Personal Learning Path #3

Background

I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0003 - Functions. Within this Competency, I have chosen the following performance indicator: "analyzes arithmetic and geometric sequences both recursively and with an explicit formula, translates between the two forms, and uses them to model situations." For simplicity, I will only focus on arithmetic sequences, though the activity can easily be modified to focus on geometric sequences as well.

Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic:

My goal is to design a creative activity which requires students to create their own arithmetic sequences rather than solving pre-written problems.

It will be assumed that students already understand the basics of arithmetic sequences including the recursive and explicit formulas. This activity could act as an assessment at the end of a lesson or unit on arithmetic sequences.

For reference, the recursive and explicit formulas for arithmetic sequences are as follows:

The Activity

The central idea is this: Each student will be provided with one worksheet. On the top half of this worksheet is a "Mad Libs" style fill-in-the-blanks math problem. The goal is to let students be creative and humorous with their scenarios they create. Once every student has filled in the blanks, they will swap papers with a nearby student. On the bottom half of each paper, the students can complete the problem created by their partner.

I have placed an example worksheet below. In the first image, the worksheet is left blank. The second image shows one possible solution as an example. Click on the images to see the scenarios in greater detail.

The worksheet could be modified in any number of ways. The scenario itself could be changed, and I have included two other example scenarios below.

The teacher can use this activity in many ways. The teacher could collect and grade the students on their work. It could also be used as an informal, ungraded activity to practice working with sequences. One suggestion could be to have student volunteers share their more humorous examples with the class.

Reflection

The goal of this post was to create an activity to practice working with arithmetic sequences. I am quite pleased with this activity. I think it seems fun and easy to implement. It requires very little preparation on behalf of the teacher, since the scenarios have already been written. The central idea can also be used for geometric sequences, though the scenarios will have to be modified. This is an activity that could work for students working individually, with partners, or in groups. Students could simply write a problem and complete their own problem if working with partners is not an option (in a virtual environment, for example). The activity could be improved by changing the phrasing of the scenarios to ensure that the fill-in-the-blanks words are clear. One could imagine a situation in which Student #1 is unclear in their phrasing (by not specifying "at the end of..." or "at the beginning of..." in the final blank, for example). However, the core of the idea would fit perfectly in any lesson regarding arithmetic and geometric sequences.

Reference

• Arithmetic sequence formulas: https://quizizz.com/admin/presentation/5fd256ae69e5a8001b35ec8d/arithmetic-sequences