Visual Patterns

We started a new semester today, and we hit the ground running in grade 10.

we continued the pattern, made tables of values and equations, and figured out how many’d be in figure 13.

We worked at the boards in small random groupings, sharing a marker, and working together on these tasks.

Some students saw this and ignored the colours. They saw a large square and a small square overlapping.

The larger square is (x+1)^2, and the smaller square is x^2, and they overlap, so they overcount the 1 square that is contained in both, so that’s why there’s a subtract 1 at the end.

others used the table of values to find the common 2nd difference of 4. We had already see that this is double of the “a” value. We can see that the constant is 0, so the next step is to calculate the b value.

A potentially easier way to find the equation is visually. We see in figure 3, when x is 3, there are two 3×3 squares, in other words, 2x^2, and there are also 2 groups of 3 (2 groups of x) remaining. The equation is y=2x^2+2x.

We also had a look at what linear patterns look like (this is a review from grade 9). Our goal was to make a table, graph, and equation for patterns presented. Some patterns were linear, and some quadratic.

We worked on our math skills and our groupwork skills, and have a little bit of practice to do tonight.

well done grade 10s! A good start to a new semester.