Chain of Thought integrated active learning lesson plans in secondary Algebra
Lesson 2G Plan in Algebra
1. What is "Chain of Thought" (CoT) Prompt Engineering?
Chain of Thought (CoT) is a technique we can use to improve the LLMs' performance on certain tasks.
Instead of asking the LLM a question directly, we break down the problem into smaller parts, and guide the model through solving each part step by step.
This method can help the model generate more accurate answers, and it allows us to understand the problem-solving process more clearly.
Chain-of-Thought Prompting Elicits Reasoning in Large Language Models https://arxiv.org/pdf/2201.11903.pdf - "enables" reasoning capabilities of the LLM through intermediate steps of reasoning
Normal prompt or original question (O-Q) ChatGPT:
Find the solution to.....
Chain of Thought prompt engineering template:
Q: Problem similar to original problem to be solved
A: Full step of solution
Q: Find the solution to...
2. How does "Chain of Thought" work: 1st simple example
Example 1
Simplify:
Solution:
Let's see if ChatGPT gets it correct?
Putting O-G into ChatGPT, get
(4a^2) / (5b)
which is wrong!
https://poe.com/s/UbyBaIaY21VHEmbLMjXB
Let's see if ChatGPT gets it correct?
Where did it go wrong?
Nonsense!
Putting O-G into ChatGPT, get
(4a^2) / (5b)
which is wrong!
https://poe.com/s/UbyBaIaY21VHEmbLMjXB
Example:
Consider teaching the LLM how to solve a "similar problem":
i.e., Simplify 3a^3b^4/(27a^6b^2)
Let's produce the model answer:�
To simplify the expression ((3a^3b^4)/(27a^6b^2)), you first divide the numerical coefficients and subtract the exponents of like terms. Here's how it works:
When you put it all together, the simplified form of the expression is:
[\frac{b^2}{9a^3}]
Use the above example to "train" the LLM on how to solve these problems, step by step
Plug (Q, A, Q) into ChatGPT
https://poe.com/s/WokNr9DrKtmhjnel5ODs
Got it CORRECT!!!
Because we "trained/taught" the LLM how to solve such problems, step by step.
�3. How does CoT Prompt Engineering work: �Algebra Example
Example 1: Solve for u: (5-u)/(-6) = 2
Answer:
Given: (5-u)/(-6) = 2
Multiply both sides by -6 (the denominator):
(5-u) = -12
Simplify:
5-u = -12
Add u to both sides:
5 = -12 + u
Add 12 to both sides:
17 = u
Therefore, u=17.
Let's see if Google PaLM gets it correct?
Putting O-G into ChatGPT, get
-7
which is wrong!
https://poe.com/s/LCDY6Zopx9yHltp9Be1C
https://poe.com/s/OavyPtcsFcZVJy52oF7A
Example:
Consider teaching the LLM how to solve a "similar problem":
i.e., Example 2:
Solve
Let's produce the model answer:�
-2 * (7 + u) / -2 = -2 * 8
7 + u = -16
u=-7-16
u=-23
Use the above example to "train" the LLM on how to solve these problems, step by step
Let's see if Google PaLM gets it correct?
Putting O-G into ChatGPT, get
-7
which is wrong!
https://poe.com/s/LCDY6Zopx9yHltp9Be1C
https://poe.com/s/OavyPtcsFcZVJy52oF7A
Where did it go wrong?
Plug (Q, A, Q) into Google PaLM:
https://poe.com/s/6BbF9VhuHuYkH2bMpEwz
Got it CORRECT!!!
Because we "trained/taught" the LLM how to solve such problems, step by step.
4. Using CoT to get LLM to get the correct answer
Example 2:
Solve the following for c:
7 - (c-2)/4 = 5
Answer:
7-5= (c-2)/4 ==> 2 = (c-2)/4
==> 8 = c-2 ==> c=10.
Therefore, c=10.
4. Using CoT to get LLM to get the correct answer
Google PaLM
LLM answer WRONG
4. Using CoT to get LLM to get the correct answer
Example 3:
Solve the equation for y: 4=-2 + (y+3)/3
2. Plug your answer into your LLM Google PaLM in the form of (Q, A, Q) to see if you got the right answer. First one who posts on YoTeach! Wins!
4. Using CoT to get LLM to get the correct answer
Google PaLM
Correct (CoT-Q, CoT-A, O-Q)
4. Using CoT to get LLM to get the correct answer
Note: Students can post up a screenshot, or a poe.com sharelink to the ChatGPT prompt and answer, and
It is TIME-STAMPED, so you know who posted first!
Questions?
Please contact either
for any further questions, comments or feedback.