Day 155: Graphing

Today was rough.

Algebra is just getting into solving quadratic equations. We looked first looked at solving linear equations like 3x + 4 = 10 and talked about how these were solved and what was happening to x in equation.

After a while I threw up x² + 4x = -3.

Students tried to solve it by moving the 4x over and were frustrated that they couldn’t get the equation down to just one x. They whole group divided and conquered on different values of x, and eventually they reached two solutions.This took a lot of time, time students don’t have, they asked for a better way.

Then I messed everything up.

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No matter how I modified the lesson between periods, students struggle with the process of setting the equation equal to 0, graphing the related function, heading back to the equation to remember they were looking for x-values that produced y-values of 0, then using the graph to help them.

Too much.

I had blank stares all day, something is wrong on my end. Maybe I haven’t emphasized WHY graphs are useful, but, we talked a lot about how graphs generate y-values based on chosen x-values. This is almost the same thing.

I also probably shouldn’t have made them suffer by graphing each equation by hand…

Let me know below how you navigate into solving equations by graphing.

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Day 10: Crossing The River

Today in Algebra, students started with Estimation180. We have been slowly working our way through the first three days, then this happened:

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After students worked through Crossing The River which is out of Mark Droscoll’s Fostering Algebraic Thinking.

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What steps do you find yourself repeating over and over and over and over?

For some reason I just can’t get enough of this problem, I have been using it before I was a preservice teacher. The objective of the day was to introduce creating and solving two-step equations but students went well beyond my expectations. Here are some of the scaffolding questions I used to build up to our final equations.

Stretch student's thinking; it is painful to draw out pictures for 100 adults. I told em the next question I was going to ask was 559 adults.
Stretch student’s thinking; it is painful to draw out pictures for 100 adults. I told em the next question I was going to ask was 559 adults.

We talked about how Algebra makes our lives a whole lot easier.

But what does the equation mean...?
But what does the equation mean…?
Has anyone ever seen an equation like this?
Has anyone ever seen an equation like this?
It has more than one solution... why's that?
It has more than one solution… why’s that? Kinda weird.

I was too excited today to take pictures of student’s work, there were some awesome solution methods out there though! Tomorrow I am going to follow up with a quick review of two-step equations then some practice problems.

In Geometry students had a work day and practiced problems on various pairs of angles/angle addition postulate. They were cranking the problems out today. I like to give students one day a week to work through problem sets in class instead of assigning them as homework (more to come on how we do homework in a future post)!