Engaging students: Adding and subtracting a mixture of positive and negative integers

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Diana A’Lyssa Rodriguez. Her topic, from Algebra: adding and subtracting a mixture of positive and negative integers.

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A2. How could you as a teacher create an activity or project that involves your topic?

Algebra tiles are a fun, hands-on way to help students understand how to add or subtract positive and negative integers. Using a mat with a positive and negative side, students can manipulate the 1-tiles. Using the yellow side of the tile for the positive numbers and the red side for the negative numbers, students pair together opposing colors and take those away. The tiles leftover is the answer to the problem. Here is an example:

Step 1:


Step 2:


Step 3:


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B1. How can this topic be used in your students’ future courses in mathematics or science?

Adding and subtracting positive and negative integers is a one of the most crucial foundation skills that students must learn. This concept is demonstrated and needed in almost every math scenario. In its simplest form, students begin to learn this concept around the first grade, 1+1=2. This process is carried over into third grade with multiplication. Then negative numbers are introduced while in sixth grade. Adding and subtracting opposing integers is a continuous concept that consistently builds upon itself, even through algebra, geometry, calculus, or most especially the real world. There is not just one future math course students will use this in; they will use it for the rest of their lives, even if they do not realize it.


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E1. How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

YouTube is always a great resource when trying to engage students. The video below explains how positive and negative numbers work when adding and subtracting them.

A lot of the time students struggle with numbers in general, which makes it harder for them to understand why a concept in math works. This video explains how positive and negative numbers work in relation to each other by using characters from Batman instead of numbers. Using the balance and watching the arrow move in either direction, depending on the type of character that was added into or taken out, allows students to see why positive and negative numbers work the way they do. Once they understand this, it makes working with numbers a whole lot easier. This video also does a wonderful job of maintaining the students’ interest by keeping it related to popular culture by incorporating Batman and the Matrix.


Leave a comment


  1. I likee the video !
    This is the first time I have seen the approach of A N Whitehead done well. I particularly liked “Subtraction does not exist”. One of the points that is generally not considered is that the natural numbers are for counting and counts, the unsigned numbers including fractions are for measuring amounts of “stuff”, and the signed numbers are for describing position and change.
    Here’s Whitehead:


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