Image of the Week: Dissecting Dice Patterns

Dissecting Dice Patterns

Recently here at multiplicity lab, we’ve been working with a lot of teachers on noticing and appreciating the complexity in dice patterns. We find that, as adults, we often reduce patterns to the most basic and skip over the intricacies and consequences of these patterns. Crucially, if we as teachers don’t see all the richness in these patterns, we don’t expect that there will be much to talk about with students. That’s exactly what happened with the Image of the Week when we shared it with teachers at NCTM’s Annual Meeting in 2022 and in PD sessions throughout the year that followed. When we asked teachers what patterns they noticed in this image, conversation started off slow, but as people talked to one another we heard a lot of excitement about the variety of color, number, and positional patterns in this image.

Try it: What patterns do you see? If you focus on color, you might see:

• A row of four green dice, then a row of 7 orange dice, then another row of 4 green dice, or
• Following the blue arrows, you might move in alternating pathways: green, orange, green, orange…

If you focus on number, you might see:

• 3, 3, 3, 1, repeating, following the same blue arrows as above, or
• A stack of 9, followed by a single 1, repeating, or
• Groups of 10, or
• The number of dice, 3 and 1, alternating in each column, or
• The sum of each row, 12 and 15 alternating, or
• The number of threes in each row, 4 threes in green, then 5 threes (collecting the ones into a three), repeating.

If you focus on position, you might see:

• A zigzag of threes, followed by a dot, repeating, or
• A series of interconnected H shapes
• Arrows pointing left or right

There are a LOT of patterns in this image, and a lot to talk about. One intriguing question, whose answer depends on how you see the pattern itself, is: How could you extend this pattern? Those who see the pattern moving horizontally will be apt to add to the right of the image with an orange one and possibly another stack of threes. Those who see the pattern moving vertically are apt to add to the bottom with another row of seven orange dice, alternating 3s and 1s. How would adding to the pattern change the patterns you could see? If you have access to lots of dice, consider building and adding onto this pattern as a class and seeing what each new layer adds to the pattern. Give this – or any of our dice pattern activities – a try with your students tomorrow!

To multiplicity, cheers!

Jen Munson and the multiplicity lab group