Take Out a Ten

Understanding "Take Out a Ten"

When working with two-digit numbers, one powerful way to understand their structure is to "take out a ten"—mentally or physically removing one group of ten and seeing what remains. This skill helps you understand place value deeply, prepares you for subtraction strategies, and builds flexibility in how you think about numbers.

What Does "Take Out a Ten" Mean?

"Taking out a ten" means removing one ten (10) from a two-digit number and identifying what's left. This process helps you see that any two-digit number can be broken apart and put back together in different ways.

Example: Take out a ten from 67 - Start with 67 - Remove 10 - Left with 57 - We can write this as: 67 - 10 = 57 or 57 + 10 = 67

Both equations show the same relationship—they're just viewed from different angles!

Why This Skill Matters

Understanding how to take out a ten is important because: - It deepens place value understanding: You see that numbers are made of tens and ones - It prepares you for subtraction: Taking out ten is a form of subtraction - It builds number flexibility: You learn to break numbers apart and recombine them - It supports mental math: You can use this skill to solve problems in your head - It connects to regrouping: This is foundational for understanding carrying and borrowing

The Basic Process

Let's break down how to take out a ten step by step.

Step 1: Identify Your Starting Number

Look at your two-digit number and recognize its tens and ones: - 67: 6 tens and 7 ones - 45: 4 tens and 5 ones - 82: 8 tens and 2 ones

Step 2: Take Out One Ten

Remove one ten from the tens place: - 67 → Take out 10 → 57 (went from 6 tens to 5 tens) - 45 → Take out 10 → 35 (went from 4 tens to 3 tens) - 82 → Take out 10 → 72 (went from 8 tens to 7 tens)

Quick Pattern

Notice the pattern: - The tens digit decreases by 1 - The ones digit stays exactly the same - You've simply removed one of the tens!

Step 3: Express the Relationship

You can write this relationship in two ways:

Subtraction form: Original - 10 = Result - 67 - 10 = 57

Addition form: Result + 10 = Original - 57 + 10 = 67

Both are correct! They show the same relationship from different perspectives.

Detailed Examples

Let's work through various examples to see the pattern clearly.

Example 1: Take out a ten from 34

Step 1: Starting number: 34 (3 tens and 4 ones)

Step 2: Take out one ten: 34 → 24 (2 tens and 4 ones)

Step 3: Express the relationship: - Subtraction: 34 - 10 = 24 - Addition: 24 + 10 = 34

Verification: The ones stay the same (4), tens decreased by 1 (from 3 to 2) ✓

Example 2: Take out a ten from 78

Step 1: Starting number: 78 (7 tens and 8 ones)

Step 2: Take out one ten: 78 → 68 (6 tens and 8 ones)

Step 3: Express the relationship: - Subtraction: 78 - 10 = 68 - Addition: 68 + 10 = 78

Verification: The ones stay the same (8), tens decreased by 1 (from 7 to 6) ✓

Example 3: Take out a ten from 50

Step 1: Starting number: 50 (5 tens and 0 ones)

Step 2: Take out one ten: 50 → 40 (4 tens and 0 ones)

Step 3: Express the relationship: - Subtraction: 50 - 10 = 40 - Addition: 40 + 10 = 50

Verification: The ones stay the same (0), tens decreased by 1 (from 5 to 4) ✓

Example 4: Take out a ten from 91

Step 1: Starting number: 91 (9 tens and 1 one)

Step 2: Take out one ten: 91 → 81 (8 tens and 1 one)

Step 3: Express the relationship: - Subtraction: 91 - 10 = 81 - Addition: 81 + 10 = 91

Verification: The ones stay the same (1), tens decreased by 1 (from 9 to 8) ✓

Example 5: Take out a ten from 26

Step 1: Starting number: 26 (2 tens and 6 ones)

Step 2: Take out one ten: 26 → 16 (1 ten and 6 ones)

Step 3: Express the relationship: - Subtraction: 26 - 10 = 16 - Addition: 16 + 10 = 26

Verification: The ones stay the same (6), tens decreased by 1 (from 2 to 1) ✓

Visual Representations

Seeing this concept visually strengthens understanding.

