I was trying to make limits more interesting for my students and promote better understanding, and I came across this blog post that compared limits a moment when you are watching a video (in this case a soccer game) and your computer goes black for “buffering”. Click on this link for a better explanation:
Putting these screen shots on separate slides, students used what they knew about minutes 3:58, 3:59, 4:01, and 4:02 to predict what happened at exactly minute 4:00.
This led to students making tables for functions and comparing”buffering” to ERROR (on the calculator).
After the first day, I noticed a few students who were exploring a limit as x approaches 4 by making a table with x-values 1, 2, 3, 4, 5, 6. I wanted to emphasize the importance of “zooming in” further. So on day two I made my own set of screen shots (this time using a volleyball game), and I showed screen shots of minutes 2:00, 3:00, 5:00 and 6:00. We discussed how screen shots of these moments was not enough info to predict what happened at 4:00. Too much could have happened between minute 3:00 and minute 5:00!
We were able to come back to the comparison between the soccer game and the volleyball game screen shots throughout the week.
Lastly, I want to mentioned that Bowman has a great blog post on limits with an activity that I also used one day:
Thanks to Julie R, I started teaching adding integers (my first topic of the year) using army men. The students LOVED it! So here’s how I did it:
- Ordered over 100 red and 100 grey army men online.
- Put 10 grey and 10 red army men into a ziploc baggie for each pair in my class.
- Passed out a baggie full of army men (10 red, 10 grey) to each pair
- Gave students the following rules on a slide:
- Each partner gets 10 army men of one color.
- The grey men are called the Positive Army.
- The red men are called the Negative Army.
- Partners have to clear a “battlefield” between their army men.
- Anytime a grey army man meets a red army man on the battlefield, it is a fight to the death.
- Walked through three examples with them:
- Starting with “1 + (-1)” I had each partner put one army man onto the battlefield. Since it is a fight to the death, we know there will be 0 men left on the battlefield. Hence 1 + (-1) = 0.
- We defined this as a zero pair.
- Then we did “5 + (-2)”, discussing what the answer is and why it must be positive.
- Lastly, we did “7 + 1”, where there is no battle (the positive army is just adding reinforcements) because there are no negative army men on the battlefield to fight.
- Then, I gave the students a dozen adding integers problems to work out. I insisted that they act out the “battles” with their army men.
This was such an awesome hands on lesson, and even though we didn’t come back to army men again, the students still brought it up. They knew that 63 + (-80) was going to have a negative answer because there were more negative army men. They also would discuss how 63 army men on both teams will cancel out (subtract).
Huge thanks to Julie for the great recommendation!