Function Flow Teacher Guide
Function Flow
Teacher Facilitation Guide • Algebra I
Objective
Students will apply inverse operations to solve functions with varied variables (x, t, p) for the input value.
Pacing
- Warm-up 5 min
- Video/Notes 5 min
- Guided Practice 15 min
- Partner Work 15 min
- Reflection 5 min
Materials
- • Mini Whiteboards & Markers
- • Input Investigation Slides
- • Variable Switch Worksheet
1. Warm-up: Two-Step Sprint
Display equations on the slide. Students solve on mini-whiteboards and "Show" on your signal.
-
\(3x - 5 = 10\) x=5
-
\(-2x + 4 = 12\) x=-4
2. Video Pauses & Discussion
Anchor your discussion using these key moments:
0:39
Decoding the Statement
"What does \(f(x)=7\) actually mean in plain English? How is it different from \(f(7)\)?" (Clarify: one is the output value, the other is an instruction to plug in 7).
1:19
Final Notation
"Why do we write the answer as \(f(4)=7\) instead of just \(x=4\)? What extra information does this give us?" (Answer: it shows both input and output in one view).
2:11
Variable Independence
"Does changing the letter from x to p change the math? Why use different letters?" (Connect to real world: t for time, p for profit, etc).
3. Guided Practice: The Variable Shift
Model the following problem on the board, emphasizing the verbal phrasing:
// Modeling Example
If \(h(k) = -4k + 2\), find \(k\) when \(h(k) = -18\)
1. Replace \(h(k)\) with \(-18\)
2. Subtract 2 from both sides \(\rightarrow -20 = -4k\)
3. Divide by -4 \(\rightarrow k = 5\)
Final Notation: \(h(5) = -18\)
Key Phrase: "When the input is 5, the output is -18."
4. Variable Switch Activity
Partners write a function for each other using a random variable letter, choose an input, calculate the output, then give ONLY the output and the formula to their partner to solve back for the input.
Watch For
Students often mistakenly think \(f(x)\) means \(f \cdot x\). Circulate and ensure they are treating the entire symbol as a single entity (the output).
Differentiation
Support: Provide a scaffold card: "1. Replace Symbol. 2. Undo Addition. 3. Undo Multiplication."
Extend: Challenge students to create a "Scrambled" function machine where the equation isn't simplified first (e.g., \(g(x) = 2x + 5 - 3\)).
Input Investigation Slides
Algebra I Unit 3
Input Investigation
Cracking the code to reverse-engineer function machines.
f(x) = ?
Warm-up Sprint
Solve on your mini-whiteboards:
-
3x - 5 = 10
-
-2x + 4 = 12
Time Remaining: 05:00
The Mystery Output
"We know the rule of the machine. We know the final result. But what did we put in at the start?"
Observation Zone
Finding Function Inputs
Embedded media
Task
On your notes sheet, record the three equations solved in this video.
1
f(x) = ...
2
f(t) = ...
3
f(p) = ...
Guided Practice
Example 4: The New Variable Challenge
If h(k) = -4k + 2
find k when h(k) = -18
"When the input is 5, the output is -18."
Variable Switch
1
The Secret Build
Choose a random letter. Write a function. Pick an input. Calculate the output.
2
The Swap
Give your partner the Function and the Output only.
3
The Solve
Reverse the machine to find the original input!
Final Reflection
Why doesn't the letter choice affect the math?
Be ready to share your "Aha!" moment with the class.
Variable Switch Worksheet
Variable Switch
Student Lab Sheet • Algebra I
Name:
Date:
Part 1: Video Observation
As you watch "Finding Function Inputs", record the three functions being solved below.
Example 1 (x)
Example 2 (t)
Example 3 (p)
Part 2: Guided Practice
Problem: If \(h(k) = -4k + 2\), find \(k\) when \(h(k) = -18\)
Translate your answer: "When the input is _______, the output is _______."
Part 3: Variable Switch
Round 1: My Secret Function Variable: ____
Step 1: Write Function & Pick Input
Step 2: Partner Solves Here
Round 2: Partner's Mystery Variable: ____
Step 1: Write Partner's Function & Output
Step 2: You Solve Here
Final Reflection:
Why doesn't the choice of letter (x, t, p, k) affect how you solve the equation? Use the word "inverse" in your explanation.
