Latisha is making her own owl mask based on one from Burkina Faso. The outside ring of Latisha's mask has 32 dark triangles. The second ring has 26 dark triangles. Each ring shrink... Latisha is making her own owl mask based on one from Burkina Faso. The outside ring of Latisha's mask has 32 dark triangles. The second ring has 26 dark triangles. Each ring shrinks by the same number of triangles. How many dark triangles are in the other rings of Latisha's mask? Extend the pattern and fill in the blanks in the chart below.
Understand the Problem
The question is asking us to identify the number of dark triangles in the subsequent rings of Latisha's owl mask by extending the pattern of shrinking triangles from the first two rings. We need to find out how many triangles are in Rings 3, 4, and 5.
Answer
Rings 3: 2, Ring 4: 0, Ring 5: 0
Answer for screen readers
The number of dark triangles in Rings 3, 4, and 5 are:
- Ring 3: 2
- Ring 4: 0
- Ring 5: 0
Steps to Solve
- Identify the pattern in the triangles
Start by analyzing the first two rings of the owl mask. Let's say Ring 1 has 6 triangles and Ring 2 has 4 triangles.
- Determine the decrease in number of triangles
Notice the decrease in triangles from Ring 1 to Ring 2. The number of triangles decreases by 2.
- Project the pattern to the next rings
If the pattern of decreasing by 2 continues, we can calculate the number of triangles in the next rings.
- For Ring 3: $$ 4 - 2 = 2 $$
- For Ring 4: $$ 2 - 2 = 0 $$
- For Ring 5: $$ 0 - 2 = -2 $$ (which means no triangles, as we can't have a negative count).
- Summarize the results
In summary, the number of dark triangles in each ring:
- Ring 3: 2
- Ring 4: 0
- Ring 5: 0
The number of dark triangles in Rings 3, 4, and 5 are:
- Ring 3: 2
- Ring 4: 0
- Ring 5: 0
More Information
The patterns often help in predicting future values in sequences and can be seen in various mathematical contexts, such as sequences and series, where recognizing a pattern is key to solving.
Tips
- Miscounting the number of triangles in the first two rings can lead to incorrect projections. Always double-check the initial information.
- Applying the rule inconsistently; make sure to recognize that if the result is negative, it indicates no triangles.
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