On Wednesday, I had a double period with one 6th grade class and I got lazy. I decided to let them work in their Eureka Workbooks on a lesson about solving Problems with Percents. I decided to let them work at their tables since they would be doing the lesson in their workbooks. They began working and I began circulating through the room following my normal route and not chasing hands.
They stayed at their tables in groups. Even though the lesson claimed to be about solving real-world problems, it was still abstract and didn’t give much opportunity for creativity in the math. Within a very few minutes, it became obvious that they did not have a conceptual understanding of “percent” and also did not feel the need to think very much since they had the workbooks.
It became a game of Wacamole. I would arrive at a table and spend a minute getting them back on task and try to guide them without teaching too much. Then I would move to the next group and notice that I was leaving frustrated and confused students in my wake.
Most of them raised their hands for help at first. When I didn’t get there quick enough they got off task and started fooling around. I began moving faster from group to group creating even more frustration and probably wearing ruts in the carpeting. The room became louder and more off task. I actually resorted to writing names on the board and threatening loss of recess.
Then I stopped and reflected. These were the same kids who worked so well the previous day when I gave them better activities and had them work at white boards. I realized it was not them and it was not me, It was the lesson.
I stopped the class, got their attention (which took some effort) and had a heart-to-heart with them. I apologized for the way the class had gone. I congratulated them for being excellent students and explained that I had given them a bad task that did not allow them to explore the concept of percent. These kids needed a more rich and concrete task.
Percent lessons are notorious for being formulaic and rote. It is a very simple small idea that is used for convenience, but it has opportunity to get them thinking deeply about what is meant by “percent”. (Literally “Per One Hundred”)
I did not use this task the next period. I heard one of students talking about black holes from their science class. I decided to flex my Physics muscles and have a class discussion. We talked about the nature of black holes which evolved into the nature of reality. One of them mentioned that we all see colors differently. This led to the proposition that perhaps we all have the same favorite color but we describe it differently. We never touched on percent, but I did get to stop them at the end and reveal to them that the class had been a math discussion and by learning more math, they would be able to have a better understanding of such abstract concepts. They left smiling. I took a nap.
Two Days Later............
After I wrote this, I realized I did something that is a pet peeve of mine. I presented a problem without suggesting a real solution. So I needed to put together some activities that do a good job of getting kids thinking about percent. Here is what I did with the same class two day’s later:
The image at right is from the Mindset Mathematics Series Grade 5.
I have used this with fifth-grade students for estimation. For This activity, I wanted something less challenging so they could get a more accurate percent estimate in less time.
I posted this on the screen and asked:
"What percentage of this parking lot is full?"
They asked me:
How many cars are there: I Don’t Know?
How many parking spots are there: I Don’t Know?
Does it matter what color they are? No
Do we include the parking spots on the sides? Up to you
What about the car driving on the road? Up to you
The kids were running back and forth counting cars and parking spots and came up with some good estimations of the percentage. I didn’t give them enough time to count every car and parking spot.
I asked them:
What is your estimate? 35%
Are there 35 cars? No
Then what do you mean by 35%? [silence]
Someone needs to explain what 35% means. Take a few minutes in your groups and think about it.
I also asked them (as I circulated from group to group):
If I gave you some more time, would you be able to come up with an exact percentage? Yes
Then I asked them to look at the bulletin board next to the door and asked them: What percentage of the bulletin board is yellow?
How do we do that?
Well, is it more than half or less than half? Less than half.
So it is less than 50%? Yes
How could you get a more accurate answer? [awkward pause followed by whispering in their groups followed by kids going up to measure the yellow spots]
In each class, the first thing I noticed was that they were improvising a unit of area. In the photo above, the unit of area is his calculator.
Can you get an exact answer? No
Then I stood between the screen and the bulletin board and pointed out that in the first case, they are determining a percent of something that is countable. In the second case, the areas are difficult to count, but you can still talk about percent of the bulletin board.
They stayed on task and thought about each question and came up with others. An excellent class.
The Next Day.....
The next day, I drew some random shapes on graph paper and asked the kids to shade a specific percentage. I assigned each group a different percentage and let them work on the problem. After they were done (about ten minutes), I collected their work and showed each of them on the document camera from smallest to largest percentage.
My goal was to give them another concrete example of percent with areas. I also wanted them to think about visual examples of percent area as they saw them on the screen.
The concrete activities went much better. The kids stayed on task and later said they enjoyed the activity.