Mrs. Freed, you taught me that!

Here is another one good thing post!

Yesterday my students were practicing evaluating functions using function notation, which really is just another excuse to practice order of operations and exponents work.  One of my students was working on a problem and called me over because he got stuck.  "Mrs. Freed, I don't know what I'm doing wrong."  I took a look, saw that he had already tried it twice, looked over what he had done and pointed out a mistake.  He was able to quickly fixed it and moved on with the problem.  I recognized this as a huge improvement from last year, and took the time to acknowledge it.

"One thing I see you doing right now is persevering when you encountered something that was challenging.  You didn't give up.  You didn't quit.  You asked for help.  You persevered.  You moved on and kept going.  This is a huge improvement from last year that I think is helping you be more successful."

He looked at me, laughed a little and replied, "Mrs. Freed, you're the one who taught me to do that!"

Next week, I'm planning on asking him what I did that helped him learn it, because I want all my students to learn it!

-Kathryn

Desmos Picture

My students in Algebra 1 are learning about functions, and we start with domain and range of relations.  Due to amazing #MTBoS resources, I had some excellent resources to integrate into a week long lesson, which started with pictionary thanks to +John Scammell (@scamdog) and his post here.

My one good thing, however, is about the performance assessment I assigned to students using +Desmos free online graphing calculator.  On our PD day at the beginning of the semester I attended a session by our curriculum director @montemunsinger about creating rubrics for performance assessments, so I used it to help set up this rubric based on my standard related to domain and range:

The assignment was to create a picture in Desmos with at least 10 relations.  In addition, students must restrict the domain for three relations and the range for three relations.  Then students complete a reflection where they explain one domain choice they made and one range choice they made.  The reflection is important to me because it is their opportunity to share what they learned, not just what they created via trial and error. Don't get me wrong, the trial and error aspect of Desmos is the only thing that makes this assignment at all possible for my students, but I want to make sure that through the trial and error process they are learning something.

So my #onegoodthing is watching my students create!  We worked on it off and on throughout almost the whole week.  Some students jumped right in and have created some awesome things, others wanted to copy a previous Desmos picture they saw, but could explain polar coordinates to me (shocker!) so I made them start over (aka not copy).  Some students needed a lot of guidance at first ("Try y=mx+b and substitute some things in for m and b until you get what you want.  Now what part of the line do you want for your picture?  How do we do that?") and then were able to take off and just ask me for help with troubleshooting when they made an error ("Why did my whole line just disappear when I did the domain?" *I check and see -7.5<=x<=-8*  "Remember to put the minimum on the left and the maximum on the right...").

Hopefully, I can get permission to post some pictures here, but let's just say I've seen Olaf, a Christmas tree w/star and presents, batman symbol, personal designs, etc.  My favorite part, however, is when the students learn about new types of relations.  "How do I make a circle?"  "How do I make an oval?"  "Can you help me make this rounded?" I don't usually get to share about circles and ellipses in Algebra 1, but we did this week!

-Kathryn

Rearranging Equations

To start solving multivariable equations for a variable, I have been using this task.  (Note:  For viewable files, you must download them in word.)

Here are the instructions:

 And here is an example of the cut-outs I give to each group of students:

The gist is that they have to decide which equations are derived from the "start" and explain what happened.

This is the students' first exposure to this in my classroom, so they must rely on their background knowledge solving one variable equations and with multivariable equations in the past.  Some students look for equations that have one solution in common with the "start" equation.  Some students using adding/subtracting/multiplying/dividing reasoning as we do in solving one-variable equations.  But this time I had a student use reasoning that was totally new to me, but also super-awesome :)

Her reasoning was based on comparing these equations to her prior knowledge of adding/subtracting from elementary school.  Consider the following set of equations "5 + 3 = 8" and "5 = 8 - 3"  In elementary school they were taught the relationship between these statements.  So my student used this reasoning to explain that "2x + 6y = 12" must bet the same as "6y = 12 - 2x"  ISN'T THAT AWESOME!

I feel that this is the impact conceptual understanding taught at all ages (in this case driven by common core) can be so beneficial to students.  Also can we just celebrate for a second that this student was 100% comfortable extending from numbers to algebra?  I think that is the epitome of deep conceptual understanding!

I'm excited to share this reasoning with my classes on Monday so that others can benefit from it.
-Kathryn