### Create the Problem #75FACTS

This past week I attempted "Create the Problem" (#11 page 80) as my #75FACT.  In this FACT students are given a solution and they need to create a problem that would be solved using that solution.

Here is my solution for Create the Problem:

#### Eight Standards for Mathematical Practice:

Math Standard #1:  Make sense of problems and persevere in solving them.  In this problem student need to create a problem that would be modeled with quadratics and would be solved by finding the vertex.

#### FACTS and Teaching Goals:

We just finished our lesson on applications of quadratics and I wanted to see if students understood when to find the vertex of a parabola and what that meant in different situations.

After teaching the lesson, I gave each student a copy of the solution and asked them to create the problem as an exit ticket.  That afternoon I made copies of their problems and cut off their names.  The next day I put students into pairs and had them write comments on the papers.  We used the document camera to look at a few together and discuss our thoughts.  That night I went through each problem and picked the ones that matched the work and made copies for each student to have.

Correct student problems:

#### Small Steps:

Were your students engaged?  Yes, many of the students were able to use their creative side when creating the problem.

Were you confident and excited about using the FACT?  Yes, I love a great lesson plan.

How did use of the FACT affect the student-to-student or student-teacher dynamic?  Student-to-student:  I don't think students are use to commenting on each other's work.  Also, not often do they have the opportunity to see what other students are doing in class unless the student himself decides to share his work.  Student-teacher:  The students are still in the zone where they need to ask me for assurance for everything they do.  In this FACT, I tried to sit out as much as possible.  Because of this I played a roll of more of a questioner rather than an evaluator.

Was the information gained from the FACT useful to you?  Yes.  What I was looking for in this problem was "how high" and "when does it reach this maximum height".  However, most of what I received was "when will it hit the ground?".  Because I used this FACT I knew I had to review what information was given from a parabola's vertex.

Would you have gotten the same information without using the FACT?  Yes, I could have created problems that asked students to find maximum height, and when will it hit the ground to see if they would solve them correctly.  But this FACT allowed students a nice entry point even if they didn't know how to find the vertex.  This FACT allowed students to express that they knew what it meant.

What added value did the FACT bring to teaching and learning?  Because the students had more ownership in the problem they were more willing to figure out why it was correct or incorrect.  Also, because the students' work was anonymous, they were safe in creating their problem.

Did using the FACT cause you to do something differently or think differently about teaching and learning?  Yes, I didn't realize that so many students didn't know what information was given from the vertex?  I mean, I taught it, that means they learned it, right? <-- Sarcasm.

Would you use this FACT again?  Yes, I felt that it helped the students learn about the meaning of the vertex.

Are there modifications you could make to this FACT to improve its usefulness?
First, I would give the students examples of the correct work before they were to comment on other students problems.  So, I would go in this order:  1) create the problem 2) discuss some problems together with the document camera 3) show examples of good problems 4) comment on other's problems.
Second, I used a lot of paper to do this FACT.  I completed this with two classes, a total of 43 students. Then I made two copies of each students work.  Finally, I copied examples of correct problems.  That's a total of 172 sheets of paper!  Maybe to cut back on waste, I will scan their problems and put them in a google doc (can you do that).  Other students can make comments on the google doc.