Sequences of evolving yellow square patterns demonstrating geometric transformations and growth.
A grid of four panels showing sequences of yellow square patterns forming various geometric shapes, including crosses, L-shapes, and stepped structures, illustrating a progression or transformation.
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Show Answer Key & Explanations
Step-by-step solution for: Engaging Math: Visual Pattern Cards
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Show Answer Key & Explanations
Step-by-step solution for: Engaging Math: Visual Pattern Cards
- The first row, left panel, shows a sequence of three figures. Each figure is made of yellow squares arranged in a cross-like pattern. The first figure has 5 squares, the second has 9 squares, and the third has 13 squares. The number of squares increases by 4 with each step.
- The first row, right panel, shows a sequence of three figures. Each figure is made of yellow squares arranged in a staircase-like pattern. The first figure has 6 squares, the second has 10 squares, and the third has 15 squares. The increase is not constant: +4, then +5.
- The second row, left panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 1 square, the second has 3 squares, and the third has 5 squares. The number of squares increases by 2 with each step.
- The second row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 3 squares, the second has 5 squares, and the third has 7 squares. The number of squares increases by 2 with each step.
- The third row, left panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 1 square, the second has 3 squares, and the third has 5 squares. The number of squares increases by 2 with each step.
- The third row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 3 squares, the second has 7 squares, and the third has 11 squares. The number of squares increases by 4 with each step.
- The fourth row, left panel, shows a sequence of three figures. Each figure is made of yellow squares arranged in a plus-sign pattern. The first has 5 squares, the second has 9 squares, and the third has 13 squares. The number of squares increases by 4 with each step.
- The fourth row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 4 squares, the second has 8 squares, and the third has 12 squares. The number of squares increases by 4 with each step.
The problem is to identify which of these eight panels follows a consistent arithmetic progression with a common difference. All panels show an increasing number of squares, but the rate of increase varies.
- Panels 1 (top-left), 3 (middle-left), 5 (bottom-left), and 8 (bottom-right) all have a common difference of 4.
- Panels 2 (top-right), 4 (middle-right), and 6 (bottom-middle) have a common difference of 2.
- Panel 7 (bottom-middle-right) has a common difference of 4.
However, the question implies there is one correct answer, likely the one that is most distinct or fits a specific rule not just based on the count. Re-examining the shapes:
- In panels 1, 4, 5, and 8, the figures are growing in a way that adds a fixed number of squares each time, but the shape changes significantly.
- In panel 2 (top-right), the figures are growing by adding a row or column, but the increase is not constant (+4, +5).
- In panel 3 (middle-left), the figures are simple stacks: 1, 3, 5 — a clear arithmetic sequence with difference 2.
- In panel 6 (bottom-middle), the figures are also simple stacks: 3, 7, 11 — a clear arithmetic sequence with difference 4.
- In panel 7 (bottom-middle-right), the figures are L-shapes growing in height and width: 3, 7, 11 — again, difference 4.
The most straightforward and consistent pattern is in panel 3 (middle-left), where each figure is simply a vertical stack of squares, increasing by 2 each time: 1, 3, 5. This is the simplest arithmetic progression shown.
Therefore, the solution is panel 3 (middle-left).
- The first row, right panel, shows a sequence of three figures. Each figure is made of yellow squares arranged in a staircase-like pattern. The first figure has 6 squares, the second has 10 squares, and the third has 15 squares. The increase is not constant: +4, then +5.
- The second row, left panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 1 square, the second has 3 squares, and the third has 5 squares. The number of squares increases by 2 with each step.
- The second row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 3 squares, the second has 5 squares, and the third has 7 squares. The number of squares increases by 2 with each step.
- The third row, left panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 1 square, the second has 3 squares, and the third has 5 squares. The number of squares increases by 2 with each step.
- The third row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 3 squares, the second has 7 squares, and the third has 11 squares. The number of squares increases by 4 with each step.
- The fourth row, left panel, shows a sequence of three figures. Each figure is made of yellow squares arranged in a plus-sign pattern. The first has 5 squares, the second has 9 squares, and the third has 13 squares. The number of squares increases by 4 with each step.
- The fourth row, right panel, shows a sequence of three figures. Each figure is made of yellow squares. The first has 4 squares, the second has 8 squares, and the third has 12 squares. The number of squares increases by 4 with each step.
The problem is to identify which of these eight panels follows a consistent arithmetic progression with a common difference. All panels show an increasing number of squares, but the rate of increase varies.
- Panels 1 (top-left), 3 (middle-left), 5 (bottom-left), and 8 (bottom-right) all have a common difference of 4.
- Panels 2 (top-right), 4 (middle-right), and 6 (bottom-middle) have a common difference of 2.
- Panel 7 (bottom-middle-right) has a common difference of 4.
However, the question implies there is one correct answer, likely the one that is most distinct or fits a specific rule not just based on the count. Re-examining the shapes:
- In panels 1, 4, 5, and 8, the figures are growing in a way that adds a fixed number of squares each time, but the shape changes significantly.
- In panel 2 (top-right), the figures are growing by adding a row or column, but the increase is not constant (+4, +5).
- In panel 3 (middle-left), the figures are simple stacks: 1, 3, 5 — a clear arithmetic sequence with difference 2.
- In panel 6 (bottom-middle), the figures are also simple stacks: 3, 7, 11 — a clear arithmetic sequence with difference 4.
- In panel 7 (bottom-middle-right), the figures are L-shapes growing in height and width: 3, 7, 11 — again, difference 4.
The most straightforward and consistent pattern is in panel 3 (middle-left), where each figure is simply a vertical stack of squares, increasing by 2 each time: 1, 3, 5. This is the simplest arithmetic progression shown.
Therefore, the solution is panel 3 (middle-left).
Parent Tip: Review the logic above to help your child master the concept of linear patterns worksheet.
