit: 5 - Add 1: 5 + 1 = 6 - Add zero: 60 - Next ten is 60!

Special Case: Numbers Ending in Zero

If your number already ends in zero (like 20, 30, 40), it's already AT a ten, so the next ten is simply adding 10: - 20 → 30 (need 10 more) - 50 → 60 (need 10 more) - 80 → 90 (need 10 more)

Finding How Many Ones Are Needed

Once you know the next ten, you need to figure out how many ones it takes to get there.

The Subtraction Method

Formula: (Next Ten) - (Current Number) = (Ones Needed)

Example: Starting at 28 - Next ten: 30 - Calculation: 30 - 28 = 2 - Need 2 ones to make 30

Example: Starting at 64 - Next ten: 70 - Calculation: 70 - 64 = 6 - Need 6 ones to make 70

The Counting Method

Another way is to look at the ones digit and think "What do I need to make 10?"

Example: Starting at 28 - Ones digit: 8 - Question: "What plus 8 makes 10?" - Answer: 2 (because 8 + 2 = 10) - So you need 2 ones to make the next ten

Example: Starting at 64 - Ones digit: 4 - Question: "What plus 4 makes 10?" - Answer: 6 (because 4 + 6 = 10) - So you need 6 ones to make the next ten

The "Fill the Ten Frame" Method

Imagine a ten frame with 10 spaces: - Fill in spaces equal to your ones digit - Count the empty spaces - That's how many more you need!

For 37: - Ones digit is 7 - Fill 7 spaces in ten frame - 3 spaces empty - Need 3 ones to make 40

Detailed Examples

Let's work through various examples systematically.

Example 1: Make the Next Ten from 23

Step 1: Identify the next ten - Current number: 23 - Tens digit: 2 - Next ten: 30 (2 + 1 = 3, add zero)

Step 2: Find how many ones needed - Method 1 (Subtraction): 30 - 23 = 7 - Method 2 (Partners): 3 + ? = 10 → 7 - Need 7 ones

Verification: 23 + 7 = 30 ✓

Example 2: Make the Next Ten from 68

Step 1: Identify the next ten - Current number: 68 - Tens digit: 6 - Next ten: 70 (6 + 1 = 7, add zero)

Step 2: Find how many ones needed - Method 1 (Subtraction): 70 - 68 = 2 - Method 2 (Partners): 8 + ? = 10 → 2 - Need 2 ones

Verification: 68 + 2 = 70 ✓

Example 3: Make the Next Ten from 45

Step 1: Identify the next ten - Current number: 45 - Tens digit: 4 - Next ten: 50 (4 + 1 = 5, add zero)

Step 2: Find how many ones needed - Method 1 (Subtraction): 50 - 45 = 5 - Method 2 (Partners): 5 + ? = 10 → 5 - Need 5 ones

Verification: 45 + 5 = 50 ✓

Example 4: Make the Next Ten from 91

Step 1: Identify the next ten - Current number: 91 - Tens digit: 9 - Next ten: 100 (9 + 1 = 10)

Step 2: Find how many ones needed - Method 1 (Subtraction): 100 - 91 = 9 - Method 2 (Partners): 1 + ? = 10 → 9 - Need 9 ones

Verification: 91 + 9 = 100 ✓

Example 5: Make the Next Ten from 56

Step 1: Identify the next ten - Current number: 56 - Tens digit: 5 - Next ten: 60 (5 + 1 = 6, add zero)

Step 2: Find how many ones needed - Method 1 (Subtraction): 60 - 56 = 4 - Method 2 (Partners): 6 + ? = 10 → 4 - Need 4 ones

Verification: 56 + 4 = 60 ✓

Visual Representations

Visualizing the concept helps understanding and memory.

Number Line Representation

For 28 → 30:

|----|----|----|----|
24   26   28   30
          ↑    ↑
       [need 2]

• Start at 28
• Jump to 30
• Count the jumps: 2

Ten Frame Visualization

For 37 → 40:

Ten Frame for ones digit (7):
[●][●][●][●][●]
[●][●][○][○][○]

• 7 filled circles
• 3 empty circles
• Need 3 more to fill the frame = need 3 more to make 40

Hundred Chart

On a hundred chart: - Numbers in the same column all have the same ones digit - Moving down one row = adding 10 = reaching the next ten - Count the spaces to the next row

For 34:

31 32 33 34 35 36 37 38 39 40
          ↑              ↑
       [need to jump 6 spaces]

The Role of Partners of Ten

This skill relies heavily on knowing partners of ten (pairs that make 10): - 1 + 9 = 10 - 2 + 8 = 10 - 3 + 7 = 10 - 4 + 6 = 10 - 5 + 5 = 10 - 6 + 4 = 10 - 7 + 3 = 10 - 8 + 2 = 10 - 9 + 1 = 10 - 10 + 0 = 10

If you instantly know these, finding what's needed to make the next ten becomes automatic!

Mental Math Strategies

This skill is perfect for mental math.

