Use a Number Bond to Take from Ten When Subtracting

Understanding the "Take from Ten" Strategy

When subtracting a single-digit number from a two-digit number, sometimes the easiest approach is to "take from the ten" first. This strategy uses number bonds to help you visualize and understand how to break down a subtraction problem into simpler parts. It's especially useful when the ones digit in your starting number is smaller than the number you're subtracting.

What Does "Take from Ten" Mean?

"Take from ten" means breaking your two-digit number into tens and ones, then subtracting from the ten part first. Let's look at an example:

Problem: 67 - 9

Instead of struggling with taking 9 away from 7 (which isn't possible without regrouping), we can: 1. Think of 67 as 57 + 10 2. Take 9 from the 10 first: 10 - 9 = 1 3. Add that 1 to the 57: 57 + 1 = 58

So 67 - 9 = 58!

Why This Strategy Works

This strategy works because: - It avoids borrowing/regrouping: You don't need to "borrow" from the tens place - It uses friendly tens: Taking from 10 is easy because you know your partners of ten - It's visual: Number bonds make the process clear and concrete - It builds number sense: You learn to see numbers as flexible combinations of parts

The Role of Number Bonds

A number bond is a visual tool that shows how a number can be broken into parts. For "take from ten" subtraction, we use number bonds to show how we're splitting our two-digit number.

Number Bond Structure

For the number 67:

      67
     /  \
   57    10

This shows that 67 = 57 + 10. We've separated one ten from the rest of the number.

Why We Separate a Ten

When subtracting a single digit (like 9), we separate out one ten because: - Ten is easy to subtract from (we know our partners of ten!) - It leaves the rest of the number intact - We can then combine what's left after subtracting

Step-by-Step Process

Let's break down the complete process for using this strategy.

Step 1: Identify Your Starting Number

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

Step 2: Separate One Ten

Take one ten away from your tens digit and add it to your ones: - 67 becomes 57 + 10 (took one ten from the 60) - 82 becomes 72 + 10 (took one ten from the 80) - 45 becomes 35 + 10 (took one ten from the 40)

Step 3: Create Your Number Bond

Draw a simple number bond showing this split:

Original Number
      /  \
  (tens-10)  10

Step 4: Subtract from the Ten

Now subtract your single-digit number from the 10: - For 67 - 9: 10 - 9 = 1 - For 82 - 8: 10 - 8 = 2 - For 45 - 6: 10 - 6 = 4

This is where knowing partners of ten becomes essential!

Step 5: Add Back to the Remaining Part

Add your result from Step 4 to the other part of your number bond: - 67 - 9: 57 + 1 = 58 - 82 - 8: 72 + 2 = 74 - 45 - 6: 35 + 4 = 39

Detailed Examples

Let's work through several examples step by step.

Example 1: 53 - 8

Step 1: Starting number is 53 (5 tens and 3 ones)

Step 2: Separate one ten: 53 = 43 + 10

Step 3: Number bond:

      53
     /  \
   43    10

Step 4: Take from the ten: 10 - 8 = 2

Step 5: Add to the remaining part: 43 + 2 = 45

Answer: 53 - 8 = 45

Example 2: 76 - 9

Step 1: Starting number is 76 (7 tens and 6 ones)

Step 2: Separate one ten: 76 = 66 + 10

Step 3: Number bond:

      76
     /  \
   66    10

Step 4: Take from the ten: 10 - 9 = 1

Step 5: Add to the remaining part: 66 + 1 = 67

Answer: 76 - 9 = 67

Example 3: 34 - 7

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

Step 2: Separate one ten: 34 = 24 + 10

Step 3: Number bond:

      34
     /  \
   24    10

Step 4: Take from the ten: 10 - 7 = 3

Step 5: Add to the remaining part: 24 + 3 = 27

Answer: 34 - 7 = 27

Example 4: 91 - 5

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

Step 2: Separate one ten: 91 = 81 + 10

Step 3: Number bond:

