Instructions
Hello, Math Detective! Today, you're on a special mission to investigate subtraction. We know that in addition, you can swap numbers around (like 2+3 = 3+2) and group them differently. But does subtraction follow the same rules? Let's find out!
Part 1: The Order Rule Investigation
The Order Rule (or Commutative Property) means you can flip the numbers and get the same answer. Does it work for subtraction? Solve the pairs of problems below to see!
Are the answers the same? Circle one: Yes / No
Are the answers the same? Circle one: Yes / No
(Hint: For a problem like 4 - 9, you can't take 9 away from 4. The answer is not the same!)
Part 2: The Grouping Rule Investigation
The Grouping Rule (or Associative Property) means you can change how you group numbers in parentheses and get the same answer. Let’s test this with subtraction. Remember: Always solve what's in the parentheses ( ) first!
- 2 =
10 - =
Are the final answers the same? Circle one: Yes / No
- 3 =
18 - =
Are the final answers the same? Circle one: Yes / No
Your Final Report
Great work, Detective! Fill in the blanks below to summarize your mission.
1. For subtraction, changing the o _ d _ _ of the numbers will change the answer.
2. For subtraction, changing the g _ _ _ p _ _ _ of the numbers will change the answer.
3. This means that for subtraction, order and grouping D O matter!
Answer Key
Part 1: The Order Rule Investigation
- 9 - 4 = 5
- 4 - 9 = (Different Answer / Not 5)
- Are the answers the same? No
- 12 - 5 = 7
- 5 - 12 = (Different Answer / Not 7)
- Are the answers the same? No
Part 2: The Grouping Rule Investigation
- (10 - 5) - 2 -> 5 - 2 = 3
- 10 - (5 - 2) -> 10 - 3 = 7
- Are the final answers the same? No
- (18 - 8) - 3 -> 10 - 3 = 7
- 18 - (8 - 3) -> 18 - 5 = 13
- Are the final answers the same? No
Your Final Report
- For subtraction, changing the o r d e r of the numbers will change the answer.
- For subtraction, changing the g r o u p i n g of the numbers will change the answer.