Visual Pattern Go Fish

Recently we have been delving into patterning and I’ve noticed that a common student misconception is to interpret patterns that appear to “go up by one” as having a rule of “plus one” (I use quotes here to denote common student language). For example, I recently showed the following visual pattern to a group of grade 5 students:

Some students saw that the number of dots increased by one every time, therefore the rule, many of them said was “plus one”. A similar misconception often arises with the following visual pattern (and others like it):

Students frequently notice that the number of dots is increasing by two, and misinterpret this as the pattern rule. I believe this misconception arises because students are interpreting what they notice about the pattern (it goes up by one, by two, etc.) as the equation associated with it. During younger years, this is what we want students to do; notice (and wonder). When students are later asked to notice multiple things and interpret what their noticings mean, it is important to recognize that this is a complex task.

I wanted to give students an opportunity to make meaning of their noticings about patterns (visual or otherwise) without the trappings of worksheets and the like. Visual Pattern Go Fish is the resulting game. The deck contains cards with patterns represented in more than one way (visually, numerically, and by equations). I’ve had the opportunity to test out the game and while some guidance is required in interpreting and matching patterns at first, I found students became increasingly adept in correctly interpreting and matching patterns to make pairs (and of course, win the game).

Please note that I had 5th grade students play with one-step multiplication rule patterns at first and added in different operations and two-step patterns later.

An audio recording of this post is available below courtesy of Marina Griffin.