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Sagot :
Sure, let's break down the problem step-by-step:
### 3.2.1 Explanation of Each Learner's Computation (9 marks)
The learners Sifiso, Zola, and Q computed the perimeters of the combined shape and found the values to be 38, 41, and 44, respectively. This section requires explaining how each learner might have arrived at their values. Here is a detailed breakdown:
1. Sifiso's Computation (Perimeter=38):
- Sifiso might have measured each side of the combined shape and then summed them up to find the total perimeter.
- There could have been some measurement inaccuracies or assumptions that led to the total being slightly lower.
- However, the specific measurements taken by Sifiso are not provided, so it's assumed that his technique or slight errors brought him to a value of 38 units.
2. Zola's Computation (Perimeter=41):
- Similarly, Zola would have measured each side of the combined shape.
- Zola's measurements might be slightly different from Sifiso's due to different handling of rounding, different placements of the measuring tool, or considering additional segments not counted by Sifiso.
- Zola ended up with a perimeter value of 41 units through her method.
3. Q's Computation (Perimeter=44):
- Q would have also measured each side of the shape and added them together.
- Like Sifiso and Zola, Q's measurements might include small discrepancies, possibly measuring more segments or more accurately capturing corners and connections.
- Q concluded with a higher perimeter value of 44 units.
Since the provided measurements range from 38 to 44, it shows there are slight variations in each learner's process or interpretation of the combined shape's perimeter.
### 3.2.2 Determining the Perimeter of the Combined Shape (5 marks)
Now, the goal is to determine a logical and reasonable perimeter for the combined shape based on the given measurements.
1. Evaluate the Values:
- Sifiso: 38
- Zola: 41
- Q: 44
These values vary, indicating some measurement tolerances or errors.
2. Choosing a Logical Approach:
- When faced with different measurements, a common approach is to find an average or a statistic that minimizes the impact of outlier errors.
- Using the median as a central tendency measure is sensible since it is less affected by outliers compared to the mean.
3. Determine the Median:
- Arrange the perimeter values in ascending order: 38, 41, 44.
- The median is the middle value in this ordered list.
Here, the median value is 41. This makes sense as it balances Sifiso’s lower value, Zola’s central value, and Q’s higher value, thereby providing a middle ground that would be less biased by individual measurement errors.
4. Justification:
- Using the median is a logical choice because it is not skewed by extremely high or low values. Hence, it effectively represents the most reliable estimate among the three.
- Therefore, it is reasonable to conclude the perimeter of the combined shape is 41 units.
In summary, we determined that the perimeter of the combined shape, considering the logical and sense-making approach, is 41 units.
### 3.2.1 Explanation of Each Learner's Computation (9 marks)
The learners Sifiso, Zola, and Q computed the perimeters of the combined shape and found the values to be 38, 41, and 44, respectively. This section requires explaining how each learner might have arrived at their values. Here is a detailed breakdown:
1. Sifiso's Computation (Perimeter=38):
- Sifiso might have measured each side of the combined shape and then summed them up to find the total perimeter.
- There could have been some measurement inaccuracies or assumptions that led to the total being slightly lower.
- However, the specific measurements taken by Sifiso are not provided, so it's assumed that his technique or slight errors brought him to a value of 38 units.
2. Zola's Computation (Perimeter=41):
- Similarly, Zola would have measured each side of the combined shape.
- Zola's measurements might be slightly different from Sifiso's due to different handling of rounding, different placements of the measuring tool, or considering additional segments not counted by Sifiso.
- Zola ended up with a perimeter value of 41 units through her method.
3. Q's Computation (Perimeter=44):
- Q would have also measured each side of the shape and added them together.
- Like Sifiso and Zola, Q's measurements might include small discrepancies, possibly measuring more segments or more accurately capturing corners and connections.
- Q concluded with a higher perimeter value of 44 units.
Since the provided measurements range from 38 to 44, it shows there are slight variations in each learner's process or interpretation of the combined shape's perimeter.
### 3.2.2 Determining the Perimeter of the Combined Shape (5 marks)
Now, the goal is to determine a logical and reasonable perimeter for the combined shape based on the given measurements.
1. Evaluate the Values:
- Sifiso: 38
- Zola: 41
- Q: 44
These values vary, indicating some measurement tolerances or errors.
2. Choosing a Logical Approach:
- When faced with different measurements, a common approach is to find an average or a statistic that minimizes the impact of outlier errors.
- Using the median as a central tendency measure is sensible since it is less affected by outliers compared to the mean.
3. Determine the Median:
- Arrange the perimeter values in ascending order: 38, 41, 44.
- The median is the middle value in this ordered list.
Here, the median value is 41. This makes sense as it balances Sifiso’s lower value, Zola’s central value, and Q’s higher value, thereby providing a middle ground that would be less biased by individual measurement errors.
4. Justification:
- Using the median is a logical choice because it is not skewed by extremely high or low values. Hence, it effectively represents the most reliable estimate among the three.
- Therefore, it is reasonable to conclude the perimeter of the combined shape is 41 units.
In summary, we determined that the perimeter of the combined shape, considering the logical and sense-making approach, is 41 units.
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