Grade 10 patterns

Since our projector was not cooperating today I couldn’t say as much as I wanted about these patterns. We were looking at what questions might be interesting to ask, and how we could represent the patterns with algebra. Questions are referring to the patterns ABOVE them. (Patterns are from visualpatterns.org)

Figures 0,1,2,3,4 are shown. We looked at representing each colour with an equation, or modelling the growth of the entire set of circles.

There’s another one to look at. What do the colours represent?

What form of equation would be the most logical for expressing this relationship?

We could look at area and perimeter here. Would they ever be equal? Would the perimeter ever be double the area? Would the area ever be double the perimeter?

What do you notice about this pattern? What do you see in a table of values?

We can look at the area and perimeter here too. 2 different equations. Are they both quadratic? How do you know?

How can you show the growth of the area? Simplify your equation to standard form. Is there a way to visually modify the pattern to match your simplified equation? Can you show this in factored form? Can you modify the pattern to match your factored form equation?

Same questions as above…this looks complex! Is there a way that we can visually simplify things? Rearrange blocks? Does that help us with the creation of an equation?