Visual Patterns
One of the fun things about visual patterns is that people see a pattern growing differently and we can learn from each other. Here's an example of a visual pattern and two different ways that students saw the pattern growing.
One of the fun things about visual patterns is that people see a pattern growing differently and we can learn from each other. Here's an example of a visual pattern and two different ways that students saw the pattern growing.
Ray saw a square on the right side of the pattern, with two segments of length \(n\) on the left side and one square added to the top and another to the bottom. This led him to come up with the equation \(n^2+n+n+1+1=n^2+2n+2\)
Miki saw the pattern differently. She saw the whole middle as a rectangle with dimensions \(n\) and \(\left(n+2\right)\) with the same additional two that Ray saw. This led her to come up with the equation \(n\left(n+2\right)+2=n^2+2n+2\).
Different visual patterns lend themselves to having an equation that is easier to write in a particular form while others, like the one above, can be written in multiple forms depending on the observer. Come up with an equation for each pattern below. Notice what types of patterns lend themselves to be written in intercept, vertex or standard form. If you're struggling, before you check the solutions, check the hints page for a visual help.
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