Integer numbers help
I had used “keep, change, change” to little success, but it wasn’t until I used the hot air balloon example that I saw students completely grasp why subtracting a negative would cause the answer to increase. Subtracting integers has always been my Achilles’ heel. You could ask students what patterns they see and to derive some of the integer rules. It’s interactive, so you could have students play with the website before introducing models or the algorithm. Geogebra is a great tool to show addition and subtraction with vertical number lines. By modeling a few familiar problems, you avoid trying to teach two new skills at the same time. I learned that some students had not been exposed to number lines for any operations. Side note: Before jumping into showing students integer addition and subtraction using number lines, show students examples of addition and subtraction problems with positive whole numbers using number lines. (I use a border to clean up my not so beautiful edges.) Most real-world examples are more vertically inclined: a thermometer and above and below sea level. If you don’t use vertical number lines, I would highly recommend you start using them! They give more context to above and below zero. Students are likely familiar with the following real-life scenarios:
Before jumping into integer operations, provide real-world examples of integers. While the term “integers” and the concept of using operations to solve integer problems are new to students, the idea of an integer is not new.
#Integer numbers help how to#
If you have ever heard a student say, “Keep, change, flip” in response to how to solve an integer subtraction problem, then you know what I mean! Ideas for Supporting Conceptual Understanding Provide Context The tic-tac-toe to help with multiplication and division rules was taught to me! The problem with these tricks and shortcuts is that 100% of students will forget the trick or mix up the tricks with something else. No shame if you have taught tricks over conceptual understanding I have! They are well intended.
Each year, I spent more time investing students into the models, and each year, I saw my students’ confidence in working with integers improve. I had one day to teach models, so I would cram the models for all of the operations into one or two days, and then make students practice using the algorithm over and over again. For example, math students have heard from a young age that, “You cannot take a larger number from a smaller number” when, in fact, you can! Unfortunately, as teachers, we can often say or do things that are actually detrimental to our students’ understanding of integers. Students often think they are rocking it (it’s simple math, after all) only to be making the same mistakes over and over again. They will be required to solve integer problems that include multiple steps, in order of operations problems, in solving for variables, and graphing. Students will not be asked to just solve these integers problems in isolation.