Unit Mechanics Slides CHAIN LOGIC
Dimensional Analysis Mechanics
The Substitution Rule
If A = B, then:
\[ \frac{A}{B} = 1 \]
and
\[ \frac{B}{A} = 1 \]
Multiplying by these fractions never changes the total value.
The Unit Machine
GIVEN
UNIT A
×
UNIT B
UNIT A
=
DESIRED
UNIT B
The Unit Machine only works if the diagonal units match.
Chain Mechanics
Sometimes the "Destination" is multiple steps away.
Given [A]
×
B
A
×
C
B
=
Result [C]
"If you don't see the unit in the denominator of the next step, you aren't canceling anything."
The Plug & Chug Algorithm
1
Write the GIVEN NUMBER and UNIT.
2
Pick the factor that has the SAME UNIT on the bottom.
3
Repeat until the DESIRED UNIT is on top.
4
Multiply across the top. Divide by the bottom.
Grid Mastery Worksheet GRID MASTER
DIMENSIONAL ANALYSIS MECHANICS
NAME: __________________________________________
DATE: __________________________________________
PART 1: SYMBOL SUBSTITUTION
Use the provided substitution rules to solve for the target symbol. Do not worry about "what" the symbols are. Focus on the grid setup.
Substitution Rule Bank
1 Δ = 12 ◊
1 ◊ = 5 Σ
1 Σ = 2.5 Ω
1. Solve for Σ if you are given 3.0 Δ.
3.0 Δ
=
2. Solve for Ω if you are given 0.5 ◊.
0.5 ◊
=
PART 2: CHEMICAL UNIT MECHANICS
Follow the same logic as Part 1. Match the units diagonally to ensure they cancel out.
CHEM-DATA-SET-01
1.00 mol \(A\) = 44.0 g \(A\)
1.00 mol \(A\) = 22.4 L \(A\)
1.00 mol \(A\) = 6.02 x 1023 molecules \(A\)
1.00 L = 1000 mL
3. Convert 88.0 g \(A\) to L \(A\).
Chain Level: 2-step
88.0 g \(A\)
=
4. Convert 0.25 mol \(A\) to mL \(A\).
Chain Level: 2-step
Construct your own unit grid machine here
5. Find molecules \(A\) if you start with 112 L \(A\).
Chain Level: 2-step
Construct your own unit grid machine here
"If the units don't cancel, the numbers don't matter."
Logic Key Teacher Guide TEACHER LOGIC KEY
CHAIN LOGIC MASTERY • INSTRUCTIONAL GUIDE
VER: 1.0.4
WHY THE SYMBOLS?
Students in 11th/12th grade often get "unit fatigue." By stripping away the chemistry (moles, grams) and using abstract symbols, you force them to focus on the algebraic mechanics of diagonal cancellation. If they can move ◊ to Σ, they can move mol to g.
THE "FLIP" TRAP
The #1 error is putting the unit on top because "that's the number I saw first." Constantly repeat: "Where does it go to die?" (The bottom). If a unit doesn't "die" on the bottom, it's still alive in the answer.
Answer Key: Grid Mastery Worksheet
Part 1: Symbol Solutions
#1 (3.0 Δ to Σ):
3.0 Δ
12 ◊
1 Δ
5 Σ
1 ◊
= 180 Σ
#2 (0.5 ◊ to Ω):
0.5 ◊
5 Σ
1 ◊
2.5 Ω
1 Σ
= 6.25 Ω
Part 2: Chemistry Solutions
#3 (88.0 g to L):
88.0 g
1 mol 44.0 g
22.4 L 1 mol
= 44.8 L
#4 (0.25 mol to mL):
0.25 mol
22.4 L 1 mol
1000 mL 1 L
= 5,600 mL
#5 (112 L to molecules):
112 L
1 mol 22.4 L
6.02x1023 mlc 1 mol
= 3.01 x 1024
Plug & Chug Quiz PLUG & CHUG EXIT TICKET
ASSESSING UNIT CANCELLATION MECHANICS
NAME: _____________________________
DATE: _____________________________
Rule Bank
1.00 mol \(X\) = 60.0 g \(X\)
1.00 mol \(X\) = 22.4 L \(X\)
1. Which grid setup correctly converts 120.0 grams of X to Liters of X?
A)
120.0 g
60.0 g
1 mol
22.4 L
1 mol
B)
120.0 g
1 mol
60.0 g
22.4 L
1 mol
C)
120.0 g
1 mol
60.0 g
1 mol
22.4 L
2. Solve the problem below using the Unit Machine method. Show every step.
Convert 11.2 Liters of X to grams of X.
Work Area: Draw your grid machine here
FINAL ANSWER:
Diagonal cancellation check: [ ] Yes [ ] No
Top unit matches goal: [ ] Yes [ ] No
Quiz Key Teacher Resource QUIZ KEY
PLUG & CHUG EXIT TICKET SOLUTIONS
ADMIN ONLY
1. SETUP SELECTION
B
Correct Choice: B
Why B is correct:
Starts with 120.0 g (the Given).
First conversion factor has grams on the bottom to cancel (120 g / 60 g).
Second conversion factor has moles on the bottom to cancel.
Leaves Liters as the final unit on top.
Distractor A: Upside down first step (60g on top).
2. FREE RESPONSE CALCULATION
Path: 11.2 L \(X\) \(\rightarrow\) mol \(X\) \(\rightarrow\) g \(X\)
11.2 L
1 mol
22.4 L
60.0 g
1 mol
= 30.0 g
Math Breakdown:
(11.2 \(\times\) 1 \(\times\) 60.0) / (22.4 \(\times\) 1)
Grid Setup
2 pts
Cancellation
1 pt
Final Units
2 pts
