Minus zero facts: Subtraction facts where the subtrahend is 0. Any number minus 0 equals the original number.
Note: This is known as the zero property of subtraction. When you subtract zero from any number, you get the same number.
- Recognize that you're subtracting zero
- Understand that nothing is being taken away
- The answer is the same as the minuend
- Memorize this pattern: n - 0 = n
When you take away 0 from 5, you still have 5
When you take away 0 from 8, you still have 8
When you take away 0 from 12, you still have 12
When you take away 0 from 15, you still have 15
When you take away 0 from 20, you still have 20
When you take away 0 from 3, you still have 3
5 - 0 = 5, 8 - 0 = 8, 12 - 0 = 12, 15 - 0 = 15, 20 - 0 = 20, 3 - 0 = 3
• Zero property: Any number minus 0 equals itself
• Pattern recognition: n - 0 = n for any number n
• Conceptual understanding: Nothing taken away means nothing changes
• Practice Tip: This is the easiest subtraction fact family to memorize
Minus one facts: Subtraction facts where the subtrahend is 1. The answer is always one less than the minuend.
Note: When you subtract 1 from any number, you get the number that comes just before it in counting order.
- Recognize that you're subtracting one
- Count back one from the minuend
- The answer is the previous number in counting order
- Memorize this pattern: n - 1 = (n-1)
Take away 1 from 6, which gives you the number before 6: 5
Take away 1 from 9, which gives you the number before 9: 8
Take away 1 from 13, which gives you the number before 13: 12
Take away 1 from 17, which gives you the number before 17: 16
Take away 1 from 4, which gives you the number before 4: 3
Take away 1 from 11, which gives you the number before 11: 10
6 - 1 = 5, 9 - 1 = 8, 13 - 1 = 12, 17 - 1 = 16, 4 - 1 = 3, 11 - 1 = 10
• Minus one rule: Any number minus 1 equals the previous number
• Pattern recognition: n - 1 = the number before n in counting
• Counting connection: This connects to counting backwards
• Practice Tip: Think of the number that comes just before in counting
Minus two facts: Subtraction facts where the subtrahend is 2. The answer is always two less than the minuend.
Note: When you subtract 2 from any number, you get the number that comes two places before it in counting order.
- Recognize that you're subtracting two
- Count back two from the minuend
- The answer is two numbers before in counting order
- Memorize this pattern: n - 2 = (n-2)
Take away 2 from 7, which gives you two numbers before 7: 6, 5
Take away 2 from 10, which gives you two numbers before 10: 9, 8
Take away 2 from 14, which gives you two numbers before 14: 13, 12
Take away 2 from 18, which gives you two numbers before 18: 17, 16
Take away 2 from 5, which gives you two numbers before 5: 4, 3
Take away 2 from 12, which gives you two numbers before 12: 11, 10
7 - 2 = 5, 10 - 2 = 8, 14 - 2 = 12, 18 - 2 = 16, 5 - 2 = 3, 12 - 2 = 10
• Minus two rule: Any number minus 2 equals the number two places before
• Pattern recognition: n - 2 = the number that is two less than n
• Counting connection: This connects to counting backwards by two
• Practice Tip: Count back two numbers from the starting number
Minus three facts: Subtraction facts where the subtrahend is 3. The answer is always three less than the minuend.
Note: When you subtract 3 from any number, you get the number that comes three places before it in counting order.
- Recognize that you're subtracting three
- Count back three from the minuend
- The answer is three numbers before in counting order
- Memorize this pattern: n - 3 = (n-3)
Take away 3 from 8, which gives you three numbers before 8: 7, 6, 5
Take away 3 from 11, which gives you three numbers before 11: 10, 9, 8
Take away 3 from 15, which gives you three numbers before 15: 14, 13, 12
Take away 3 from 19, which gives you three numbers before 19: 18, 17, 16
Take away 3 from 6, which gives you three numbers before 6: 5, 4, 3
Take away 3 from 13, which gives you three numbers before 13: 12, 11, 10
8 - 3 = 5, 11 - 3 = 8, 15 - 3 = 12, 19 - 3 = 16, 6 - 3 = 3, 13 - 3 = 10
• Minus three rule: Any number minus 3 equals the number three places before
• Pattern recognition: n - 3 = the number that is three less than n
• Counting connection: This connects to counting backwards by three
• Practice Tip: Count back three numbers from the starting number
Minus four facts: Subtraction facts where the subtrahend is 4. The answer is always four less than the minuend.
