4th Grade Lesson: Variables (Video)

In this lesson fourth grade students, who have not had any experience working with variables, are instructed on how to make and use “variable machines”. These easy to make machines are made out of strips of paper and help students to understand the effect that changing the value of one variable has on another variable. The students work in groups of four, each with their own machines, to determine the sum of the value of all of the letters in their names. As the lesson progresses, students manipulate the variables to spell a variety of words and to control the sum. The main purpose of this lesson was to expose the students to variables for the first time and to teach them the effect of changing a variable.

1) Describe how the teacher’s questioning, and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment.

The teacher’s questioning is definitely a positive contribution to the classroom learning environment and a vital part of the lesson. She has taught her students over the course of the school year to think about and discuss how they should go about solving mathematical problems and why. She challenges her students to explain their thought process in a clear and organized fashion in front of the class. In fact, her class has grown so accustomed to this practice that they do not seem to view it as a challenge, but rather something that is expected. The teacher speaks in a kind tone of voice and expresses genuine interest in what each group is doing. This creates a caring and safe classroom atmosphere where students are more inclined to speak up in class. The teacher offers praise for their verbal responses and probes them for more detail when necessary.

2) What techniques does the teacher use to determine whether students have learned the material you are teaching?

In this lesson the teacher uses a very informal method of assessment. She simply walks around the classroom making sure to visit each table and talks with her students about what they are doing and why. In one video she even mentions to the other teachers that she was in particular looking for children to be able to tell her, “well if I assign this letter with that number, then this other letter will be worth ___ points”. The core idea is that if you change the value of a variable in an equation, then the value of all of the variables in that equation will also change accordingly.

3) Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.

The primary task in this lesson is to create and use a “variable machine” in order to assign numbers to variable letters in a word so that they add up to either the highest or the lowest amount possible. One major mathematical skill needed in this exercise is the understanding of cause and effect. Another more basic but necessary skill is to be able to add and subtract large numbers with a calculator, as it is allowed in this particular lesson. This task is also designed, in large part, to help students understand the concept of assigning a number value which can change to a letter.

I feel that viewing this video was a positive contribution to my learning as a future teacher of math. This helped me to visualize and contextualize the concepts of active learning, cooperative learning, inquiry based learning and mathematical discussion that we have focused on in class. Seeing this teacher in action has given me a better idea of how to be a math teacher who facilitates active learning and discussion, rather than reads from the textbook and hands out worksheets. I thought this was an excellent lesson and I would definitely use it in my own classroom.