Subtraction within 20: A basic subtraction operation where both the minuend and subtrahend are numbers from 0 to 20.
Note: These facts form the foundation for more complex subtraction and should be memorized for quick recall.
- Start with the minuend (12)
- Count backward by the subtrahend (5)
- Count how many you have left
We begin at 12 on the number line
Move 5 spaces to the left: 12 → 11 → 10 → 9 → 8 → 7
We land on 7, so 12 - 5 = 7
12 - 5 = 7
• Count back strategy: Move left on number line by subtrahend
• Number relationship: 12 is made up of 5 and 7
• Verification: Add back: 7 + 5 = 12 ✓
• Practice Tip: Count backward: 12, 11, 10, 9, 8, 7 (stop after 5 counts)
- 11 - 3 = 8 (start at 11, count back 3)
- 15 - 6 = 9 (start at 15, count back 6)
- 18 - 7 = 11 (start at 18, count back 7)
- Use your fingers to count backward
- Think of subtraction as "taking away"
- Always verify by adding the answer back to the subtracted number
Q: Can I subtract a bigger number from a smaller number?
A: Not yet! In 1st grade, we only subtract smaller numbers from bigger numbers.
Q: What if I count wrong?
A: Count slowly and carefully. You can also use your fingers to help.
Count back strategy: Starting from the minuend and counting backward by the number of steps equal to the subtrahend.
Note: This strategy helps build number sense and is a bridge to mental subtraction without physical counting.
- Start with the minuend (first number)
- Count backward one number at a time
- Stop after counting back the number of steps equal to the subtrahend
We begin counting from 15
15 → 14 → 13 → 12 → 11 → 10 → 9 → 8 → 7 (that's 8 steps)
We land on 7, so 15 - 8 = 7
15 - 8 = 7
• Sequential counting: Count each number as you move back
• Step tracking: Keep track of how many steps you've taken
• Stopping rule: Stop after the number of steps equals the subtrahend
• Practice Tip: Use fingers to track the steps: 15, 14, 13, 12, 11, 10, 9, 8, 7
- 14 - 6 = 8 (14, 13, 12, 11, 10, 9, 8)
- 17 - 9 = 8 (17, 16, 15, 14, 13, 12, 11, 10, 9, 8)
- 13 - 5 = 8 (13, 12, 11, 10, 9, 8)
- Use your fingers to keep track of steps
- Count out loud to stay focused
- Start with the larger number and count backward
Q: What if I lose track while counting back?
A: Use your fingers to track each step, or start over and count more slowly.
Q: Can I count forward instead?
A: Counting back is the subtraction strategy. Counting forward is for addition.
Number bond: A visual representation showing how numbers can be split into parts that make up the whole number.
Note: Number bonds help understand the relationship between addition and subtraction, showing that 13 can be broken into 4 and 9.
- Identify the whole number (minuend)
- Identify one part (subtrahend)
- Find the missing part (difference)
13 is the whole number we start with
4 is the part we are taking away
What part combines with 4 to make 13? Answer: 9
13 - 4 = 9
• Part-whole relationship: 13 = 4 + 9, so 13 - 4 = 9
• Addition connection: Subtraction reverses addition
• Number bond: Shows how numbers relate to each other
• Practice Tip: Remember: if 4 + 9 = 13, then 13 - 4 = 9
- 11 - 3 = 8 because 3 + 8 = 11
- 16 - 7 = 9 because 7 + 9 = 16
- 14 - 6 = 8 because 6 + 8 = 14
- Think of subtraction as finding a missing part
- Use addition facts to help with subtraction
- If you know 5 + 8 = 13, then 13 - 5 = 8
Q: How are addition and subtraction connected?
A: They are opposite operations. If 5 + 8 = 13, then 13 - 5 = 8 and 13 - 8 = 5.
Q: What are number bonds good for?
A: They help you see how numbers fit together and make mental math easier.
Missing number subtraction: Finding the unknown subtrahend in a subtraction equation where the minuend and difference are known.
Note: This helps develop algebraic thinking early by understanding the relationship between the parts of a subtraction equation.
- Start with the minuend (16)
- Think about what needs to be subtracted to get the difference (7)
- Count how many steps from difference back to minuend
We have 16 - ? = 7, so we need to find what number subtracted from 16 gives us 7
16 is made up of 7 and another number. If 16 = 7 + ?, then ? = 16 - 7 = 9
Check: 16 - 9 = 7 ✓
The missing number is 9.
• Relationship understanding: Minuend - Subtrahend = Difference
• Reversibility: Difference + Subtrahend = Minuend
• Verification: Always check your answer by substituting back
• Practice Tip: Think: "What number added to 7 makes 16?" Answer: 9
- 15 - ? = 8, so ? = 7 because 15 - 7 = 8
- 18 - ? = 9, so ? = 9 because 18 - 9 = 9
- 14 - ? = 6, so ? = 8 because 14 - 8 = 6
- Think of subtraction as "what to take away"
- Use addition to check: if 16 - ? = 7, then 7 + ? = 16
- Count from the answer to the starting number
Q: How do I know which number is missing?
A: Look at the equation format: Minuend - Subtrahend = Difference. Usually the subtrahend is missing.
Q: Can the missing number be bigger than the starting number?
A: No, in subtraction the number being subtracted must be equal to or less than the starting number.
Fact family: A group of related addition and subtraction facts that use the same three numbers.
Note: Fact families show the inverse relationship between addition and subtraction, helping students understand how operations connect.
- Identify the three numbers in the family (8, 5, 13)
- Create two addition facts
- Create two subtraction facts
From 8 + 5 = 13, our numbers are 8, 5, and 13
8 + 5 = 13 and 5 + 8 = 13 (commutative property)
13 - 5 = 8 and 13 - 8 = 5 (starting with the largest number)
The related subtraction facts are: 13 - 5 = 8 and 13 - 8 = 5
• Fact family principle: Three numbers create four related facts
• Inverse operations: Addition and subtraction reverse each other
• Commutative property: Order doesn't matter in addition
• Practice Tip: Always start subtraction facts with the largest number
- If 7 + 4 = 11: 4 + 7 = 11, 11 - 4 = 7, 11 - 7 = 4
- If 9 + 2 = 12: 2 + 9 = 12, 12 - 2 = 9, 12 - 9 = 2
- If 6 + 8 = 14: 8 + 6 = 14, 14 - 8 = 6, 14 - 6 = 8
- Always start subtraction facts with the biggest number
- Know one fact, and you know three others
- Fact families help with both addition and subtraction
Q: Why do we learn fact families?
A: They show how addition and subtraction are connected and help with mental math.
Q: Do all numbers make fact families?
A: Any three numbers that work in addition/subtraction can form a family.