Base-Ten Blocks

For 67:

Before: [10][10][10][10][10][10] + [●●●●●●●]
         6 tens rods           7 unit cubes

Take out one ten: Remove [10]

After: [10][10][10][10][10] + [●●●●●●●]
        5 tens rods         7 unit cubes = 57

The ones (unit cubes) don't change—we only removed a tens rod!

Number Line

For 45 → 35:

|----|----|----|----|----|----|
25   30   35   40   45   50
          ↑              ↑
          [jump back 10]

• Start at 45
• Jump back 10
• Land at 35

Place Value Chart

For 82:

Before:
Tens | Ones
  8  |  2

Take out one ten:

After:
Tens | Ones
  7  |  2

The ones column stays the same; only the tens column changes!

Ten Frames

For 34:

Before: 3 filled ten frames + 4 in a partial frame

Take out one filled ten frame

After: 2 filled ten frames + 4 in a partial frame = 24

The Two-Way Relationship

One of the most important things to understand is that these relationships work both ways.

From Subtraction to Addition

If you know: 67 - 10 = 57

Then you also know: 57 + 10 = 67

From Addition to Subtraction

If you know: 35 + 10 = 45

Then you also know: 45 - 10 = 35

Why This Matters

Understanding this two-way relationship: - Shows that addition and subtraction are inverses (opposites) - Helps you check your work (if 67 - 10 = 57, then 57 + 10 should equal 67) - Builds algebraic thinking (if a - b = c, then c + b = a) - Makes you flexible in problem-solving (you can approach problems from different angles)

Mental Math Strategies

This skill is perfect for mental calculation.

Strategy 1: Quick Rule

To take out a ten mentally: 1. Look at the tens digit 2. Decrease it by 1 3. Keep the ones digit the same

For 73: Tens = 7, decrease to 6, ones stay 3 → 63

Strategy 2: Count Back by Tens

Start at your number and count back one ten: - From 58: "48"—said one ten back - From 86: "76"—said one ten back

Strategy 3: Use Your Fingers

Hold up fingers to represent tens: - For 43: Hold up 4 fingers (4 tens) - Take out one: Put down 1 finger (3 fingers up) - That represents 3 tens, so answer is 33

Strategy 4: Think "Ten Less"

Ask yourself: "What's ten less than this number?" - Ten less than 67 is 57 - Ten less than 92 is 82 - Ten less than 35 is 25

Real-World Applications

Taking out a ten appears in many everyday situations:

Money

"I had $45 and spent $10. How much is left?" - Take out a ten from 45 - Left with $35

Time

"We have 78 minutes. If we wait 10 minutes, how much time remains?" - Take out a ten from 78 - 68 minutes remain

Measurement

"The rope is 63 inches long. If we cut off 10 inches, what's left?" - Take out a ten from 63 - 53 inches left

Collections

"I have 84 stickers. If I give away 10, how many do I have?" - Take out a ten from 84 - 74 stickers remain

Distance

"The trail is 56 yards. We've walked 10 yards. How far is left?" - Take out a ten from 56 - 46 yards to go

Practice Activities

Make learning interactive and engaging:

Activity 1: Take-Out-a-Ten Cards

Materials: Index cards

Create cards: - Front: A number (like 67) - Back: Number with ten taken out (57) and both equations (67 - 10 = 57 and 57 + 10 = 67) - Practice until automatic!

Activity 2: Base-Ten Block Modeling

Materials: Base-ten blocks (or drawings)

Activity: 1. Build a two-digit number (like 45) 2. Physically remove one tens rod 3. Count what remains 4. Write both equations

Activity 3: Number Line Jumps

Materials: Number line from 0-100

Activity: 1. Start at any two-digit number 2. Jump back 10 spaces 3. Mark where you land 4. Write the subtraction and addition equations

Activity 4: Quick Fire Challenge

Materials: Timer, list of numbers

Challenge: - Partner calls out a number - You quickly say the number with ten taken out - How many can you get right in one minute? - Switch roles!

Activity 5: Real-Life Problem Creation

Activity: - Create your own word problems involving taking out ten - Use real situations from your life - Solve them and check your answers

Activity 6: Dice Game

Materials: Two dice

Game: 1. Roll two dice to create a two-digit number 2. Take out a ten from that number 3. Write both equations 4. Roll again and repeat—how many can you do in 5 minutes?

Building Fluency

Fluency means instant recognition and calculation.

