Subtraction within 20: Taking away one number from another where the result is also within the range of 0 to 20
Note: Subtraction within 20 builds foundational skills for more complex arithmetic.
- Start with the first number (minuend)
- Take away the second number (subtrahend)
- Count how many are left (difference)
We have 15 objects: ⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
Remove 7 objects: ⭐⭐⭐⭐⭐⭐⭐ (⭐⭐⭐⭐⭐⭐⭐)
8 objects remain: ⭐⭐⭐⭐⭐⭐⭐⭐
15 - 7 = 8
• Subtraction: Take away the subtrahend from the minuend
• Counting: Count how many remain after taking away
• Within 20: Both operands and result are ≤ 20
- 14 - 6 = 8 - Practice with different combinations
- 18 - 9 = 9 - Practice with doubles facts
- 13 - 5 = 8 - Practice with smaller differences
- Subtraction is the opposite of addition
- You can check by adding: 8 + 7 = 15 ✓
- Always start with the bigger number when subtracting
Q: What does "within 20" mean?
A: All numbers in the problem (minuend, subtrahend, and difference) are 20 or less.
Q: How do I know if I'm doing subtraction within 20?
A: Check that the first number is 20 or less and the result is also 20 or less.
Number bond: Shows how numbers are related in addition and subtraction within 20
Note: Number bonds help us understand that 16 can be broken into 9 and 7.
- Think about what number goes with 9 to make 16
- Use the relationship: 9 + ? = 16
- Since 9 + 7 = 16, then 16 - 9 = 7
We want to break apart 16
So 16 = 9 + ?
9 + 7 = 16, so 16 - 9 = 7
16 - 9 = 7
• Number bond: 16 can be split into 9 and 7
• Relationship: Addition and subtraction are inverse operations
• Within 20: All numbers in the problem are ≤ 20
- 15 = 8 + 7, so 15 - 8 = 7
- 18 = 9 + 9, so 18 - 9 = 9
- 14 = 6 + 8, so 14 - 6 = 8
- Number bonds help you see subtraction as "what's missing?"
- Know your number bonds to 20: pairs that add up to 11, 12, ..., 20
- Use addition to check: 7 + 9 = 16 ✓
Q: What are number bonds within 20?
A: Number bonds that involve numbers 0-20, showing how a number can be split into parts.
Q: How do number bonds help with subtraction within 20?
A: They help you think "what number added to 9 gives me 16?" which leads to 16 - 9 = 7.
Counting back: Starting from the first number and counting backwards by the second number within 20
Note: This is a mental math strategy for subtraction within 20.
- Start at the first number (18)
- Count backwards by the second number (5)
- Land on the answer (13)
Begin counting: 18
18 → 17 → 16 → 15 → 14 → 13 (count 5 steps back)
We land on 13
18 - 5 = 13
• Counting back: Move backwards on the number line
• Strategy: This helps with mental math
• Within 20: All numbers in the problem are ≤ 20
- 17 - 4: Start at 17, count back 4 → 17, 16, 15, 14, 13 → Answer: 13
- 15 - 3: Start at 15, count back 3 → 15, 14, 13, 12 → Answer: 12
- 20 - 6: Start at 20, count back 6 → 20, 19, 18, 17, 16, 15, 14 → Answer: 14
- Count back slowly and carefully
- This strategy works best for small numbers being subtracted
- Use your fingers to help keep track of counting back
Q: When should I use counting back within 20?
A: Use it for small subtrahends (like subtracting 1, 2, 3, 4, or 5).
Q: What if I count back too far?
A: Start over and count more carefully, or use objects to help.
Fact family: A group of related addition and subtraction facts using the same numbers within 20
Note: The numbers 7, 5, and 12 form a fact family: 7+5=12, 5+7=12, 12-5=7, 12-7=5.
- Recognize that 7, 5, and 12 are in the same fact family
- If 7 + 5 = 12, then 12 - 5 = 7 (the other addend)
- Verify: 7 + 5 = 12 and 12 - 5 = 7
Numbers 7, 5, and 12 are related
If 7 + 5 = 12, then 12 - 5 = 7
7 + 5 = 12 ✓ and 12 - 5 = 7 ✓
12 - 5 = 7
• Fact family: Addition and subtraction facts using same numbers
• Inverse operations: Addition and subtraction undo each other
• Within 20: All numbers in the fact family are ≤ 20
- If 6 + 8 = 14, then 14 - 8 = 6
- If 9 + 4 = 13, then 13 - 4 = 9
- If 8 + 7 = 15, then 15 - 7 = 8
- Fact families show the connection between addition and subtraction
- Knowing one fact helps you know three others
- Use fact families to check your work
Q: What is a fact family within 20?
A: A group of related addition and subtraction facts using the same three numbers, all ≤ 20.
Q: How do fact families help with subtraction within 20?
A: If you know an addition fact, you automatically know the related subtraction facts.
Missing number: Finding the unknown value in a subtraction equation within 20
Note: We need to find what number subtracted from 16 gives 9.
- Think: "What number taken from 16 leaves 9?"
- Use addition: 9 + ? = 16
- Since 9 + 7 = 16, then 16 - 7 = 9
We need to find what number subtracted from 16 equals 9
Instead of subtracting, we add: 9 + ? = 16
9 + 7 = 16, so the missing number is 7
16 - 7 = 9 ✓
The missing number is 7
• Inverse operations: Addition and subtraction undo each other
• Missing number: Use the inverse operation to find it
• Verification: Always check your answer
• Within 20: All numbers in the problem are ≤ 20
- 18 - ? = 11 → 11 + ? = 18 → ? = 7
- ? - 6 = 10 → 6 + 10 = ? → ? = 16
- 15 - ? = 8 → 8 + ? = 15 → ? = 7
- Turn subtraction with missing numbers into addition problems
- Always check your answer by substituting back
- Use number lines or objects to visualize the problem
Q: How do I solve missing number problems within 20?
A: Use the inverse operation. If subtracting, add the known numbers to find the missing one.
Q: What if the missing number is the first one?
A: For ? - 6 = 10, add the two known numbers: 6 + 10 = 16, so ? = 16.