Being STUCK!

 Being STUCK

 

To concisely describe my response to this reading, here are two "stops" (moments of reflection or insight) I encountered:

1. Recognition of being STUCK as a learning opportunity: The text highlights the importance of acknowledging and embracing the state of being stuck, transforming it into a productive process rather than a source of frustration. This reframing stood out as a mindset shift essential for tackling challenging problems.
2. Using systematic strategies to get unstuck: The suggestion to return to the Entry phase (identifying what is KNOWN, WANTED, and what can be INTRODUCED) provided a structured approach to navigating mental blocks, emphasizing the power of organization and reflection in problem-solving.

These points resonated as they underline growth through persistence and structure in mathematical thinking.

Two-Column Solution for the "Weighing Fish" Puzzle

Puzzle:
A fisherman caught three fish. The fish were not weighed separately, but in pairs.

• The big fish and the medium-sized fish together weigh 16 kg.
• The big fish and the small fish together weigh 14 kg.
• The medium-sized fish and the small fish together weigh 12 kg.
  Question: How much does each fish weigh?

 

Mathematical Work	Process, Emotional Reactions, Dead Ends, and Productive Approaches…
Step 1: Define variables	At first, I felt a bit overwhelmed by the amount of information, but I decided to stay organized.
Let B be the weight of the big fish, M be the weight of the medium-sized fish, and S be the weight of the small fish.	I decided to use simple letters for the fish weights to make the math easier to follow.
From the puzzle, we have three equations:	I read the problem carefully several times to make sure I understood the relationships between the fish weights.
1. B+M=16B + M = 16	This equation was simple and clear. I felt confident about it.
2. B+S=14B + S = 14	The second equation followed a similar pattern, which reassured me.
3. M+S=12M + S = 12	The third equation gave me hope that I had enough information to solve for all three fish weights.
Step 2: Solve the system of equations	I thought about how to combine these three equations to find the individual weights.
Add all three equations together:	I felt optimistic that combining them would simplify the system.
(B+M)+(B+S)+(M+S)=16+14+12(B + M) + (B + S) + (M + S) = 16 + 14 + 12	I realized I could combine the equations by grouping similar terms.
2B+2M+2S=422B + 2M + 2S = 42	I was happy to see a pattern, as I noticed a common factor (2) in all the terms.
Divide by 2:	This step felt logical and straightforward.
B+M+S=21B + M + S = 21	I now had a total weight for the three fish combined, which felt like progress.
Step 3: Solve for individual fish weights	I felt that I was close to finding the individual weights.
Subtract equation 1 from this new equation:	I decided to subtract to eliminate B+MB + M and focus on SS.
(B+M+S)−(B+M)=21−16(B + M + S) - (B + M) = 21 - 16	I double-checked my subtraction to avoid mistakes.
S=5S = 5	I felt happy to have found the first fish's weight — a small victory!
Subtract equation 2 from the new equation:	I repeated the same strategy, feeling more confident this time.
(B+M+S)−(B+S)=21−14(B + M + S) - (B + S) = 21 - 14	This approach seemed to work well, so I continued.
M=7M = 7	I felt satisfied because I now had the weight of the medium fish as well.
Subtract equation 3 from the new equation:	I felt excited, knowing I was close to finding the final weight.
(B+M+S)−(M+S)=21−12(B + M + S) - (M + S) = 21 - 12	I followed the same process, hoping it would work again.
B=9B = 9	I was thrilled to find the weight of the big fish. All the pieces had fallen into place.
Step 4: Verify the solution	I wanted to make sure my answers were correct.
Check the three original equations:	I felt that verifying my work was important to avoid mistakes.
1. B+M=9+7=16B + M = 9 + 7 = 16 ✅	Perfect! The first equation works. I felt reassured.
2. B+S=9+5=14B + S = 9 + 5 = 14 ✅	Great! The second equation is also correct.
3. M+S=7+5=12M + S = 7 + 5 = 12 ✅	Yes! The third equation is correct too. I felt accomplished.
Conclusion	I felt happy and satisfied that I had solved the puzzle using a logical, step-by-step approach.
The weights of the fish are:	I reviewed the entire process to ensure I didn't make any mistakes.
Big fish = 9 kg, Medium fish = 7 kg, Small fish = 5 kg	I felt proud of my work and the clarity of my process.