Lesson Plays

Earlier this week we had our final face-to-face class for this semester. We were instructed to create a ‘lesson play’ for a small section of a lesson that we had already created and submitted. This task was designed to encourage us to think about what students will say and the struggles that they may have during our lessons. In saying this, it was interesting to think about the conversations that will take place with students ahead of time. It was difficult to think of the issues that they will have, since every class is different. We included some disagreements and contrasting opinions that would generally occur in a mathematics classroom. We wanted to show some classroom management and think about how we would regain the order in our class if a discussion began. It was critical to ask the students the proper questions and dig deeper when this occurred. We asked for their reasoning, which in turn would deepen their understanding of the math skills that we are working with. In general, ‘Lesson plays’ are a useful tool, especially to ensure that you have something that you can refer back to in case some questions develop. Creating them also makes the instructor consider the exact problems that might occur within a lesson, preparing them for discussion and questioning at the right times. 

Teacher: Today we will be talking about linear and non-linear relations. To begin, please take out the sheet titled “stack them.” I will be passing around drinking cups to help visualize the relationship between linear and non-linear relations. Can I have a volunteer draw the fourth frame on the smart board.

Emily: (draws correct frame on the board)

Teacher: So why did you draw the frame with ten cups?

Kyle: I just added another row to the bottom.

Teacher: Well, that is correct, however, do you notice anything about the pattern of first differences?

Ryan: I guess the total number of cups is going up by the same as the cups on the bottom row.

Teacher: So what exactly is happening to the first differences?

John: So the first differences are going up by one every time then.

Teacher: Thank you Bobby. Considering what we now know about the first differences, how many cups will be in the next frame?

Bevan: Fifteen!

Teacher: Thank you Bevan. We are now going to fill out the remainder of the chart. Can someone tell me how many cups will be added in the sixth and seventh frame?

Sarah: twenty-one and twenty-eight.

Ryan: No it’s twenty-one and twenty-seven.

Sarah: Mrs.! He’s wrong. Shouldn't it be twenty-one and twenty-eight?

Ryan: No are you crazy, it’s twenty-one and twenty-seven.

Teacher: Ok, let’s not yell at each other. Ryan, why do you think the answer should be twenty-seven instead of twenty-eight.

Ryan: because you added six to fifteen to get twenty-one so I added another six again.

Teacher: Ok, Sarah, why do you think the answer is twenty-eight?

Sarah: Well, the pattern of the first differences is increasing by one more cup each. So I added seven to twenty-one to give us twenty-eight.

Teacher: Sarah, that is correct. Did everyone hear Sarah explain how we found that or does anyone have any questions about how we reached those answers?

Now we are going to graph the data. Can anyone tell me what values should be on the x-axis?

Carol: Number of cups added.

Teacher: Close, but let’s think about this. What characteristics usually belong along the x-axis?

Rob: Something that changes over time?

Teacher: Yes usually the independent variable, or the one that is in control of the other is placed on the x axis. So Carol, is your answer going to change?

Carol: Yes. So it should be the frame number along the x-axis. And that means the y-axis is the number of cups added or total.

Teacher: Can I have a volunteer come to the smartboard and plot the graph?

Ben: plots the graph (starting point is in the incorrect position- everything is shifted up)

Teacher: Close! Does anyone notice anything wrong with the points that have been plotted on the board?

Kyle: I think it started too high?

Teacher: Would you like to come fix it?

Kyle: Sure, so am I just moving the points down one value each?

Teacher: Would anyone else like to answer Kyle’s question? Do you think he is right or wrong?

Sarah: Yes, Kyle you just need to move it down one value each frame.

Kyle: Alright!