In preparation for the school year, I was approached by one of our Algebra teachers to create a set of Desmos lessons for both face-to-face and online instruction. It is important to note that these lessons are not perfect, and I would recommend looking through the more polished mathematical experiences found at teacher.desmos.com before the ones that I have created. I post the lessons I build to contribute to the math teacher community and receive feedback to improve my craft. Following is an outline of the first unit and some features of the lessons.
Overview of Unit 1
The set of nine lessons in this unit is a review of some of the skills students will need to succeed in Algebra. The first three lessons include order of operations, combining like terms, and the distributive property, which are algebraic tools that will be useful throughout the course. The next set of three lessons provides practice in these skills in solving equations and inequalities. Students also encounter other algebraic ideas such as modeling of equations and dividing by a negative coefficient with inequalities. The unit concludes with applying the skills reviewed in the first six lessons to “word-problem” like situations and literal equations. The transition from the calculation of values to the manipulation of variables is a hallmark of student mathematical progression in algebra.
Along with building the unit from computation of expressions to manipulating variables, there are few other guiding ideas behind the lessons I created. Understanding how the lessons are structured may be beneficial if you use them in your classes.
I like to begin each lesson with a slide that is open for interpretation and is accessible to everyone in the class. Too often, teachers start class with a standardized test question that may discourage some students or turn them off to the math lesson. How would you feel as a student if you missed a problem two minutes into the class starting?
In the first video below, students see an animation of a red and yellow counter meeting and disappearing. Students are asked what do you notice? There is no right or wrong answer to the question. It is there to provoke thought and set up the lesson for the day. In the second example, Mario jumps a gap between two hills, and students can choose how they would like to express what they are observing. I love the idea of students having options on how to share their mathematical thoughts.
One of the benefits of using a technology such as Desmos is connecting mathematical ideas to visual models or animation. In the distribution lesson, students can visualize an area model by seeing the distribution of a quantity or variable across multiple added values. This type of visualization provides a conceptual level of understanding to support the algebraic process. Visual models also provide meaningful feedback that may help anchor mathematical knowledge. For example, in the make it balance lessons, students receive feedback in the form of the model balancing or tipping one way or another based on student response. This type of visual feedback is more purposeful and powerful than just right or wrong.
A key feature of being a mathematician is analyzing a situation and discovering what is going on. I like presenting students an answered mathematical problem and having them determine if it is correct or not and why. I will often throw in a wrinkle that they may not have encountered yet to push their thinking a little bit further. For example, shown below, I ask students to put a series of steps to solve a problem in order, but an alternative way to solve the problem appears when they do. I ask them, would this also work? Students often believe there is only one way to solve a problem in mathematics. I try to think about ways to push students to move away from this mode of thought by having them analyze a variety of related mathematical situations.
The creation of these lessons are an attempt to support our Algebra 1 teachers in this time of uncertainty by having a set of mathematical experiences that can be taught virtually or in person. I am happy to share anything that I create to support the mathematics teacher community. If you choose to use them, please let me know how it goes and how they can be improved. You can find the entire collection here: https://kurtsalisbury.com/algebra-1/