To begin this lesson, I preview the complex shape students will be working with throughout the lesson. This is just a visual preview, and I choose not to include any discussion at this point. I want the students to consider about their own opinions and thinking before sharing with the class. I have the students write their position in their journal, which will be used throughout the lesson, and I also have them write their position on a small Post It note.
I record their opinion on a graph that is numbered to correspond to their class identification number 1-25. Using their small notes, the students show me their position, and I mark the box in the corresponding column. This also provides some accountability for the students keeping their position, and it helps me to determine my next step in the lesson.
Because the entire class chose the same position, I changed my plan to extend this lesson to two separate days.
At the beginning of the second day, I start with a very brief mini lesson. Because this lesson is designed to be a debate, this mini lesson is very short and contains only one question.
"What shapes do you see in this picture?"
I then ask the students to write in their journals all the different shapes they see, as well as record some of the attributes of those shapes.
When students have completed their journal writing, I ask them to share their information with a class partner. Most students identify the two triangles and two smaller squares, and about half of the students also mention the larger single square for the outline.
I ask the students if anyone needs to change their position at this point, and everyone still holds their original position.
I distribute the shape at this point and encourage the students to use the shape in any way they choose. It can be cut, they can also use whiteboards to duplicate the shape. Some students ask if they can use a ruler as well. I have the students work with a partner, and I give them 10 minutes to work with the shape.
During this time, I circulate through the room observing students and listening to their conversations. I am looking for strategies in manipulating the shape and explanations about the fractions.
After the first round of partner work the debate begins. The rules for the debate are:
1. Only one person speaks at a time.
2. Switch sides after one speaker.
3. I choose the speaker.
4. Debate continues until at least two people speak on each side, or everyone on the minority side has had a chance to speak.
I had two students switch their thinking even though they could not come up with a clear explanation as to why the shape shows equal fourths. These students were not partners, and could not convince their partners this was equal fourths. Their explanation in the debate was there were four pieces, so it must be fourths.
The students were sent back to work with their partners, and continue to work with the shape. I gave the students a real life context to consider. I asked, "What if this shape was a pan of brownies? Would each person get the same amount?"
Providing the real world context seemed to help the students look at the shape in a different context and revise their thinking. The students below demonstrate their thinking.