Lesson Study: Cycle 1

Students share and reflect on unique strategies they used to approach a problem with other students in class (either small group or whole class).

Our group of math teachers researched for and co-created a math lesson together. We focused on a Math 1 classroom where they have been studying linear equations.

Previous Goals:

Solve equations and inequalities in one variable (HS.A-REI.A.2)
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (HS.A-REI.B.3)
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (HS.A-REI.A.1)

Current Goals:

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. (8.F.A.3)
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. (8.F.B.4)

Future Goals:

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (HS.A-REI.A.2)

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (HS.A-REI.B.3)
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (HS.A-CED.A.2)

Our Focal Students

Focus Student 1: FS1 is a fourteen year old hispanic student that likes to meet new people and spend time with friends and family.

FS1 believes that in order to be successful in math you have to understand how to use the equations and formulas but also how to apply them to real life events. FS1 believes she can become a better math student by paying attention, getting less distracted, and asking for help as much as possible. She enjoys working independently but also enjoys working with teams as long as they are willing to put in the same effort as her.

Focus Student 2: FS2 is a fifteen year old sophomore. FS2 believes that all students can get better at math by growing out of bad habits. FS2 understands that success in math means not just being smart but in helping his peers and in having confidence. Although FS2 is struggling with other courses, such as AP World History, he always remains optimistic.

Lesson Slides

Our Lesson

We had 2 main goals for our lesson:

1. Connect student ideas

2. Guide students towards the need for the point-slope equation

For our lesson, students were given two points (far away from each other) and students needed to connect their previous knowledge of linear equations and graphing to guide them through the lesson. The goal is to have students exhaust all their options until they cannot find the exact y-intercept or slope so they have a need for a new, more precise equation.

End of Cycle Reflection

I loved the opportunity to look at myself as an educator. I learned a lot about what it takes to get students engaged in work, how to make lessons meaningful, and how to co-create with educators. I learned how to try new things in my classroom through the PDSA cycles and how to come to terms with things not working well. It was great to practice as a first year teacher and I learned a lot about myself and my practices.

In hindsight, there were some things we could have done different with the lesson. We could have framed the lesson better. We prompted them with the idea that we are working with linear graphs and lines, so the students resorted to the y=mx+b formula since that is where they were most comfortable. We got a lot of great student work and I think better framing could have given the students an opportunity to have even better conversations and steer them towards needing the point slope equation.

I really enjoyed working on open ended questions and making it accessible for different grade levels. A goal of mine this year was to make math accessible to all students. We spent two months working on different cycles of research and practice, something that is not typically done as a teacher outside of a class. I extended the same grace to myself that I do to my students. I practiced new things and made mistakes, but I was able to walk away feeling more confident as a teacher.

Student Work

Our goal was for students to use their own knowledge and understanding of linear equations and graphs to pull together information about two coordinate points to get students wondering how they can find an exact equation. Both focal students created graphs and started plotting points. FS1 showed how she found the slope from prior lessons and other students created slope triangles to try to piece together the missing information. FS2 started plotting points, but engaged in conversation with his group about their ideas. FS2 expressed his concern and uncertainty in this ambiguous activity, but ultimately lead the group in their thinking and work. FS1 is very social and enjoys group work, she ended up collaborating with a separate group that was also using the whiteboard. They came to new conclusions and created an X and Y t-chart to push their thinking. Ultimately, though, they found an equation for a line.