Background: I teach Algebra 1… in high school. In the state of Virginia. In the state of Virginia, in order to graduate high school you must pass ONE math SOL (end of year test). Some of the students who come to me have never passed a math SOL in their entire educational career. I am challenged with reaching the most vulnerable learners - they are neurodiverse, linguistically diverse, racially diverse, and economically diverse. They struggle with maturity and many have internalized that they “aren’t good at math.” But these kids deserve to be successful in math… and they deserve quality instruction in mathematics.
Because of my students’ high stakes for this end of year test, my lessons ALL start with a standard (because, after all, if they don’t know these by the end of the year, they may not graduate high school). Today’s standard was A.6b - The student will....
b) write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.
I always try to keep my “notes” portion of my lesson brief. The more they are doing the math the better. The premise of this lesson is simple, and every tool to write the equation of a line when given two points had already been given to them:
Step 1 - Calculate the slope using the slope formula.
Step 2 - Substitute the slope and one point into the point-slope formula.
Step 3 - Solve for y.
Step 4 - Check your work graphically, using Desmos or paper.
In a typical day, I would provide a brief set of notes saying exactly these things… do these things in this order, now go do the math. Notes at the beginning… math at the end. Faced with the last day before winter break, I feared this day would be a wash… Our day was shortened due to an assembly, and many kids would be absent. I decided to run an experiment. Knowing my students had every tool they needed in order to successfully complete this standard… what if… what if I let them puzzle it out and try to figure it out on their own? And summarized their findings as ‘notes’ at the end? (Knowing not every student learns in the same way… I also pre-recorded the ‘notes’ section and ran the copies for whoever felt like they need that to access the lesson anyway.)
The warmup for the day would be calculating slope using the slope formula - it was the previous lesson. So instead of giving them four problems to calculate the slope of for review, and then going over it, and then taking new notes, and then doing math… I landed on this as a warmup:
Warm Up 38:
Because of my students’ high stakes for this end of year test, my lessons ALL start with a standard (because, after all, if they don’t know these by the end of the year, they may not graduate high school). Today’s standard was A.6b - The student will....
b) write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.
I always try to keep my “notes” portion of my lesson brief. The more they are doing the math the better. The premise of this lesson is simple, and every tool to write the equation of a line when given two points had already been given to them:
Step 1 - Calculate the slope using the slope formula.
Step 2 - Substitute the slope and one point into the point-slope formula.
Step 3 - Solve for y.
Step 4 - Check your work graphically, using Desmos or paper.
In a typical day, I would provide a brief set of notes saying exactly these things… do these things in this order, now go do the math. Notes at the beginning… math at the end. Faced with the last day before winter break, I feared this day would be a wash… Our day was shortened due to an assembly, and many kids would be absent. I decided to run an experiment. Knowing my students had every tool they needed in order to successfully complete this standard… what if… what if I let them puzzle it out and try to figure it out on their own? And summarized their findings as ‘notes’ at the end? (Knowing not every student learns in the same way… I also pre-recorded the ‘notes’ section and ran the copies for whoever felt like they need that to access the lesson anyway.)
The warmup for the day would be calculating slope using the slope formula - it was the previous lesson. So instead of giving them four problems to calculate the slope of for review, and then going over it, and then taking new notes, and then doing math… I landed on this as a warmup:
Warm Up 38:
- Calculate the slope: (6,4) and (-12,-2)
- Find the equation of the line that (6,4) and (-12,-2) passes through and be prepared to justify your answer. (Work with your team.)
Sure enough, most came in complaining we were actually ‘learning’ today (on a school day?! Outrageous!) I broke them into groups, sent them off with giant pieces of graph paper, and said “go nuts… I’m giving you ten minutes, I want you to see if you can figure it out. I promise you have every tool you need in order to complete this task.”
I gave them ten minutes, and then we circled around each giant piece of graph paper and listened as the elected speaker discussed how they came to their response. When we were finished, I did a brief summary (“notes”) and told them they could attempt the homework if they felt ready. For those who would like further instruction, the recorded notes were waiting on Google Classroom or we could break into a small group and talk about it more.
Overall this was a positive experience. I was proud of how my students worked - proud enough to take these pictures and write this post. My students did most of the talking and most were respectful to their peers and listened. My favorite line of the day was this: “Ms. B, I got that! I got that equation! I don’t know how I did it, but I got it!”
I gave them ten minutes, and then we circled around each giant piece of graph paper and listened as the elected speaker discussed how they came to their response. When we were finished, I did a brief summary (“notes”) and told them they could attempt the homework if they felt ready. For those who would like further instruction, the recorded notes were waiting on Google Classroom or we could break into a small group and talk about it more.
Overall this was a positive experience. I was proud of how my students worked - proud enough to take these pictures and write this post. My students did most of the talking and most were respectful to their peers and listened. My favorite line of the day was this: “Ms. B, I got that! I got that equation! I don’t know how I did it, but I got it!”
Maybe it was just a Festivus miracle… I know not every day can be a lesson like this, but I will be looking for opportunities to do something like this again as we continue through the year.
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