Segment Surgeon Worksheet
Geometry Lab Series
SEGMENT SURGEON
TOPIC: SEGMENT ADDITION & ALGEBRAIC PARTITIONING
NAME:
DATE: PD:
The Surgeon's Golden Rule: Part-Whole Subtraction
When you slice a segment into pieces, the math remains identical whether you use numbers or variables. If you know the WHOLE length and slice off a KNOWN PART, what is left is always:
WHOLE − KNOWN PART = REMAINING PART
1 Phase 1: Cutting with Concrete Numbers
Let's cut a segment of length 15. If the orange piece is cut to length 6, what remains of the teal piece?
WHOLE = 15
PART: 6
REMAINING PART: ?
Calculation: 15 − 6 = 9
EX. A WHOLE: 20
8
?
20 − 8 = 12
EX. B WHOLE: 12
3
?
12 − 3 = 9
2 Phase 2: Transitioning to Variables
Now, we replace the known numerical part with a variable x. The subtraction rule remains identical!
IF THE PART IS...
THE SUBTRACTION IS...
THE REMAINING PART IS...
5
15 − 5
10
8
15 − 8
7
x
15 − x
15 − x
SURGEON'S WARNING: Don't Fall Into the Variable Traps!
❌ TRAP 1: Writing "x − 15"
If the whole is 15 and the cut part (x) is 4, then 4 − 15 = −11. A negative length is impossible!
❌ TRAP 2: Writing "15x"
15x means multiplication. If you cut a board, you are subtracting a piece from the total, not multiplying them.
SEGMENT SURGEON: INDEPENDENT PRACTICE
APPLYING THE PART-WHOLE SUBTRACTION LAW
PAGE 2 OF 2
Section A: The Dimension Lab
For each segment diagram, write down the correct algebraic expression that represents the length of the unknown part. Remember: Whole − Part!
PROBLEM 1
WHOLE = 24
x
?
Teal piece =
PROBLEM 2
WHOLE = L
5
?
Teal piece =
PROBLEM 3
WHOLE = 45
?
y
Orange piece =
PROBLEM 4
WHOLE = 3x
x
?
Teal piece =
Section B: The Advanced Level Up
PROBLEM 5 DOUBLE VARIABLE
A wooden beam has a whole length of w inches. A carpenter chops off a chunk that is z inches long. Write the expression representing the leftover beam.
Expression: ___________________________
PROBLEM 6 EXPRESSION PART
A pipeline has a whole length of 40 feet. Section A is (x + 5) feet long. Write and simplify the algebraic expression for Section B.
Expression: ___________________________
Section C: The Surgeon's Explanation
Your apprentice claims that if a segment has a total length of 50 and we cut off a piece of length y, the remaining part is represented by y − 50. Explain why this is incorrect using mathematical reasoning.