Progressive Practice Plan

Week 1: Focus on numbers in the 20s and 30s - 21-29, 31-39 - Smaller numbers are easier to visualize

Week 2: Add numbers in the 40s and 50s - 41-49, 51-59 - Build confidence with medium numbers

Week 3: Add numbers in the 60s and 70s - 61-69, 71-79 - Extend to larger numbers

Week 4: Add numbers in the 80s and 90s - 81-89, 91-99 - Complete the range

Week 5: Mix all ranges randomly - Any number from 11-99 - Test your full fluency

Daily Practice Routine

Morning (3 minutes): - Write 10 random two-digit numbers - Take out a ten from each - Write both equations for each

Afternoon (3 minutes): - Mental practice only - Look at numbers around you - Mentally take out a ten

Evening (2 minutes): - Review any challenging numbers - Focus on the pattern: tens decrease by 1, ones stay the same

Multiple Formats

Practice in different ways: - Written: Write equations on paper - Verbal: Say problems and answers out loud - Visual: Draw base-ten blocks or number lines - Physical: Use actual manipulatives - Digital: Use apps or online games

Common Challenges and Solutions

Challenge: "I forget which digit changes"

Solution: Remember: only the TENS digit changes (decreases by 1). The ONES digit always stays exactly the same. Use the phrase "Tens take, ones stay."

Challenge: "I accidentally change the ones digit"

Solution: Circle or underline the ones digit before you start. Remind yourself that this digit doesn't move—it's only along for the ride!

Challenge: "I subtract from the wrong place"

Solution: Write out your number in expanded form first: - 67 = 60 + 7 - Take out 10: 60 - 10 = 50 - Add back the ones: 50 + 7 = 57

Challenge: "I mix up adding and subtracting"

Solution: "Take out" means subtract. But remember, you can express the same relationship as addition going the other way! Practice writing both forms.

Connecting to Other Concepts

Place Value Understanding

Taking out a ten reinforces: - Two-digit numbers have tens and ones - Each digit's position determines its value - We can work with tens and ones separately - One ten equals 10 ones

Subtracting Tens

This is the foundation for subtracting any multiple of ten: - If you can take out 10, you can take out 20 (take out ten twice) - If you can take out 10, you can take out 30 (take out ten three times) - Pattern: 67 - 20 = 67 - 10 - 10 = 57 - 10 = 47

Addition Strategies

Understanding this helps with adding tens: - If 57 + 10 = 67, you understand adding tens - This extends: 57 + 20 = 77 (add ten twice) - Mental math becomes easier

Regrouping in Subtraction

When you later learn to "borrow" in subtraction: - You're actually taking out a ten and breaking it into ones - Understanding "take out a ten" makes borrowing make sense - The concept is the same!

Inverse Operations

This skill shows that addition and subtraction are inverses: - Taking out undoes adding - Adding undoes taking out - They're opposite operations

Assessment Checkpoints

You've mastered this skill when you can: - ✓ Instantly take out a ten from any two-digit number - ✓ Explain why only the tens digit changes - ✓ Write both the subtraction and addition equation - ✓ Use base-ten blocks or drawings to show the process - ✓ Apply this skill to real-world problems - ✓ Connect it to place value understanding

Looking Ahead

This skill prepares you for:

Subtracting Multiples of Ten

• 67 - 20, 67 - 30, 67 - 40
• Use repeated "take out a ten"

Two-Digit Subtraction

• Understanding regrouping (borrowing)
• Breaking tens into ones when needed

Mental Math Strategies

• Quick calculations without paper
• Estimating by working with tens

Three-Digit Numbers

• Taking out ten from three-digit numbers
• Taking out one hundred
• Same principles, larger numbers!

Understanding Equations

• Seeing that 67 - 10 = 57 and 57 + 10 = 67 show the same relationship
• Foundation for algebraic thinking

Conclusion

Learning to take out a ten is a fundamental skill that builds deep understanding of place value and number relationships. By practicing this skill, you're developing flexibility in how you think about numbers—seeing that they can be broken apart and recombined in useful ways. This understanding will serve you well as you encounter more complex subtraction, work with larger numbers, and develop advanced mental math strategies. Remember, the pattern is simple: take one from the tens, keep the ones the same. Practice regularly with various representations, and soon this will become automatic. You're building mathematical foundations that will support your learning for years to come!