Strategy 1: Focus on the Ones

For any number, just look at the ones digit: - Ones digit 1 → need 9 - Ones digit 2 → need 8 - Ones digit 3 → need 7 - Ones digit 4 → need 6 - Ones digit 5 → need 5 - Ones digit 6 → need 4 - Ones digit 7 → need 3 - Ones digit 8 → need 2 - Ones digit 9 → need 1 - Ones digit 0 → need 10

Strategy 2: Count Up

Start at your ones digit and count up to 10: - For 47: "7, 8, 9, 10" (counted 3 numbers) → need 3 - For 83: "3, 4, 5, 6, 7, 8, 9, 10" (counted 7 numbers) → need 7

Strategy 3: Use Your Fingers

Hold up fingers equal to the ones digit, then count how many fingers are still down: - For 36: Hold up 6 fingers → 4 fingers still down → need 4 ones

Real-World Applications

This skill appears in many everyday situations:

Money

"I have 43 cents. How many more cents until I have 50 cents?" - Next ten: 50 - Need: 50 - 43 = 7 more cents

Time

"It's 28 minutes past the hour. How many minutes until 30?" - Next ten: 30 - Need: 30 - 28 = 2 more minutes

Measurement

"The board is 67 inches long. How much more until it's 70 inches?" - Next ten: 70 - Need: 70 - 67 = 3 more inches

Collections

"I have 54 cards. How many more until I have 60?" - Next ten: 60 - Need: 60 - 54 = 6 more cards

Games and Scores

"My score is 76. How many points until I hit 80?" - Next ten: 80 - Need: 80 - 76 = 4 more points

Practice Activities

Make learning engaging and fun:

Activity 1: Next Ten Flash Cards

Materials: Index cards

Create cards: - Front: A number (like 47) - Back: Next ten (50) and ones needed (3) - Practice until instant!

Activity 2: Number Line Jumps

Materials: Number line from 0-100

Activity: 1. Choose a starting number 2. Identify the next ten 3. Draw jumps of one to get there 4. Count your jumps!

Activity 3: Ten Frame Challenge

Materials: Ten frame and counters

Activity: 1. Roll a die to get a ones digit (1-6) 2. Place that many counters in the ten frame 3. Count empty spaces 4. That's how many ones needed!

Activity 4: Race to the Next Ten

Materials: Two dice, paper

Game for 2 players: 1. Each player rolls two dice to make a two-digit number 2. Whoever needs fewer ones to reach the next ten wins the round 3. First to 5 round wins overall!

Activity 5: Real-World Scavenger Hunt

Activity: - Find two-digit numbers in your environment - Addresses, prices, page numbers - For each, determine the next ten and ones needed - Keep a list of your findings!

Building Fluency

Fluency means instant identification without calculation.

Progressive Practice

Week 1: Focus on ones digits 1-3 - Numbers like 21, 32, 43, 51, 62, 73 - These need 9, 8, or 7 to make the next ten

Week 2: Add ones digits 4-6 - Numbers like 24, 35, 46, 54, 65, 76 - These need 6, 5, or 4 to make the next ten

Week 3: Add ones digits 7-9 - Numbers like 27, 38, 49, 57, 68, 79 - These need 3, 2, or 1 to make the next ten

Week 4: Add numbers ending in 0 - 20, 30, 40, 50, etc. - These need 10 to make the next ten

Week 5: Mix all types randomly

Daily Practice Routine

Morning (3 minutes): - Practice 10 random numbers - Write the next ten and ones needed for each

Afternoon (3 minutes): - Mental practice: look at numbers around you - Mentally determine next ten and ones needed

Evening (2 minutes): - Review any that were challenging - Focus on the ones digit patterns

Multiple Representations

Practice the same concept differently: - Symbolic: 47 + 3 = 50 - Verbal: "Forty-seven needs three to make fifty" - Visual: Draw on a number line - Physical: Use counters and ten frames

Common Challenges and Solutions

Challenge: "I can't remember which ten comes next"

Solution: Add 1 to the tens digit and put a zero at the end. Practice counting by tens: 10, 20, 30, 40, 50...

Challenge: "I don't know how many ones I need"

Solution: Focus on just the ones digit and ask "What plus this number makes 10?" Practice partners of ten separately!

Challenge: "I keep getting confused with subtraction"

Solution: Remember you're subtracting the current number from the next ten, not the other way around. 50 - 47 = 3 (not 47 - 50).

Challenge: "Numbers ending in 7, 8, 9 are hard"

Solution: These need only 3, 2, or 1 to make the next ten—they're actually the easiest! Practice these specifically until they become automatic.

Connecting to Other Concepts

Addition with Regrouping

Understanding making tens helps with carrying: - 47 + 8: First make 50 (need 3), then add remaining 5 = 55 - You've made the next ten!

Rounding

Making the next ten is related to rounding: - 47 rounds to 50 (3 away) - 43 rounds to 40 (3 away from previous ten) - Understanding distance to tens helps with rounding decisions

Mental Math Strategies

Many mental math tricks use making tens: - Adding: break addends to make tens first - Subtracting: take from ten strategies - Both rely on this foundational skill

Place Value Understanding

This reinforces: - When you have 10 ones, they regroup into 1 ten - Each ten is a benchmark number - Numbers progress systematically toward the next ten

Assessment Checkpoints

You've mastered this skill when you can: - ✓ Instantly identify the next ten for any two-digit number - ✓ Quickly state how many ones are needed - ✓ Use this skill in mental math strategies - ✓ Explain why knowing this is useful - ✓ Apply it to real-world situations - ✓ Connect it to place value understanding

Looking Ahead

This skill prepares you for:

Three-Digit Numbers

• Making the next ten in the ones place
• Making the next hundred
• Same principles, larger numbers!

Advanced Mental Math

• Breaking addends to make tens
• Compensation strategies (add too much, subtract the extra)
• Estimating sums and differences

Rounding and Estimation

• Rounding to the nearest ten
• Estimating answers before calculating
• Checking if answers are reasonable

Multiplication

• Skip counting relates to making tens
• Understanding multiples of 10
• Estimating products

Conclusion

Learning to identify the next ten and determine how many ones are needed to reach it is a foundational skill that builds number sense and prepares you for advanced mental math. This skill connects partners of ten, place value understanding, and strategic thinking. Practice regularly with different representations, and soon you'll find yourself automatically seeing numbers in relation to the next ten. This awareness of where numbers sit in our number system is a sign of strong mathematical thinking that will serve you well throughout your mathematical journey!