Note: When you subtract 4 from any number, you get the number that comes four places before it in counting order.
- Recognize that you're subtracting four
- Count back four from the minuend
- The answer is four numbers before in counting order
- Memorize this pattern: n - 4 = (n-4)
Take away 4 from 9, which gives you four numbers before 9: 8, 7, 6, 5
Take away 4 from 12, which gives you four numbers before 12: 11, 10, 9, 8
Take away 4 from 16, which gives you four numbers before 16: 15, 14, 13, 12
Take away 4 from 20, which gives you four numbers before 20: 19, 18, 17, 16
Take away 4 from 7, which gives you four numbers before 7: 6, 5, 4, 3
Take away 4 from 14, which gives you four numbers before 14: 13, 12, 11, 10
9 - 4 = 5, 12 - 4 = 8, 16 - 4 = 12, 20 - 4 = 16, 7 - 4 = 3, 14 - 4 = 10
• Minus four rule: Any number minus 4 equals the number four places before
• Pattern recognition: n - 4 = the number that is four less than n
• Counting connection: This connects to counting backwards by four
• Practice Tip: Count back four numbers from the starting number
Minus five facts: Subtraction facts where the subtrahend is 5. The answer is always five less than the minuend.
Note: When you subtract 5 from any number, you get the number that comes five places before it in counting order.
- Recognize that you're subtracting five
- Count back five from the minuend
- The answer is five numbers before in counting order
- Memorize this pattern: n - 5 = (n-5)
Take away 5 from 10, which gives you five numbers before 10: 9, 8, 7, 6, 5
Take away 5 from 15, which gives you five numbers before 15: 14, 13, 12, 11, 10
Take away 5 from 20, which gives you five numbers before 20: 19, 18, 17, 16, 15
Take away 5 from 12, which gives you five numbers before 12: 11, 10, 9, 8, 7
Take away 5 from 8, which gives you five numbers before 8: 7, 6, 5, 4, 3
Take away 5 from 17, which gives you five numbers before 17: 16, 15, 14, 13, 12
10 - 5 = 5, 15 - 5 = 10, 20 - 5 = 15, 12 - 5 = 7, 8 - 5 = 3, 17 - 5 = 12
Mixed facts 0-5: Subtraction facts where the subtrahend is between 0 and 5. Requires identifying the appropriate strategy for each problem.
Note: Students must recognize which subtraction strategy to apply based on the numbers in each problem.
- Identify the minuend and subtrahend
- Determine which subtraction strategy to use
- Apply the appropriate counting strategy
- Memorize the result
Count back 3 from 7: 6, 5, 4
Count back 2 from 9: 8, 7
Count back 4 from 11: 10, 9, 8, 7
Count back 1 from 8: 7
Zero property: 10 - 0 = 10
Count back 5 from 6: 5, 4, 3, 2, 1
7 - 3 = 4, 9 - 2 = 7, 11 - 4 = 7, 8 - 1 = 7, 10 - 0 = 10, 6 - 5 = 1
Mixed facts 6-10: Subtraction facts where the subtrahend is between 6 and 10. Requires identifying the appropriate strategy for each problem.
Note: These problems help students apply subtraction strategies to larger numbers within 20.
- Identify the minuend and subtrahend
- Determine which subtraction strategy to use
- Apply the appropriate counting strategy
- Memorize the result
Count back 7 from 13: 12, 11, 10, 9, 8, 7, 6
Count back 9 from 16: 15, 14, 13, 12, 11, 10, 9, 8, 7
Count back 6 from 14: 13, 12, 11, 10, 9, 8
Count back 8 from 18: 17, 16, 15, 14, 13, 12, 11, 10
Count back 10 from 15: 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
Count back 8 from 17: 16, 15, 14, 13, 12, 11, 10, 9
13 - 7 = 6, 16 - 9 = 7, 14 - 6 = 8, 18 - 8 = 10, 15 - 10 = 5, 17 - 8 = 9
Mixed facts 11-15: Subtraction facts where the subtrahend is between 11 and 15. Requires identifying the appropriate strategy for each problem.
Note: These problems help students apply subtraction strategies to numbers within 20.
