Low Floor, High Ceiling Tasks.

While researching entry tickets, I stumbled across something called Low Floor High Ceiling Tasks.  By definition low floor, high ceiling tasks are tasks that can be done by everyone but can be extended to higher levels.    In other words, everyone can start at the same level but students can easily take these tasks to higher levels if the beginning one is too easy.

In order to plan such a task, there are several things to keep in mind as you look for one or you write it.

1.  What is the learning goal of the task?

2. How can you tell if the students are successful?

3. What knowledge or skills did the task address?

4. What stumbling blocks might arise during the task and what questions can you as the teacher use to help get the student moving.

5. How can the task be adapted for students with special needs?

6. Do you have all the supplies you need for this task?

The great thing about these types of activities is they focus on showing students what they know, not what they don't know.  It automatically provides differentiation to all students.  For confident students, they can explore the idea in greater detail while the students who still struggle are able to consolidate their thinking.  In addition, it promotes discussion among students as they share a common activity.  It helps create a positive atmosphere and mirrors real life math.

An example of this type of problem is as follows:

Folding Papers.
1.  Make a square out of a rectangular piece of paper.
2.  Make another square that is 1/4th the area of the first.  Convince yourself it is a square and its area is a quarter of the original.
3. Make a triangle that has 1/4th of the area of the first.  Convince yourself it is a triangle with one fourth of the area of the original.
4.  Make another triangle that is not congruent to the triangle in step three with 1/4 the area of the original.  Convince yourself it is a triangle with a quarter of the area of the original.
5. Make another square that is one half the original square.  Convince yourself it is a square with half of the area.

I provided a link for the activity so you can check it out.  This type of activity could be turned into a gallery walk to share the reasoning of students with each other.  This type of activity can also encourage students to be less afraid of math and being to blossom.

Let me know what you think, I'd love to hear.  Have a great day.