Staircase Patterns

There is a lesson in the first grade Investigations in Number, Data, and Space (Dale Seymour Publications, 1995) curriculum exploring the idea of a "staircase pattern," a pattern in which quantities grow.  This lesson is based on the Eric Carle book, Rooster's Off to See the World in which a rooster is joined in his travels by two cats, three frogs, four turtles, and five fish.  Carle includes a graphic on each page showing the number of animals in the group arranged in a staircase-type design.  The Investigations lesson suggests that the teacher begin reading-aloud the book, then stop partway through so that students can make predictions about what will come next by extending the pattern.   This is a nice example of an open-ended task which can accomodate a range of learners, but in my multi-age class, I generally need to stretch the task a bit more for the second-graders. 

   

Today we started with a read-aloud of Phyllis Root's One Duck Stuck. Obviously, Carle's book is the best book for this lesson since he includes the "staircase graphic" but many other books play with the same pattern.  Because I teach this lesson each year, and some of my students will have had the lesson the previous year, I alternate my read-aloud book.   One Duck Stuck is similar to Rooster's Off to See the World in that an increasing number of animals continue to join the group on each page.  

After a brief discussion of the staircase pattern in the book:

What might happen next?

Is this a pattern?

How is it a pattern?

What is the pattern unit?

Could we translate this pattern into letters? 

Could we translate this pattern into numbers?

Could we translate this pattern into pictures?

Could we translate this pattern into snap cubes?

I asked the class to make and record their own staircase patterns.  First graders generally made simple counting patterns, but I asked many of the second graders to try to make staircases that skip counted.   

During our share session at the end of the workshop period the group became very interested in the idea of making a really big snap cube staircase and worked together as a class to make the staircase you see above.  This led into counting how many cubes made up the total staircase. (We used 276 cubes!) Tomorrow I'd like to push students to investigate how many cubes make up the staircase patterns they created individually.

I also have thought that it would be neat to make some kind of large staircase pattern to display in the stairwell of our school, but I will need to think more about how to carry that out...