Category Archives: flipped

‘A Negative Times A Negative’

Another busy week in the Math classroom. However, this unit is SO much easier for me and the students than the Pythagorean Theorem was. Next year I definitely think I’ll start with the integer unit instead.

I began by reviewing (in most cases) how to add positive and negative integers. We used number lines to visualize the process and then manipulatives (two-sided red and yellow counters) to practice. Students eventually got the idea, but, of course, the subtraction of negative numbers from a negative number was the hardest concept to get across.

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Next class, we were ready to move on to multiplying. Here I ran into a roadblock. It is almost impossible to illustrate the concept of negative times negative equals positive on a number line. In fact, the textbook even switches to the integer counters to explain it, rather than the number line. I knew that this wouldn’t be enough for my inquisitive crew of grade 8’s: if I can illustrate the other rules of integer multiplication with a number line, I should be able to show negatives times negatives.

After wracking my brain and scouring the internet, I did find one site that attempted a reasonable explanation:


Imagine a number line on which you walk. Multiplying x*y is taking x steps, each of size y. Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps. So, -x*-y means to stand on zero, face in the negative direction, and then take x backward steps, each of size y.


It sounds so reasonable! As soon as I go to explain it however, the logic of it falls apart. I sound like a babbling idiot insisting on something the grade 8’s are sure is patently false. So I switched to the integer counters, but I felt like a bit of a failure. I really wanted to be able to use the number line consistently! Anybody have any suggestions? How do you explain this concept to your class?

On the bright side, I did find this video which was my ‘flipped instruction’ for the day. The students loved it (who wouldn’t love a singing ninja?) and it is catchy!


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Diversity of Learners in Math

The flip is working better this week. Or I’m working smarter. Probably both.

I finally have allowed myself to also use other people’s resources. So instead of creating my own explanation of Pythagorean Theorem, I embedded one from Khan Academy. It explained exactly the concept I wanted  and pretty much in the same way I would have recorded it. I didn’t even tie a google form questionnaire to it this time because I didn’t require the viewing – just made it available for extra help.

I found that helped a lot – it takes the pressure off me to produce every class. Which is a very good thing – because, as I recently have discovered, there’s a lot, a lot, more things demanding my attention in the math classroom. One of the most significant being the diverse learning needs.

It’s not like I’m a new teacher. I have 12 years in this profession and I’ve taught everything from math to drama. Plus, I’ve always believed that every teacher of every subject has his/her own challenges to face. But none of that compares to what I’ve seen this week in math.

I know that students learn at different rates and in different styles. I’ve read the research and applied techniques in my other classes. But nothing prepared me for the breadth I face in this math classroom. From the student who finishes every problem as soon as I assign it to the student who can only complete an equation as I sit next to her. The disparity is actually shocking.

I don’t have an answer to how to meet all these needs (nor do I expect a magic one to appear), but I’m definitely going to have to spend some time on some solutions this weekend. Any thoughts?

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Setback in the Flipped Classroom

So I’ve begun attempting flipping my math classroom in absolute earnestness and I’ve hit my first roadblock. It began last Friday in class when I set up stations in the library. With our school’s new set of 25 iPads (and the fantastic support of our teacher-iibrarian who had purchased some awesome math apps), I planned out some stations. I had planned 5 stations: three with the iPads and 2 with practice exercises.

The problem came when I realized (seems somewhat stupid in retrospect) that I would be needed at all 5 stations. Since this was our first time with stations and the first time with the iPads, the students needed more support than I could give – at least without more than one of me! So I found myself bouncing from station to station and never getting settled at any one place to actually help my students. So, inevitably, when it came time to assign the homework, I quickly realized that a majority of the class had not completed the practice questions in class and few understood what the lesson had meant.

So I was faced with a dilemma: do I go ahead and assign the practice questions as homework (thus negating the whole purpose of the flip) or should I just accept their misunderstanding, write the class off, and start again next class? In retrospect, I probably should have written the class off and started again next day. However, since this is my first time through Math 8 at this school, I felt under pressure to keep pushing through the curriculum (I knew the other classes were already ahead of me). So against instinct, I assigned the problems as homework.

The next day in class I was greeted by several students who told me they ‘didn’t get’ the homework and (of course) were worried because they couldn’t finish it. So I ended up (as I suspected I might) reteaching what I hadn’t managed to do last class. What surprised me about that is how bad I felt that I had let my class down by sending them away to work on something that I knew they were ill-prepared to be successful at.

The entire episode does point out an issue with the flipped classroom. What do you do when you don’t finish the work you planned to do in class? I don’t want to make my students that frustrated again, but I also need to make sure I’m moving along with the curriculum.

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First Flipped Lesson

With my first Math 8 class this week, it was also my first flipped class. I was a bit worried about how the students would react to the idea.

I began by introducing the idea with the handout I had created. After I had given the basic explanation of what a flipped classroom meant and before I explained why I was planning to do this, I asked the students why a teacher might want to do this. The answers were exactly my rationale: “Because then if we are frustrated with the problems the teacher is there” and “We’ll have more time in class”. As much as any class is when you talk course outlines, they seemed excited.

I kept the first video very simple. I used the explain everything app on the iPad to record and set up a google form for the students to record some simple information as a test. Before the school day was even over I had about half the class’s responses turned in.

The biggest problem I foresee this week is keeping that momentum going. I want the students to be as engaged this week as they were on that very first day. So, back to the planning today!

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