Tag Archives: integers

Reviewing Integers with iPads

As we finished our integer unit, our math class had a fantastic opportunity for review using new technology. Since our school is lucky to have 25 iPads, the class was able to use them in lieu of a more traditional review class.

First, I split the class into 6 groups (each group was 4 to 5 students) and assigned each group to a section of review (multiplying integers, dividing integers and order of operations – two groups did each topic).  Then, each group met with a large piece of blank white paper and planned out what were the important things to say about their topic, an example that they would use to show the use of the rule(s), and a script for the order of presentation on the recording.

After I had previewed their prewriting, each group went to a different corner of the school library to record with the app ‘explain everything‘. In the app, students can use the whiteboard function to record both what they are saying and the math equations at the same time. I explained only the very basics of the app before handing out the iPads (how to change the pen colour, pressing record, pausing, adding a new slide).

As I checked up on the groups, I couldn’t help but be impressed with how quickly the students had taken the task. Students were using the laser pointer function, re-recording bad takes and even adding their own personality to the project – all things I hadn’t even discussed with them. Every student was engaged and on task. Everyone had a role and they all were enjoying playing their parts.

When they were completed, we uploaded the the videos directly from explain everything to my math YouTube channel – this meant giving the kids the password – which I changed after class 😉

In the end, I couldn’t have been happier with the results. This particular example on order of operations shows how students had to synthesize their learning with the new technology which really did improve the students’ comprehension of the topic. Additionally, in posting the videos on YouTube, the students had ready-made reviews to help them study for the test.


And the test results? Paid off. Students had their highest scores yet this year. I can’t wait to finish the next unit to use this lesson again!

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‘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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