Teaching is really only as valuable as the learning experiences and opportunities created for the students. Crafting and choosing which experiences and opportunities are available to students should be at the forefront of any teacher’s mindset when planning lessons or units. So let’s delve a little deeper into crafting and choosing learning experiences.
One of my classes has been using the geometric study of area in order to practice and apply multiplicative thinking. Crafting and choosing specifically rich tasks that engage the students has been one of my major goals for this unit. So I’d like to just investigate different iterations of reasonably similar tasks that apply multiplicative thinking in the geometric context of area.
You could just start and end your search with:
Draw a rectangle with an area of 56 units.
This certainly gets the job done. Students have to think about factors of 56 and which make the most sense. The great thing about this task and others like it (check out Open Middle for more) is that there are a multitude of correct answers. Having many “right answers” leads to deeper group work and richer class discussions. The drawbacks to this task are the lack of visual support and the separation from a concrete representation or real world context. Also the language processing comprehension of this task is high, so students who struggle in this area would require additional supports.