Don’t Do This When Teaching Graphs

To enjoy the week before Christmas break, I decided to try out a lesson idea I had about pictographs. I built this lesson around misconceptions that students always have about keys with numbers larger than one. The day before I taught this lesson, I was asked to teach math at a moment’s notice in another third grade class. When this third grade class interpreted a pictograph with a key of four, I noticed that this was really way too easy for these smart students. I decided to change my planned lesson idea into something more challenging. This is how the lesson went…

First, I did a quick lesson for understanding. I surveyed the class about their favorite ice cream: vanilla, chocolate, or strawberry. I then made a frequency table with this information on the board. With some yellow circle die-cuts with one circle to represent two children’s votes, I asked the class how many votes needed to stand for each flavor. Students did this very well even if this required half of a circle for one person. Then I had each flavor group stand in a different area of the room and I passed out the number of circles the children told me to each group. When I passed out the circles to each group and instructed the students to write their name on a circle, some disequilibrium arose. Students said they didn’t get a circle. I told them to talk to their group and they finally understood that they would need two names on each circle. I couldn’t have been more proud of this part of the lesson and the mathematical practices that arose from their discussion. Then came the next part of the lesson…

I previously gathered real life data about students’ favorite Christmas candy.

• I chose four types of candy: fudge, candy canes, M&M’s, and chocolate Santa’s. I gave three third grade classes each a roll list with a blank beside it for the students to write their favorite candy on. I collected these vote (data) sheets right before the lesson (mistake #1 don’t do this). I made six copies of the data sheets for each of the groups.
• In the lesson I presented the children with the data and told them to create a tally chart/frequency table with the data. Students waded through this for a long time without consistent results. I should have counted the data before I passed it out even though I had estimated the results to around a total of 66 students. I ended up having to total it up while the students were counting (mistake #2 don’t do this). Have your data counted before you pass it out, so you know when your students are way off. (But, hey, in my defense, I have been pulled in all directions lately, substitute, fill in secretary, test coordinator, you name it.)
• I made one student in each group of four responsible to count each class’s data since there were three classes and one student to record the data on a table. This worked very well to keep every child involved in the group.
• We stopped the lesson to ensure the children had the correct data before we proceeded with graphing. I wanted to be respectful of the teacher’s time while I was in her room, but I may have had them check to see if their data was correct in a different way, such as, compare your data with a different group and see if you agree before I just revealed the correct answers.

Next, I told students their key had to be 5 or more (I really had 6 in mind), but the teacher was concerned that it wouldn’t come out evenly for the students. The data had to be slightly altered for the die-cut circles to come out with wholes and halves. She didn’t want the students to have to deal with smaller fractional parts. I was actually okay with the students having the data not come out evenly because I wanted this to be a challenge for them to grapple with. In the real world, data doesn’t come out all nice and clean. Third graders had already proven themselves with a key of four, and I felt like they needed a challenge. I wanted them to discuss how much of a circle to cut apart. Again, I wanted to be respectful of this teacher’s time, so I allowed this and the students’ graphs all turned out pretty much perfectly. No fun :/ There was no argument over how much of a circle to cut apart. (mistake #3, don’t make your data work out perfectly). Needless to say here, I had many reflections after this lesson. This was definitely not my best moment as a math coach (I am at a new school this year). BUUUUUT!!! I loved this lesson, it was so great, even though it wasn’t! I know exactly what to do next time to make it better, and it would be an exceptional lesson with lots of mathematical practices involved! Next steps for students after this lesson–ask students what would have happened if the key was 5 or 6 to at least get them to think about this.