Developing critical thinking using number sense and estimation

Check out Andrew Stadel’s Estimation 180 site. It’s a gold mine for daily number sense. Plus, it’s given me an idea about how to develop math tasks. First, a snapshot of Estimation 180, followed by incorporating the art of estimation when designing a major task.

Students record their guesses on the number of almonds in a quarter cup. Before revealing the answer they argued with their tablemates why they thought their answer was the closest. It was interesting listening to the arguments. Some took a wild guess; others looked at the context clues. Before revealing the answer, we discussed the context clues as a class–the quarter cup, the size of one almond, the number of almonds we can actually count, the tile countertop, etc. I gave the kids a few minutes to revise their estimate before revealing the answer. Having the kids guess invests them in the problem. The delay of revealing the answer by having the students argue and revise forces them to reflect. It also added drama!

I love the hook and the potential for reflection so much I wove it into the Super Storm Sandy volume task. Before delving into the problem the students first guess the number of dumpsters that are needed to clear away sand from a vacation home. When the first part of the task is completed they compare their solution to their guess then describe what was learned or what was confirmed. Reflecting on their guess and comparing it to their solution helps them to become better critical thinkers and problem solvers.

Dan Meyer’s Three Act Math Tasks also use guessing to hook the students. I would love to turn the Super Storm Sandy volume task into a video format. For now I’ll settle for still photos.

6 thoughts on “Developing critical thinking using number sense and estimation”

I have just completed my certification, as a result I am always looking for new ideas as a potential first year teacher. Guessing almonds in a cup is a great idea to develop critical thinking skills. It also allows the students to become engaged and allows the teacher to help explore or direct their thinking by asking conjecture questions. As a result students get to learn different ways to approach a problem from other students instead of getting hints directly form the teacher. I love the real life applications and ofcourse students like treats. Thanks for the post.

I am so pleased to read your use of the word engaged to mean intellectually stimulating rather than only “fun”. Presenting tasks and problems that allow students to talk math with each other has transformed my teaching. Direct instruction still occurs but I’m focusing more on activating learning as opposed to facilitating learning. Several previous tasks I’ve posted include the use of resource cards to direct student thinking. They don’t provide answers, some of them tend to provide even more questions.

Geraldine
I like the critical thinking in your project. I am a second year teacher and I am always looking for ways to use to open my students up to real life application and this is one. I am working on ratios and this would be great. Because I am doing ratios, I am going to add another item to the cup. I love watching my children when they are interacting with each other solving math problems. Thank you.

Our 6-12 math department has been involved with a lot of professional development and creating challenging tasks is a big part of our work. I never thought to differentiate by adding resource cards but it keeps the critical thinking at a high level while allowing entry points for all learners. Thanks for stopping by!

I have just completed my certification, as a result I am always looking for new ideas as a potential first year teacher. Guessing almonds in a cup is a great idea to develop critical thinking skills. It also allows the students to become engaged and allows the teacher to help explore or direct their thinking by asking conjecture questions. As a result students get to learn different ways to approach a problem from other students instead of getting hints directly form the teacher. I love the real life applications and ofcourse students like treats. Thanks for the post.

I am so pleased to read your use of the word engaged to mean intellectually stimulating rather than only “fun”. Presenting tasks and problems that allow students to talk math with each other has transformed my teaching. Direct instruction still occurs but I’m focusing more on activating learning as opposed to facilitating learning. Several previous tasks I’ve posted include the use of resource cards to direct student thinking. They don’t provide answers, some of them tend to provide even more questions.

Thanks for stopping by!

Geraldine

I like the critical thinking in your project. I am a second year teacher and I am always looking for ways to use to open my students up to real life application and this is one. I am working on ratios and this would be great. Because I am doing ratios, I am going to add another item to the cup. I love watching my children when they are interacting with each other solving math problems. Thank you.

Our 6-12 math department has been involved with a lot of professional development and creating challenging tasks is a big part of our work. I never thought to differentiate by adding resource cards but it keeps the critical thinking at a high level while allowing entry points for all learners. Thanks for stopping by!

Thanks for the summary and I’m glad you’re finding estimation180.com useful. I love that you’re having your students discuss the context clues.