CA I.1 Snowflake Exploration, Part I

Purpose: To introduce the students to exploration, conjecture and testing your conjecture as well as the concept of infinite processes and series.

Classroom Procedure: This is the first activity that we do in class and it is also a very open activity so students often struggle with it at the beginning. For each question they should be given a good amount of time to work first (with some minor helpful hints to small groups and/or the whole group) before whole class discussion. It is however important to have whole class discussions about the majority of this activity. This activity is usually broken into two days - sending students home with Q4 on the first day and beginning the second day by discussing that and finishing the rest of the activity. It is very helpful if you can get through the first page of Part II of the snowflake activity on the same day that you finish the Part I activity and let students go home to work on and practice sigma notation. This gives them time to become familiar with it before having to use it in a more sophisticated way to represent the area of the snowflake.

Ideas this Activity Builds On: This is the first activity of Calculus II so it does not build on any course content. It does however build on the type of investigation that students have done in Calculus I if they have come from our Calculus I.

Introduction/Motivation of the Activity: To introduce us to reading mathematics, exploration, conjecture and testing conjectures as well as helping us understand infinite processes.

Need to Establish by the End of Activity/Wrap-Up: A formula for the area that we add on at the n'th interation.

Additional Notes: This activity continues to a Part II where the focus is more on the infinite part of the process and the series that represents the area of the snowflake. As mentioned in Classroom Procedure it can be helpful to start Part II on the same day as finishing Part I.

Teacher Journal: CA I.1

  • Snowflake Exploration, Part I
    Students are usually a little hesitant to get started on this activity as they are not confident in their ability to read the instructions given for forming the snowflake. It is very common to get called over to a group and asked "What do I do?". I never answer this question but push students instead to start to make sense of the instructions given for the recursive process. Making sense of this not only helps them better understand what's going on which is helpful for the rest of the activity but it also sets the tone for the rest of the class. Students are going to have to read and puzzle things out for themselves in this class. This does not mean that we are not going to help them but it does mean that I won't stand and translate everything that is already written in an activity. Reading and doing mathematics independently is a goal of this class. I usually talk to the class quite frankly about this as it comes up. About half the students will have a lot of trouble generalizing to the n'th snowflake by themselves. This is a place where I judge the frustration level in the class - I generally leave them working on it while I feel like productive discussions are happening but bring them together for a class discussion when I feel like groups have either pretty much got it or have given up. It is very important that students end with a good understanding of this activity as the next activity builds on this and gets more difficult for students as it deals with the infinite case.
    Posted Jun 15, 2012, 8:53 AM by Mairead Greene
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Paula Shorter,
Jan 18, 2012, 2:09 AM
Paula Shorter,
Jan 18, 2012, 2:09 AM