      91
     /  \
   81    10

Step 4: Take from the ten: 10 - 5 = 5

Step 5: Add to the remaining part: 81 + 5 = 86

Answer: 91 - 5 = 86

When to Use This Strategy

This strategy is most helpful in specific situations:

Best For:

• When ones digit is smaller than what you're subtracting
• 34 - 7 (the 4 is smaller than 7)

• 52 - 8 (the 2 is smaller than 8)

• Subtracting larger single digits (6-9)

• These are harder to work with directly

• Taking from ten is often faster

• Mental math

• No paper needed once you learn the pattern

Less Useful For:

• When ones are large enough
• For 57 - 3, you can just do 7 - 3 = 4, so 54

• No need to take from ten

• Subtracting small numbers (1-3)

• Usually easier to subtract directly

The Foundation: Partners of Ten

To use this strategy efficiently, you must know partners of ten automatically: - 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

If you know these instantly, Step 4 becomes automatic!

Visual Representations

Seeing this strategy visually helps understanding.

Number Line Visualization

For 67 - 9:

[-----57-----][10]
              ↓
            (take 9)
              ↓
[-----57-----][1]
              ↓
       58

• Start at 67
• Separate the last 10
• Take 9 from that 10
• Leaves 1, which combines with 57 to make 58

Base-Ten Blocks

For 53 - 8: - Show 5 tens rods and 3 unit cubes - Break one tens rod into 10 unit cubes - Now you have 4 tens rods and 13 unit cubes - Take away 8 unit cubes - Left with 4 tens rods and 5 unit cubes = 45

Ten Frame Representation

For 34 - 7: - The 4 ones aren't enough to take away 7 - Use a ten frame to show breaking one ten - Remove 7 from the ten frame (leaving 3) - Combine that 3 with the 24 to get 27

Mental Math Practice

This strategy is designed for solving problems in your head.

Talk Yourself Through It

For 45 - 8: - Say: "Forty-five is thirty-five plus ten" - Think: "Ten minus eight is two" - Say: "Thirty-five plus two is thirty-seven"

Visualize the Split

For 62 - 7: - Picture 62 splitting into 52 and 10 - See 10 - 7 = 3 in your mind - Picture 52 + 3 = 55

Use Your Fingers

For 73 - 9: - Think: 73 = 63 + 10 - Hold up 10 fingers - Fold down 9 fingers (1 left up) - That 1 combines with 63 to make 64

Real-World Applications

Shopping

"I have 75 cents and spend 8 cents" - 75 = 65 + 10 - 10 - 8 = 2 - 65 + 2 = 67 cents left

Time Management

"Movie is 67 minutes, watched 9 minutes of commercials" - 67 = 57 + 10 - 10 - 9 = 1 - 57 + 1 = 58 minutes of actual movie

Distance

"Trail is 84 yards, completed 7 yards" - 84 = 74 + 10 - 10 - 7 = 3 - 74 + 3 = 77 yards remaining

Collections

"Had 52 stickers, gave away 8" - 52 = 42 + 10 - 10 - 8 = 2 - 42 + 2 = 44 stickers left

Practice Activities

Activity 1: Number Bond Cards

Materials: Index cards

Create cards with: - Front: Subtraction problem (67 - 9) - Back: Number bond diagram showing the split and solution - Practice until you can do it without flipping the card!

Activity 2: Base-Ten Block Modeling

Materials: Base-ten blocks (or drawings)

Activity: 1. Build a two-digit number (like 45) 2. Try to remove a single digit (like 7) 3. Break one tens rod into unit cubes 4. Now remove the single digit 5. Count what's left!

Activity 3: Number Line Practice

Materials: Number line from 0-100

Activity: 1. Start at your two-digit number 2. Draw how you split off one ten 3. Show taking away the single digit 4. Mark where you end up

Activity 4: Mental Math Speed Challenge

Materials: Timer, problem list

Challenge: - 10 subtraction problems - Use take-from-ten strategy - Time yourself - Try to improve your time each day!

