Brick Problem

 

Consider how your students might view and understand the repeating pattern in the wall above.

This wall is part of a problem posted by Balanced Assessment Project.

I want to examine how we explore repeating pattern with young learners.  Visual spatial reasoning skills support learner success across all subjects and grades, so working with visual tasks of this type can influence success for all students, both high and low performers.

I am challenging readers to take a risk and try some things with K to 3 students.

This wall pattern is drawn on dot grid paper. I included some in this pdf for download THE BRICK PROBLEM variations

 

Given dot paper are students able to reproduce a section of the pattern? Perhaps fold the paper to only see and present one column or 2 columns at a time.

Screen Shot 2019-09-07 at 4.39.37 PM

 

This student asked for a ruler during the task. Can he or she explain how a ruler helped?

Doe he or she recognize what is missing to make the patterns match?

Task Variation:

Choose a colour to use for one of the elements and colour every repetition of that element. I would consider an element to be one of the rectangles, one of the squares or one of the 4 triangle (used to be rectangles)

I coloured the rectangles blue.

Can students see where the pattern repeats itself? Predict ahead, predict back. How many repetitions before you can trust what you believe to be physical evidence? 

The triangles in bricks

I shaded the triangle pieces. This piece is changing 2 different ways. You have to go through the whole strip to see. The triangles share a vertex at the top, then a vertex at the bottom. There is a triangle in every second column. The position of the triangle pieces shifts so you need to go 8 columns into the pattern to consider there actually is a pattern in the triangle pieces.

Another Variation

I mapped the rectangles on a dot grid. Can you?

What would it look like to just map the triangle pieces?

Here is the problem as presented by the Balanced Assessment Program. Bricks for Books

 

Here are my suggestions for ways to teach and adapt this problem to use the visual a variety of ways.THE BRICK PROBLEM variations