Wednesday, 1 April 2015

MFM2P - Day 36 (Back to linear)

Before the bell rang today one of my students, one who normally needs encouragement to get a pencil out and open his warm-up book, asked me for a graphing calculator. On my way to get it I asked him why he wanted it (it is April 1st) and he replied that he needed it to do math. Turns out that he *needed* to find out how long it would take to build the house he designed yesterday. He needed to finish it up. Wow.

Here is the warm-up we did today:

My attempts to draw regular hexagons were not good so I pulled up the diagrams on the SMARTboard. Here is what we did with it:

I love that we consolidate all of our linear work within the warm-up. And today we continued with more linear work. We started by watching two short videos that Dane Ehlert made - the links are here and here.

I asked what they noticed and they came up with good responses. I liked that these videos quickly showed the slope and y-intercept visually. This really helped set them up for what came next.

My students had not done much of this handout which they got last week so we worked through questions 3 and 4. Finding the slope when the scale of the graph is not 1 unit per square is often something with which they struggle. We took up question 3 together. I try to ensure that they are understanding what the numbers mean within the context as they are coming up with an equation that describes the relationship.

In the next part they found the cost for a distance driven and the distance driven given a cost. I am encouraging them to use algebra and show their work - many can come up with the answers in their head (or using a calculator) but cannot write down a solutions that someone else could follow. It is great that they can figure it out and I believe that means that they understand the process, as opposed to having memorized and algorithm. But we are working toward solutions that look something like this:

The last part of this question asked them to compare this company to one that charged a fixed cost of $75. They did well at providing a sketch and said that the lines have to be parallel.

They spent the remainder of the period working on question 4 which had a negative slope. I circulated and found myself asking "What's the starting value?" and "How do we find the rate of change?" to get them going. I was able to help them work through some misconceptions and they seem to have a better grasp of finding the equation of a linear relationship given a graph.

The most interesting part of this class to me was the amount of arguing going on. There were heated debates and they were all about math! It was fantastic to hear them passionately defending their solutions to each other and explaining what they had done. That's a win in my book.

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