- Identify the minuend and subtrahend
- Determine which subtraction strategy to use
- Apply the appropriate counting strategy
- Memorize the result
Count back 8 from 14: 13, 12, 11, 10, 9, 8, 7, 6
Count back 12 from 17: 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
Count back 9 from 15: 14, 13, 12, 11, 10, 9, 8, 7, 6
Count back 13 from 18: 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
Count back 11 from 16: 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
Count back 14 from 19: 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
14 - 8 = 6, 17 - 12 = 5, 15 - 9 = 6, 18 - 13 = 5, 16 - 11 = 5, 19 - 14 = 5
Mixed facts 16-20: Subtraction facts where the subtrahend is between 16 and 20. Requires identifying the appropriate strategy for each problem.
Note: These problems help students apply subtraction strategies to the largest numbers within 20.
- Identify the minuend and subtrahend
- Determine which subtraction strategy to use
- Apply the appropriate counting strategy
- Memorize the result
Count back 15 from 18: 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
Count back 17 from 20: 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
Count back 16 from 19: 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
Count back 14 from 17: 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
Count back 18 from 20: 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2
Count back 13 from 16: 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
18 - 15 = 3, 20 - 17 = 3, 19 - 16 = 3, 17 - 14 = 3, 20 - 18 = 2, 16 - 13 = 3
Subtraction Facts: Basic subtraction problems where the minuend is between 0 and 20, and the subtrahend is between 0 and the minuend.
Minuend: The number from which another number is subtracted in a subtraction problem.
Subtrahend: The number that is subtracted from another number in a subtraction problem.
Difference: The result of a subtraction problem.
Number Sense: Understanding the relationships between numbers and their quantities.
Mathematical Fluency: The ability to perform calculations quickly and accurately.
Counting Back: The strategy of starting with the minuend and counting backwards by the subtrahend.
- Zero Property: Any number minus 0 equals the original number (n - 0 = n).
- Identity Property: Any number minus itself equals 0 (n - n = 0).
- Counting Back: Subtracting by counting backwards from the minuend.
- Sequential Pattern: Each subtraction fact follows a predictable pattern.
- Verification: Always check by adding the difference to the subtrahend.
Key Takeaways for Memorization
- n - 0 = n (any number minus zero equals itself)
- n - n = 0 (any number minus itself equals zero)
- n - 1 = the number before n in counting
- n - 2 = two numbers before n in counting
- Subtracting larger numbers requires counting back more steps
- Practice regularly to build automaticity
- Always verify by adding the difference back to the subtrahend
- Look for patterns in subtraction facts
• Pattern Recognition: Help students identify patterns in subtraction facts
• Concrete to Abstract: Begin with physical objects, progress to visual representations, then mental math
• Consistent Practice: Regular exposure builds automaticity and fluency
• Verification Skills: Teach students to check their work by using the opposite operation
Subtraction Facts Practice
Learning Objectives
- Master subtraction facts 0-20
- Build number sense within 20
- Improve mathematical fluency
- Develop memorization skills
- Recognize subtraction patterns
- Apply facts to larger problems
- Develop verification skills
Minus Zero
n - 0 = n (any number minus zero equals itself)
Same Numbers
n - n = 0 (any number minus itself equals zero)
| Minuend | Subtrahend | Difference | Rule |
|---|---|---|---|
| n | 0 | n | Zero Property |
| n | 1 | n-1 | Count Back 1 |
| n | 2 | n-2 | Count Back 2 |
| n | n | 0 | Identity Property |
Subtraction Facts Practice Elements
These facts provide the foundation for all future subtraction, building computational fluency and number sense.
Subtraction Facts Success Steps:
Subtraction facts: Basic subtraction problems with minuends from 0 to 20.
Number sense: Understanding the relationship between numbers and their quantities.
Memorization: Learning facts through repetition and pattern recognition.
- Identify the problem: Recognize the minuend and subtrahend
- Apply the appropriate rule: Use zero property, identity property, or counting back
- Calculate the result: Perform the subtraction mentally
- Verify the result: Check by using the opposite operation
• Zero property: Any number minus 0 equals itself
• Identity property: Any number minus itself equals 0
• Counting back: Subtract by counting backwards from the minuend
• Verify results: Always check by adding difference to subtrahend
• Memorize patterns: Learn the systematic relationships between numbers