Operations with Integers

This week we continued with our number sense and numeration discussions but focused on operations involving integers (specifically: addition/subtraction and multiplication/division which leads into discussions around BEDMAS and perfect squares/square roots).

In terms of building up to discussions around perfect squares/square roots it's important to lay a solid foundation. The diagram below demonstrates what an integer is, and it's important to spend time with moving around the number line (i.e. adding/subtracting both positive/negative integers). Below, there is an image of a number line; all whole numbers (both positive and negative) are integers. Begin by adding/subtracting whole numbers along the number line. For example, -3 + 2 = -1.

NCS Pearson (2015). Integers [Online Image]. Retrieved from http://bit.ly/1LfGsfj. 

Once students have a good understanding of what integers are and how to work with them, you can move on to multiplication/division (again using the number line or other strategies such as those found here).

Again, once students understand how to do those basic operations they can continue onto order of operations (i.e. BEDMAS).

Another concept important with understanding integers are perfect squares and square roots. An interesting problem solving question for students to work through is the locker problem. It's a fairly popular problem involving students opening/closing lockers. The solution to the problem of which lockers are still open are the perfect squares since they are the only numbers that have an odd number of factors (it's explained in more depth here  which includes an alternate way of modelling the question). Below I've made a sketch of a way of representing/working through understanding what perfect squares are and what it means to be a perfect square. They are representations using geocubes which could help students visualize the concept of perfect squares. 

In terms of the curriculum, these concepts are not introduced until grade 7/8, so while playing around with the geocubes may be good to introduce in younger grades, students don't need to truly understand them until the intermediate grades (pages 99 and 111 of the Ontario Math Curriculum).