Sequencing and Categorization Activities

It’s spring break, but I have been working most of the past week on the job search.  Fortunately, I have finally found some time to post.  And, I am taking four whole days off over the Easter weekend.  Preparing for the last sprint to the finish line at Bard.

Sequencing and categorization activities are becoming a staple in my teaching.  These are “card matching” activities that are highly recommended in Improving Learning in Mathematics.   Basically, students receive a set of cards in a random order and they either have to put them in categories based on what is on the card or they have to put them in sequence in order to solve a particular problem.

There are a number of reasons why I like these types of activities.  First, they allow students thinking to be flexible.  If a student’s thinking changes, he or she can just change the location of a card.  In comparison, writing is very permanent for students, and they are often very stressed if they write something incorrectly.  This is not as much of a problem in card matching activities.  Second, it requires students to work with many examples and many concepts at once.  For example, in categorization activities  a student is required to think about the mathematical definition of a particular category in relationship to various other categories.  It is important that students not think about concepts in isolation.  Third, these activities lend well to differentiation and remediation.  See the examples below for more details in context on this point.  Fourth, students tend to enjoy the activity.  I’m not sure why, maybe it’s just an enjoyment of puzzles.

On to some examples…

Below is an example of a sequencing activity I designed for factoring a quadratic.  I was fond of this activity because my students were getting lost in the details of factoring.  This activity allowed them to take a step back, look at the big picture, and ask themselves, “When I’m factoring a quadratic, what do I do first?  second?  third?”

Below is an example of a categorization activity I designed for categorizing triangles into the classic categories: acute, obtuse, or right and equilateral, isosceles, or scalene.  I used this as an opening activity in a demo lesson, and it was a nice “gentle” way to introduce myself to the class.  I was fond of this activity because it can be designed with various levels of scaffolding.  For example, one can leave out angles in the triangles and require students to find them, or one could have a triangle with two congruent angles and require students to identify such a triangle as isosceles.  Essentially, the teacher can make these as hard or as easy as he or she desires.

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