Restructuring...Again

Well, I'm at it again...trying to figure out how to make my classroom and curriculum better for my students.  I like a lot of things about a lot of my units, but I found myself wondering if it would be more engaging and connected for students if I reordered some of the units.  SO...this is what I'm thinking:

Unit 1:  Numbers and Units
I am hoping to collaborate some on this with the science teacher.  We will teach unit conversions together.  It will be interesting as I have never done something like this before.

Unit 2:  Functions
This is the big change.  Instead of doing all the standards that are "close" to 8th grade standards first, and then starting functions second semester, I'm going to start with functions right away.  I want have a more "function" focus throughout the year.  I also really, really want my students to develop a lot of flexibility with their functional thinking, so hopefully having more time will help. (Some of the flexibility I want to see:  evaluating from equation, graph, table; understanding function notation and y= are similar; find average rate of change and tie it into slope; thinking about "characteristics" of a graph:  x/y-int; increasing/decreasing; extrema)

Unit 3:  Linear Functions
So after a broad introduction to functions, we will focus on various types of function on and off.  Linear is first!

Unit 4:  Exponents and Radicals
As a preface to Exponential Functions unit next, we will manipulate exponential and radical expressions (hopefully with and without variables).

Unit 5:  Exponential Functions
Back to another big function group.  Going to discuss the characteristics of an exponential function algebraically, graphically, and numerically.

Unit 6:  Sequences
Here we tie arithmetic sequences to linear functions and geometric sequences to exponential functions.  Hopefully my students can see the domain of each of these functions will be restricted to the natural numbers.  Also want to make sequences more challenging by including variables in the terms.

Unit 7:  Polynomial Operations
Adding, subtracting, multiplying, and factoring polynomials.  I LOVE polynomials.  I need to make sure my students see more than just quadratics here, but it's OK if it's my focus.

Unit 8:  Quadratic Functions
I have a lot of good things here, but it is not quite a cohesive unit yet.  Needs a little bit more work to develop into that.  Hopefully by not being THE LAST unit I will be able to be more cohesive.

Unit 9:  Statistics
Saving statistics for this point will allow application of the three types of functions we study.  We can do some fun regression for various functions.

Unit 10:  Solving Equations
This will include solving linear equations (which we will constantly review throughout the year, since it is 8th grade, too), quadratic equations, and systems.  I think I'm going to like that systems can involve quadratics :).  We might have to discuss why we don't solve exponential functions yet in Algebra 1.

Five units a semester seems doable, right?  Better than 12?  I think we did 8 this year.  I'm hoping some intentional unit-specific planning this summer will allow me to progress better throughout the year.

Let me know what you think!  Am I missing something big that won't work with this?  Have you tried it this way before?  How did it go?  I'll post learning targets and unit outlines later in the summer (hopefully)!  But probably not chronologically.

-Kathryn

Stacking Cups

I did Stacking Cups by Dan Meyer again.  I haven't done it in a few years and I think my intro made it more successful this time.  I let the students lead themselves to the problem.

I just held up a cup and asked them about it.  They talked about how it could hold water and food.  I shared that they were pretty dirty because many other students had touched them.  They were less eager for food and drinks then :)

Eventually they started talking about how you could stack cups and I asked for them to keep listing different ways to stack them until the stacked them inside of each other.  Then I set a small stack next to my water bottle and had them estimate how tall my water bottle was.  We discussed how even though the the cups stacked halfway up my water bottle, we would need more than twice as many.  I take a few estimates and then we calculate.  I set it up by asking what else we could measure and three (of four) classes decided to measure me :)  The other class chose a particular student and I went with that.  I actually think that was the most fun!

I also gave them some guiding questions based on standards we've been working on.  Here are the questions I asked them to answer in their groups:

1.  Identify the independent and dependent variables.  Select a letter to represent each.
2. How tall is one cup?  How tall are two cups?  Three?  How could you organize this information?
3. Write an equation to model the situation.  Check to make sure it matches the values that you stated in [2.]
4. What is the slope?  Interpret the meaning of the slope in the context of the situation.
5. What is the y-intercept?  Interpret the meaning of the y-intercept in the context of the situation.
6. What is your estimate for how many cups tall Mrs. Freed would be (closest without going over)?  Explain how you determined your estimate.

The next day we discussed as a class.  I compiled all of the equations groups had created and we talked about how they related to the cup.  We discussed how precision was important in order to calculate a correct estimate.  Some groups had calculated an estimate and then put their actual estimate down because I said closest without going over.

This is the class that decided to measure how many cups tall this student is.

After discussing we measured and then I had them complete an individual reflection on google classroom.  I asked them about an equation I had made up.  The questions I asked were very similar to the ones in their group.

What surprised me the most was how much more willing to do the math they were when they made up the question.  And they were so surprised when they saw that I knew they were going to come up with that :)

-Kathryn

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

Checklists #MyFavorite

As I was thinking about what My Favorite thing in the classroom was I thought of checklists.  A year -and-a-half ago I wrote about why I was excited to try checklists, but now I'm on the other side of it--I have used them for a long time!

Here's a brief summary of how I have been using checklists.  Students get a blank one at the beginning of a unit.  As we progress we fill it out.  I usually project it so students can update theirs while I walk around and give out stamps.  When students have completed something they show me and I stamp it.  At the end of the unit I calculate how many stamps is 80%, 90%, and 100%.  They MUST have a least 80% of their checklist completed to take the unit test.  I enter a score in the gradebook based on what percent of the stamps they have, but it doesn't affect the final grade.

Reasons I love the checklist:

• I helps students (and me) stay organized throughout the unit
• It holds students accountable to doing the work
• Students like getting stamps :)
• Students can look back at the end of the unit and see EVERYTHING we've done.  It gives a sense of accomplishment and reminds them "we did learn this"
• It is the students' responsibility, emphasizing that they--rather than solely I--are responsible for their learning

Something I'm trying this unit:  I added a column to allow students a section to self-reflect at the end of the unit on each learning target.  Hopefully this will help them focus their studies!  Seeing a proficiency score next to the assignments we've done will show them what they can look at or work on to study for the test.  I'll report back (but it might take a year-and-a-half!)

Here is an image of what I use and a link below to a document:

Link to Checklist in Drive (download as word document to restore formatting)

-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

#5things I Need to Do this Week

5 Things I Need to Do this Week - All I have left of break is the rest of this week!

1. Organize Student Supplies
I need to do this at least once a semester.  I just put in an order to Bulk Office Supply, so once that arrives I can get to work.  I also need to make some new flower pens.

2. Label my tables
I want to have each seat at each table labeled (I'm thinking with cards) so that I can easily assign students a random seat weekly.  So far I've been doing every-other week, but I think my students would prefer weekly and I want them to see it be more random.

3. Plan the semester
As in big picture planning.  What can I accomplish?  I feel really far behind, but perhaps my goals for first semester were too ambitious.

4. Plan week one
This needs to happen in detail.  I know I want to do a group work task and that we will be starting functions in Algebra.  This is one of my favorite units and I've found even MORE great tasks to use with it!  I also want to rethink homework and bellwork and see if I need to make any changes.

5. Finalize Semester 1 Grades
All I have left to score is my Algebra final, which means I've made some good progress!  But then I have to do a second look through each class and make sure things look right.

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