Killing many birds with one stone

If you started to create the "thinking" environment with the previous rectangle problem (by the way there are a total of 9 rectangles), then you want to continue along this line. I would suggest that the next day you have a second problem similar to the previous one for students to work on. I have created a triangle problem.



This problem allows me to accomplish several goals. First, I give it to the students as soon as class begins. This allows me a chance to take care of administrative details like attendance. Second, after they have worked on it for a few minutes, I ask them to check with their neighbor to see if they agree. If they don't agree I ask them to try to decide which answer is correct. This problem is more challenging than the previous, so usually students do not agree on the answer. Consequently, I have them discussing their methods and they are engaged. I will ask them what they think the answer is and I will write these answers on the board. Now, I have the opportunity to accomplish my third goal which is to stress the importance of organizing their thoughts and their work. I will number the individual triangles and then I will make a list of triangles I am combining to form another triangle. After we discuss various strategies and discuss methods of organizing their count, the students usually beg me for another one to try. I tell them we will do another one tomorrow and there will be prizes for those who get it correct. Consequently, I have them looking forward to coming to math class! So, this quick activity from the day before which had the purpose of creating a safe thinking environment has provided me many benefits including the engagement of my students in problem solving!