Properties | Second Grade
What are Math Properties?
Concept: Math properties show the special relationships between addition and subtraction. These connections help us understand how numbers work together!
What We'll Learn:
✓ Related addition facts (number families)
✓ Related subtraction facts (number families)
✓ Fact families (4 related equations)
✓ Math vocabulary (addend, sum, difference)
💡 Tip: Addition and subtraction are opposite operations - they undo each other!
1. Related Addition Facts
Concept: Related addition facts use the same three numbers but in different orders. The order doesn't change the sum!
Commutative Property of Addition
\( a + b = b + a \)
Changing the order of addends doesn't change the sum!
📝 Example: Related Addition Facts
Using numbers: 3, 5, and 8
3 + 5 = 8
First way
5 + 3 = 8
Related fact
Both equations use the same three numbers!
Both have the same sum: 8
More Examples:
7 + 4 = 11
↕
4 + 7 = 11
12 + 8 = 20
↕
8 + 12 = 20
15 + 6 = 21
↕
6 + 15 = 21
💡 Tip: You can flip the numbers and the answer stays the same!
2. Related Subtraction Facts
Concept: Related subtraction facts use the same three numbers but start with different numbers. Addition and subtraction are related!
Addition-Subtraction Relationship
If \( a + b = c \)
Then \( c - b = a \) and \( c - a = b \)
Subtraction undoes addition!
📝 Example: Related Subtraction Facts
Using numbers: 6, 9, and 15
6 + 9 = 15
This addition fact gives us two related subtraction facts:
15 − 9 = 6
Related fact 1
15 − 6 = 9
Related fact 2
All three equations use the same three numbers!
Subtraction is the opposite of addition
More Examples:
3 + 8 = 11
11 − 8 = 3
11 − 3 = 8
7 + 5 = 12
12 − 5 = 7
12 − 7 = 5
9 + 4 = 13
13 − 4 = 9
13 − 9 = 4
💡 Tip: Use addition facts to help you solve subtraction problems!
3. Fact Families
Concept: A fact family is a group of 4 related math facts using the same 3 numbers - 2 addition facts and 2 subtraction facts!
Fact Family Triangle
The largest number goes on top (the sum)
The two smaller numbers go on bottom (the addends)
📝 Example: Complete Fact Family
Fact Family for: 5, 7, and 12
Addition Facts (2)
5 + 7 = 12
7 + 5 = 12
Subtraction Facts (2)
12 − 7 = 5
12 − 5 = 7
4 equations = 1 complete fact family!
More Fact Families:
Family: 3, 6, 9
3 + 6 = 9
6 + 3 = 9
9 − 6 = 3
9 − 3 = 6
Family: 8, 4, 12
8 + 4 = 12
4 + 8 = 12
12 − 4 = 8
12 − 8 = 4
Family: 9, 7, 16
9 + 7 = 16
7 + 9 = 16
16 − 7 = 9
16 − 9 = 7
Special Case: Doubles Fact Family
Family: 6, 6, 12 (only 2 facts!)
6 + 6 = 12
12 − 6 = 6
When two addends are the same, we only have 2 facts instead of 4!
💡 Tip: If you know one fact in the family, you can figure out all the others!
4. Addition and Subtraction Terms
Concept: Math has special vocabulary words for each part of an equation. Learning these terms helps us talk about math clearly!
➕ Addition Terms
7 + 5 = 12
7 = Addend
+ = Plus sign
5 = Addend
= = Equals
12 = Sum
✓ Addend: Numbers being added
✓ Sum: The answer/total
✓ Formula: Addend + Addend = Sum
➖ Subtraction Terms
15 − 8 = 7
15 = Minuend
− = Minus sign
8 = Subtrahend
= = Equals
7 = Difference
✓ Minuend: Number we start with
✓ Subtrahend: Number being taken away
✓ Difference: The answer/what's left
📝 Practice: Identify the Terms
23 + 17 = 40
23 is an addend
17 is an addend
40 is the sum
56 − 28 = 28
56 is the minuend
28 is the subtrahend
28 is the difference
Memory Tricks:
✓ Sum: Think "sum-thing" (something) - the total of everything
✓ Difference: Think "different" - how different the numbers are
✓ Addend: Numbers that add together
✓ Minuend: The number that gets smaller (minus happens to it)
💡 Tip: Using correct math terms makes you sound like a math expert!
Important Property Rules & Formulas
Commutative Property
\( a + b = b + a \)
Order doesn't matter
in addition
Inverse Operations
If \( a + b = c \)
Then \( c - b = a \)
Addition & subtraction
are opposites
Fact Family Rule
3 numbers make
4 equations
(2 addition + 2 subtraction)
Example: 4, 5, 9
Addition Formula
Addend + Addend = Sum
The parts make
the whole
Subtraction Formula
Minuend − Subtrahend
= Difference
Start − Take away
= What's left
🎯 Tips for Understanding Properties 🎯
- ✓ Remember: Addition and subtraction are opposite operations
- ✓ Use fact families to check your work
- ✓ If you know one fact in a family, you can find all the others
- ✓ The order matters in subtraction but not in addition
- ✓ Use the triangle to organize your fact families
- ✓ Practice identifying terms to become a math vocabulary expert!
⭐ You're a Properties Master! ⭐
Fantastic work learning about math properties! You now understand related addition facts, related subtraction facts, complete fact families with 4 equations, and all the important math terms like addend, sum, minuend, subtrahend, and difference. These properties show how numbers are connected and help you solve problems faster. Understanding that addition and subtraction are opposite operations is one of the most powerful tools in math! You're building strong connections between numbers and becoming an amazing mathematical thinker. Keep exploring these patterns - you're doing phenomenal work!