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Getting students to think critically about comparing and ordering integers

Comparing and ordering integers can be a difficult concept for students to grasp.  The issue often lies in the fact that they feel they cannot apply their prior knowledge about whole numbers to the new desired skill.  In order to ensure students are properly prepared, you need the right comparing and ordering integers lesson plan.  Many students learn how to compare whole numbers with alligators and monsters eating the larger number.  This exciting and rather graphic concept helps many students, but how can this be applied to integers?  With a little twist, your comparing and ordering integers activity can look a lot like the activities students fell in love with at a much younger age.

Helping students build a love and trust for mathematics

Over the years I’ve built a trusting relationship with math. I know that if I apply my knowledge of the real world and what I know about numbers, the math will steer me in the right direction. In contrast, this is so far from true for many of the students we work with. In their eyes, when they don’t perform well or can’t get a topic right away, they believe the math has failed them. Math becomes the victim. An easy scapegoat. It’s our job as educators to provide experiences, not just knowledge, to foster that trust in mathematics.  This was very evident to me during my comparing and ordering integers 6^th grade investigative lesson.

Comparing and ordering integers – providing that “aha” moment

Whether you’re looking for ways to help make comparing integers easier for students to grasp or looking for that “aha” moment when a student understands the topic through investigation, I have some great ideas that have done wonders for the success of my students when it comes to this topic. 

To start the lesson, I do a short investigation with comparing and ordering integers word problems.  I begin the journey with word problems to provide students with connections to the real world so they can answer questions based on experiences.  Most students will trust experiences that lead them to the right answer without feeling like they have to use any math.  The problems I provide all have to do with money, temperature, or losing points on a test or quiz.  Many students are able to relate to at least one of these, if not all of these topics.

Meaningful connections to math can be created organically

During the investigation with the word problems, I often have interactions with students that go similar to the one below.

“I think this is what it should be, but that doesn’t make any sense. I think I’m doing it wrong!  This should be the right answer, but it doesn’t make sense that negative one is greater than negative two.”

“What do you trust? Real life or what you believe to be true in math?”

“Real life.” 

“Yea me too!  Then don’t second guess yourself. Trust your real life experiences. You’re doing fine.” 

I never tell the students their math is correct or incorrect.  I simply remind students to trust what they know to be true based on real life experiences.  In doing so, almost every student is able to correctly compare the integers with little assistance.

Comparing and ordering integers – Greater than ‘gator approach

How I relate this to the alligator buffet students are used to is by tweaking the rules.  Students are taught to “eat” the larger number at a very young age.   The alligator is hungry, so he wants to eat as much as he can.  With a simple twist to this concept, students can apply it to integers as well.  Face the opening toward the number you would desire more.   Would you rather lose ten dollars or lose twelve dollars?  All of a sudden students start to think about the math and make connections on their own.  Negative twelve is less than negative ten because losing twelve dollars is worse than losing ten. 

This sounds great, but potentially you’re not sure it will work because that visual aspect the alligator provides is missing.  However, an open hand facing one direction or the other taking the desired amount provides a similar trick for visual learners on which to rely.  In fact, I often change the rules of a familiar game to provide students with another visual.  They must collect as many points as possible; however, the level they are on has a negative sign on all the points.  Which way should you go to lose the least amount of points.

Practice makes progress

Speaking of games, once the students start to grasp the concept, I like to have them pair up to do some practice.  We play a quick round of Comparing Integers Three in a Row or Tic-Tac-Toe.  During the next lesson, after learning absolute values, we continue to practice comparing and ordering integers with a deck of Integer Cards.  The students enjoy playing War and especially love playing Cheat to practice their new skills.  They also practice with some free comparing and ordering integers games online.  Both Fruit Smash and Number Balls provide fast pace action for practice with comparing and ordering integers. 

In Summary

When provided the proper experiences and examples, students can start to build a trust in math again. A space in their mind where real life experiences and math work together to provide a sense of understanding, trust and confidence, instead of fear and blame.  Building this trust takes time, but we have all year.

To continue to build this trust beyond integers and right into classifying rational numbers, read how I recently changed my instruction on the topic. Furthermore, I realized PEMDAS was providing my students with ammo to blame mathematics for it’s faults. I hate to admit it, but their thoughts of distrust are accurate. Find out how I stopped using PEMDAS and started getting students to trust in the order of operations.