Math Problem Statement
Solution
The image you have uploaded shows a pattern of tiles where the first three figures represent increasing sizes of a cross-like shape. Each figure seems to be constructed with a center square and additional tiles extending from the sides. The given mathematical expression for the number of tiles in the pattern is , where is the figure number. Below the pattern, there is a fill-in-the-blank explanation regarding how the formula corresponds to the pattern.
Here’s the explanation for the expression in context:
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The term represents the core square in the middle, which has dimensions . For figure 1, , so the center is a square. For figure 2, , so it forms a square, and so on.
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The term accounts for the extra tiles that extend from each side of the square. There are 4 sides, and additional tiles are added to each side in figure .
Filling in the blanks:
- The pattern is made up of a by square plus an additional tiles added to each side.
- The total number of tiles is given by the number of tiles in the square, , plus the number of additional tiles, .
Would you like further clarification or more details on any part of this explanation?
Related Questions:
- How can we express the number of tiles for a general figure number in terms of algebraic expressions?
- What is the growth rate of the number of tiles as increases?
- How can you visually confirm the number of tiles added to each side for any figure?
- Can the expression be factored? If yes, how would that help in understanding the pattern?
- How would the pattern evolve if more tiles were added beyond 4 per side?
Tip:
In pattern recognition, always look for how the shape evolves with each step, focusing on both the core structure and the additional elements added at each stage.
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Math Problem Analysis
Mathematical Concepts
Algebra
Pattern Recognition
Quadratic Expressions
Formulas
p^2 + 4p
Quadratic expression
Theorems
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Suitable Grade Level
Grades 7-9