Grade 10s carved a pumpkin this morning, the final decision was to carve pumpkin pi (so very mathy) Grade 9s had a look at patterns.  This is one that’s a bit challenging.  It’s interesting to see how our skills can transfer to more complex patterns.  The colours help a lot with this one. We know the yellow is the same all the time which is the constant.  The green we can see is 2 groups of “n”.  The red is what is more complex.

We found squares of “n”.  There is 1 square in the first, 2 squares of 2 in the second, and 3 squares of 3 in the third.  We see there are n groups of n squared.  n(n^2)=n^3 but we’ll talk about this more in a few weeks. Another interesting pattern we examined is this one. We used our representations…some explored tables…and saw how the dimensions changed for the rectangle. Some made tables for the number of squares in the figures, and noticed the differences are not consistent.  This means it is non linear.  We later noticed that the differences increase by 4 each time. Some examined the shape in visual groupings and looked for patterns there.  Note the middle number in the set is equal to “n”. We can look for groups of “n” here too. We can find squares of “n” and then rows/columns of “n” also. Here’s another we looked at.  We are working on being flexible with the way we look at a question.  We are looking at the number of white squares in each figure.  This representation is 4n+4. We can also see 4 groups of (n+1). Or we can see 2 groups of (n+2) and 2 groups of n. Here we see a large square minus a small square. We’ll see later how all of these expressions are actually equivalent.