I start every math lesson with a pose the problem which is a cognitively demanding task. 90% of the problems are word problems so the students have a context to deal with and not just a "naked" equation. I find these to be more demanding as well. Here is an example of a task:
L: Labels. They label the numbers and any visuals/models.
O: Our Thinking. They have to connect the answer back to the problem by writing a complete sentence answer the question. For example: Instead of just writing 6 R 1, they have to write, Bob will have 6 cookies in each bag, with 1 cookie left over.
E: Equation. And they have to label each number in the equation by referring back to the word problem.
By this time if I have not stopped them, they begin the process of explaining how they got their answer and justifying why they know it is correct.
As the students are completing the task, I am walking around, looking at their work, asking facilitating questions of some students, and choosing a sequence of student work that I want to share.
When I call the students back together, I ask several students to come up one at a time and show all of their work or part of their work on the ELMO. The other students have to try to make sense of the student's work. I ask questions of the other students to try to get them to pay attention and make sense of other people's strategies. We discuss misconceptions, strategies, and new thinking while we analyze student work. When we are finished analyzing, I will have the students who were correct or parts were correct, tear their work out to go on the chart.
We then move into our lesson. Depending on the results of the task, I use the rest of my math time to do one or more of the following:
- Have the students complete a similar problem using a newly learned strategy from another student.
- Will use a few minutes to do some conceptual understanding teaching to bridge some gaps.
- Have the entire class move to independent practice of the skill from the task.
- Have the higher students play an enrichment game or complete an enrichment activity while I do some intensive remediation and bridging of gaps for the rest of students who are lacking an entry point for the lesson.
In the meantime, here are some more examples of tasks completed by my students.