Operations and Mazes

In a few weeks my fifth grade students will start their pre-algebra unit. Before delving into the unit students often need a reminder on how to use the order of operations with fractions and decimals. Half of today’s class was dedicated to reinforcing number sense and computation skills. At some point students will need to be able to use these skills along with maneuvering variables on both sides of an equation. I find that some students struggle with pre-algebra if they don’t have sound number sense skills.   So today I ended up using an Illuminations operations activity.

Click for file
Click for file

I passed out the above sheet to each student then reviewed the directions. Students were paired and asked to find a spot in the room to work. Students were asked to hide their calculators and estimate one path that will lead to the largest number. Each group came up with their own path.

Trial and Error

Students were then asked to use a calculator to find the path that ends with the largest number. It was interesting to listen in on the student conversations. Here are a few of the statements that I picked up:


“If you divide the number it will decrease”

“Not really, if you divide less than one the number will increase”

“If you divide by a really small number than our number will skyrocket”

“But we can’t multiply by a number less than one”

“But we can multiply by a large number”

“Let’s just work with the multiplication and division paths, those will make the number jump”

“Let’s work sideways instead of making a path straight down.  Gives us more opportunities to increase”

While listening to the students I decided to not intervene. It was insightful to hear how the different strategies were planned and executed. There were some student arguments and stonewalling.  Eventually students had to defend their reasoning as groups needed to find a solution. Near the end of class students presented their final paths and the class calculated the total. Students soon started to realize that their answer would differ depending on if they followed the order of operations. This changed many of the answers as some groups completed each operation individually. In the end students all decided on one pathway to find the largest number. Students then informally reflected on this activity through a class conversation.


Before sending the students on to their next class I mentioned to them the Pick-a-Path game website. The interactive component has more options and might be a decent supplemental activity.  I’m hoping to see that a few students took the initiative to check out the site tonight. It might even be part of a classroom discussion tomorrow.

Author: Matt Coaty

I've taught elementary students for the past 14 years. I enjoy reading educational research and learning from my PLN. Words on this blog are my own.

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