Welcome to the Matrix

In Calculus and Vectors we are working on solving systems of equations to tell us points of intersection of lines and planes. We will need to solve a system of 3 equations in 3 unknowns. To get us geared up for that challenge we looked at the 3 act task “tech weigh in” (sequel).

For those new to 3 act tasks, there is usually an intro video to get us thinking. We watch the video and notice things and wonder things.

Act 2 brings more information, often at the request of students. They know that the first video didn’t have enough information in it, so the next videos provide more details that can be used to calculate something. In this case, it is the mass of an iPad, a Chromebook and an iPad mini.

My students knew that for 3 unknowns they needed a lot of information. They knew to keep asking for more scenarios!

3 unknowns need 3 equations, so here is the 3rd scenario.

Now that we have 3 situations, we can create 3 different equations to solve for our 3 unknowns.

Some groups went directly to elimination. This is a great task to use as an intro to elimination as the equations seem to invite that solution method, and students intuitively take that path.

Others use substitution, but in the end we all get to the answers no matter the method. We look to streamline our communication though, and we notice that some methods are more direct than others.

In the end we can watch the 3rd act to verify our answers.

We are working towards solving systems of 3 equations and 3 unknowns because we will be looking for the intersection of planes in the near future, using the Cartesian equations in the form Ax+By+Cz+D=0.

At the end of the lesson today we started to look at what a matrix is, and how to write them. We will practice using them in the coming days to keep our calculations organized so we don’t go around in circles like some of us experienced today!