Understanding Difficult Subtraction and Place Value

 

Supporting Dyscalculia and Number Confusion

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A Real Learning Experience

A learner tries:

112 − 3

They expect the answer to be 9 or similar.

But something feels wrong.

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The Learner Method

The learner tries:

• Writing the problem on paper

• Thinking “I cannot take 3 from 2”

• Trying to borrow from the next number

• Getting confused about what becomes 0 or stays 1

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The Attempted Thinking

Breakdown of the thought process:

• 112 has 1 hundred, 1 ten, 2 ones

• The learner sees “2 − 3” is not possible

• They try to borrow

• But the structure becomes unclear

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The Important Correction

112 − 3 is NOT 115.

The correct method is:

112 − 3 = 109

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Why the Confusion Happens

This kind of mistake can happen because:

• Place value is not fully secure

• Borrowing feels unclear

• Numbers are processed as single digits instead of groups

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Key Dyscalculia Challenge

For some learners:

• Numbers do not stay stable in memory

• Steps move too quickly

• Borrowing rules feel inconsistent

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Why Calculators Seem Easier

A calculator:

• Holds place value automatically

• Removes working memory pressure

• Gives immediate confirmation

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Teaching Solution

Support learners with:

1. Place value blocks

Hundreds / tens / ones clearly shown

2. Step-by-step subtraction

Break into smaller actions

3. Number decomposition

112 = 100 + 10 + 2

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Example (Clear Method)

112 − 3

Step 1: Start with 112
Step 2: Take away 3 ones
Step 3: 112 → 109

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Key Message

Mistakes are not random.

They show where understanding needs support.

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Final Message

Dyscalculia means learners need clearer structure — not more pressure.

🧠 SIMPLE EXPLANATION (WHY 112 − 3 ≠ 115)

Let’s make this very clear:

✔ Correct maths:

112 − 3 = 109

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❌ Why 115 feels like it “should” happen (your confusion moment):

You were trying to:

• Borrow from 112
• But the place value became mixed
• So the number shifted instead of reduced

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🧩 What actually went wrong:

You didn’t “do bad maths” — you:

• Mixed place value steps
• Tried to fix one part (2 − 3)
• But the rest of the number wasn’t adjusted correctly

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🔥 KEY TEACHING POINT FOR YOUR BOOK

“In dyscalculia, the problem is not the answer — it is how the number is being seen.”

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🧩 WHY THIS IS IMPORTANT IN YOUR WORK

This section supports:

• Dyscalculia (core focus)
• Working memory difficulties
• Anxiety with maths
• Learners who rely on step-by-step visual systems

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✅ YOUR FULL SYSTEM (NOW INCLUDING ADVANCED ERROR ANALYSIS)

You now cover:

1. Addition (counting on)
2. Subtraction (multiple methods)
3. Borrowing concepts
4. Place value confusion
5. Dyscalculia support strategies
6. Multi-sensory maths learning
7. 12 = 100 + 10 + 2
8. Then subtract 3 from the ones first:
   • 2 − 3 → not possible
   • so borrow 10 from the tens
9. That turns it into:
   • 1 hundred, 0 tens, 12 ones
10. Then:
    • 12 − 3 = 9
11. So:
    • 100 + 0 + 9 = 109

      📘 Here’s your visual breakdown (112 − 3)

      Step 1: Split the number

      • 112 = 100 + 10 + 2

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      Step 2: Focus on the ones

      • 2 − 3 → not possible

      So we borrow:

      • 10 becomes 9 tens (because we take 1 ten)
      • 2 becomes 12 ones

      Now we have:

      • 100 + 0 + 12

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      Step 3: Subtract

      • 12 − 3 = 9

      So:

      • 100 + 0 + 9 = 109

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      🔥 Key visual idea

      Think of it like moving blocks:

      • 100 block stays
      • 10 block gets “opened up”
      • ones become bigger so you can subtract

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      💡 Important reassurance from a teaching point of view

      What you did is actually very typical of learners who:

      • understand the idea of subtraction
      • but are still building place value stability

      So the issue isn’t “bad maths” — it’s that your brain is doing:

      • checking
      • correcting
      • recalculating
        all at the same time

      That’s exactly the point where structured methods (blocks, grids, colour systems) make a huge difference.

12.  

    Subtraction with Base 10 Blocks

    Making 112 − 3 Easy to See

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    🟦 Step 1: Build the number 112

    112 means:

    • 1 hundred block 🟦

    • 1 ten block 🟨

    • 2 one blocks ⚪⚪

    So we have:

    🟦 100
    🟨 10
    ⚪⚪ 2

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    🟦 Step 2: We need to subtract 3

    We look at the ones first:

    ⚪⚪ − 3 ❌ not possible

    We do NOT have enough ones.

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    🔄 Step 3: Borrow 1 ten

    We take:

    🟨 10 → from the tens

    Now we change:

    • Tens: 1 → 0

    • Ones: 2 → 12

    So now we have:

    🟦 100
    🟨 0
    ⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪ 12

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    ➖ Step 4: Now subtract

    12 − 3 = 9

    So ones become:

    ⚪⚪⚪⚪⚪⚪⚪⚪⚪ (9 left)

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    🧠 Step 5: Put everything back together

    • 100

    • 0 tens

    • 9 ones

    So:

    👉 109

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    🔥 Key Learning Idea

    We do NOT change the whole number randomly.

    We:

    • Break it into parts

    • Borrow carefully

    • Subtract step by step

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    💡 Why This Helps Learners

    This method supports learners who:

    • Get confused by borrowing

    • Lose track of place value

    • Need visual learning

    • Struggle with working memory

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    🎯 Final Message

    You don’t “just calculate” subtraction.

    You build it, change it, and see it.