Activity 5: Real-Life Problem Creation

Activity: - Create your own word problems - Use real situations from your life - Solve them using the take-from-ten strategy - Share with family or friends

Building Fluency

Fluency means using this strategy quickly and accurately.

Progressive Practice Plan

Week 1: Focus on subtracting 9 - Problems like 34 - 9, 56 - 9, 78 - 9 - 9 leaves 1, which is simple to add

Week 2: Add subtracting 8 - Problems like 35 - 8, 67 - 8, 83 - 8 - 8 leaves 2

Week 3: Add subtracting 7 - Problems like 42 - 7, 56 - 7, 74 - 7 - 7 leaves 3

Week 4: Add subtracting 6 - Problems like 33 - 6, 45 - 6, 81 - 6 - 6 leaves 4

Week 5: Mix all types - Random problems with any single-digit subtraction

Daily Practice Routine

Morning (5 minutes): - 5 problems using take-from-ten - Draw the number bonds

Afternoon (5 minutes): - 5 problems done mentally - Write just the answer

Evening (3 minutes): - Review any tricky problems - Practice the specific number facts involved

Common Challenges and Solutions

Challenge: "I forget how to split the number"

Solution: Always separate one ten. If the number is 67, take away 10 from the 60 to get 57, then you have 57 + 10.

Challenge: "I don't know what 10 minus the number is"

Solution: Practice partners of ten separately. This strategy requires instant recall of these facts!

Challenge: "I get confused adding at the end"

Solution: Write out just that part at first: - After 10 - 9 = 1 - Write: 57 + 1 = ? - Solve that simple addition

Challenge: "Why not just subtract normally?"

Solution: This is a form of normal subtraction—it's the mental version of what we do when we regroup! Once you get fast at it, it's often quicker than written methods.

Connecting to Other Concepts

Regrouping in Written Subtraction

This strategy shows the same concept: - Taking from ten is what we do mentally - "Borrowing" is what we call it in written form - Both involve breaking apart a ten

Addition Strategies

If you know 57 + 10 - 9 = 58, you also know: - 58 + 9 = 67 (the inverse operation) - Understanding subtraction helps with addition

Place Value

This strategy reinforces: - Numbers can be broken into tens and ones - One ten equals ten ones - We can trade between place values

Mental Math in General

Builds flexibility with numbers: - Seeing multiple ways to represent numbers - Choosing efficient strategies - Working with friendly numbers (like 10)

Assessment Checkpoints

You've mastered this strategy when you can: - ✓ Quickly split any two-digit number into (tens - 10) + 10 - ✓ Instantly recall what's left after subtracting from 10 - ✓ Solve problems like 67 - 9 mentally in under 10 seconds - ✓ Explain the strategy using a number bond - ✓ Choose when this strategy is most useful - ✓ Apply it to real-world situations

Looking Ahead

This strategy prepares you for:

Three-Digit Subtraction

• 367 - 9 uses the same strategy
• Take from the ten in the ones place

Subtraction with Regrouping

• Understanding this mentally helps with written algorithms
• The concept is the same

Algebraic Thinking

• Breaking numbers flexibly
• Seeing equivalent expressions
• Understanding that 67 = 57 + 10

Problem-Solving

• Having multiple strategies available
• Choosing the most efficient method
• Developing mathematical flexibility

Conclusion

Using a number bond to take from ten when subtracting is a powerful mental math strategy that makes subtraction easier and builds understanding of place value and regrouping. By learning to see two-digit numbers as flexible combinations that can be split strategically, you're developing mathematical thinking that will serve you well in more advanced mathematics. Practice this strategy regularly, especially with numbers where the ones digit is small, and soon you'll find yourself using it naturally. Remember, mathematics is about understanding relationships and having tools to solve problems efficiently—and this strategy gives you another powerful tool for your mathematical toolbox!