positives and negatives (5)

       This week was all about integers! We talked extensively about how hard it can be for everyone (students, teachers) to understand the concept of negative and positive numbers. They can get lost if we just show an equation with a mixture of integers and don't have a background explanation for what is going on.

     It is always hard to find real life examples that make sense to students but also teach them something they will remember. For this subject, I loved all the cool ways we learned how to keep track of the positive, negative relationships and their outcomes. One of my favourite graphics is this one: 

"Integers"" Don Steward. (2016). Retrieved From http://donsteward.blogspot.ca  

    Finding unique yet relatable ways to describe and explain things will be the most effective way to reach the students. I find that real life examples with a combination of pictures and words help me, so I will try and access my students through those means. I want to appeal to all learners while providing them with challenging material. I think the above image is a nice place to start, with that image I would then include temperature and think of all the ways I could demonstrate how integers actually visually work. One of the other ideas that was suggested is a sideways number line. I personally love number lines and how they provide a nice clear visual of what the numbers are doing, how they are moving or jumping around, so I think that could be very useful.
   One of the things discussed in the textbook was around the misconception of "two positives makes a negative" (351). Sometimes boxing students into rules makes them forget the other aspects of the question. In this situation, the students can forget that the rule applies for multiplication and division instead of addition and subtraction. This is an example of students not thinking about the real world applications and what the question actually means. 

"Printable Number Line- Vertical" (2016). Retrieved from https://www.printablepaper.net/preview/Numberline-Vertical

    Another one of the activities I really enjoyed was a game that was a cross between Jeopardy and Battleship. We had math equations that we had to quickly figure out that featured both positive and negative numbers, and then had a sheet with the answers that acted as our Battleship board. It was a fun way to get students to really quickly do several math problems. I found it was very helpful at reminding me what adding and subtracting positives and negatives entails. I definitely would consider thinking of a similar game to play with my students.

     We also talked about exponents this week. I do not mind exponents, because it seems to be a very straightforward topic to me. It is a set of rules that are to be followed, and because of that we have to ensure that students remember what the exponent represents. 

"Exponents". Sixth Grade Math Blog. (2016). Retrieved From http://hemsmath6.weebly.com/exponents.html

    

    

       I think like most topics, this is one that just needs to be broken down into smaller steps for students to understand. It is easy to do once we have the base of remembering the rules and knowing the terminology. For a topic like this, I think it is really important to spend time on the base work such as fully understanding the terminology used to describe these numbers. From there, I would try and explain why we simplify by making it an exponent, like the above example demonstrates. If students first have the basis of when and why to use exponents, they will then know what to do and how to do it to solve the problem. 

   

    One of the other topics we discussed was manipulatives. I know how hard it can be to decide when to introduce manipulatives into a topic. When assisting grade three's in learning multiplication, I had chosen to introduce manipulatives far too early in the conversation, and found my students did not have a good enough base to work with the manipulatives on. It was a hard lesson to learn but I definitely noticed right away that they did not have that foundation, and then the manipulatives because useless instead of being a good tool to use. I think teaching the lesson with demonstrations and visuals is always a good thing, but the students need to have that clear outlined lesson first, where they are taught how to do it, before giving them the tools to explore how it works on their own. The manipulatives are an amazing tool for kinaesthetic and visual learners, but I think mathematic lessons need to be fully explained and detailed out to students before they get to that point. 

   Overall, another great week with various advances in mathematics. I am thrilled to be learning more ways to teach and hope to continue having fun and inventive examples to present to the students.