Back up at the Boards

In Grade 11 we are done our first test, and started learning new material. As a warm-up we reviewed modelling from a visual pattern, and finding domain and range.

It was so interesting to see how many strategies popped up to model the same pattern.

Some worked from a table of values, using the 2nd differences to calculate “a”, and figure 0 to calculate “c” and substituted a point to calculate “b”. Others saw the pattern as half of a rectangle, filled in the other part of the rectangle, made an equation using area model then cut it in half. Others saw that they could move some of the dots to make rectangles, and then modelled in our usual visual manner, identifying squares of x, and groups of x.

Some found the vertex by completing the square, others by finding the zeros then the axis of symmetry, then the vertex, and others used -b/2a to find the axis of symmetry from standard form, and got the vertex from that.

I’m thrilled that groups have the flexibility to approach problems in different and creative ways. We are thinking, and not memorizing.

Next we looked at new material: how to simplify and work with fractions. We confronted a few misconceptions along the way, when we need a common denominator, when we can “cancel” out terms that divide to make 1, and if it’s possible to solve for x or not. Some students started applying equation solving skills of “doing the same thing on both sides” to the expressions, before realizing that there are not 2 sides.

I’m sure we will continue to confront more misconceptions as we dig into operations with fractions.

Finally as a fun factoring review we watched this excellent song.