Unit Conversions Piece

Before #TMC16, I had asked for some help with lesson ideas for unit conversions.  Anna Vance (@typeamathland), replied with this introduction that she has used

I was thinking this is pretty awesome!  How can I make it better?  How can I use it to create a cohesive lesson on unit conversions.  I got another good idea from Gregory Taylor (@mathtans) that I would like to incorporate as well:

At TMC, I got to talking a little more with Anna, and we had BOTH been trying to find a way to make the conversions a little more manipulative for students.  I was still thinking numbers, but Anna thought shapes!  And the beauty of shapes is that I can choose ones with symmetry, so that each fraction could be turned either way!!!  This to me was the awesome part.

So with a lot of trial and a little error, I created some cards that can be used to intro how dimensional analysis needs to be set up to cancel one thing and leave another.  Here are the "conversion factors"

There are 6 of them, but they could all be flipped the other way, making 12 possible options for students to choose from.  I also made cards to be the start and end of the conversion.  Nothing too exciting to see here:

Then I played around to make sure I had enough of everything, but not too much.  And I think I do.  I like that sometimes there is only one solution, and sometimes there are three.  At this point my plan for this activity would be to show the start and end I would like on my document camera and have students work in pairs.  Then if they find a solution I will prompt, "Can you find another?"  Sometimes they will be able to and sometimes not.  Hopefully some students will be able to justify why they can or cannot find another solution.  

I played around a lot with it and I don't want to put all the pictures here, because I tried to find all the solutions, but here are a few:

Start with a square and end with a hexadecagon has at least two solutions, but start with a octagon and end with a rhombus only has one.

Obviously this is not an entire lesson, so I still have some more planning to do, but I like what I've got so far and I think it will give my students some good playing and thinking about math opportunities.  I am trying to collaborate with the science teacher on this standard, so I've got a lot to do before I can be all the done thinking about it.

I have some other notes on what the rest of the lesson might be like, but really this next part is for me, so skip to the comments and throw questions or concerns up there.  I'll post links to the docs at the bottom too!

Notes for Me:

• Me:  Shape manipulatives
• Science:  Number manipulatives
• Think Input/Output (where input/output have the same value/amount/quantity)
• Me:  discuss conversion factors need to have a value of 1
• What can we multiply by without changing the value of the input?
• Science:  look up conversion rates
• Me:  notes
• Science:  guided practice
• Mistakes?  Video?  Student created mistakes?
• Should we make an assignment menu?  Due for both classes?  Revision encouraged throughout?
• I want students to journal after doing the shape manipulating! Need a good prompt.
• Introduce new shape.  Create one conversion factor that will allow you to convert this shape to any other shape in your set.  How do you know this works?  Maybe it doesn't, but you're close.  How do you know it doesn't work?

Here are the documents:

Conversion Factors WORD

Conversion Factors PDF

Start End WORD

Start End PDF

Let me know what you think!

-Kathryn

Checklist turned Tracking Sheet

At TMC16, I went to lunch with a group to discuss SBG and Interactive Notebooks.  We ended up mostly talking about SBG, which was great because I got a new idea!  Jessica Breur (@BreurBreur) shared how teachers at her school use tracking sheets for the students to reflect on how they are doing with each target and record scores the teacher has given them.  Then at the end of the unit the teacher collects and keeps them.  I asked her to share with me, and she kindly did!

While looking at all her resources and thinking through it all I was thinking about how it would make a lot of sense to combine this with my checklist, since most of the assignments are recorded there anyway.  Also students rarely keep their checklists after the unit is over, so it doesn't seem detrimental for me to keep them.  I would just need to add quizzes and tasks to the checklist when we do them, which wouldn't be too tricky and would be incentive for students to make those up right away when they miss them (bonus!).  So instead of using any of her wonderful resources, I worked on creating my own.

I needed to break up the spots for assignments based on learning target and provide a space for students to graph their scores for each assignment, so I have a sample that looks like this:

It has room for four assignments per learning target (3 learning targets on the front, zero or one or two on the back depending on unit), and a big miscellaneous section at the bottom of the back.  I figured I would use the miscellaneous section for assignments that related to multiple (or no) learning targets and overflow if I need more than four assignments for a given learning target.  Here is a picture of the back side:

I did an example of what I would write if there were five assignments for the first learning target.

Thoughts I still have:

• Will the stamp space be big enough for my stamps?  (I'm going to test it out tomorrow)
• I am concerned that I will end up needed more than four assignments often, making it pointless to separate it by learning target, but I need to fit three learning targets on the front when I have five learning targets in a unit.  I am especially concerned if I am adding quizzes, group tasks & reflections, and open middle type problems to this.
• I used to require students to have 80% of their checklist complete in order to take the test.  I could do it that same way, or I could say you can at most one missing from each section.  I want this to be a reflective tool, not just a punitive tool, but I also feel a need to hold them accountable.

What potential concerns do you see?  What things would you change?  Any ideas on my thoughts above?

-Kathryn

PS - I am on a blogging roll since TMC16, and I have a lot more ideas to come!

Writing in Math

At TMC I really felt pushed to have my students doing more reflection, which I had already been thinking about.  I want them to have "math journals" where they can reflect on what we're doing in class, their homework, and "I see math" entries.  I didn't go to Anna Blinstein's "Journaling and Writing in Mathematics" session, but maybe I should have.  There were a lot of sessions I wanted to go to, but didn't, so I've committed myself to look over their resources on the wiki.  I wanted to take some notes while looking over Anna's slides, so here they are.  Also here is a link to Anna's presentation.  It's way better than what I have here.

Initial Thoughts

• What do you value in your class?

Learning. I tell my students "we are here to learn" often. I also value my students. As people. I care about them and their personal growth.

• How will doing more writing help you achieve this?

I want to have my students keep a math journal so that they can reflect on lessons and share where "I see math"

• What concerns do you have about doing more writing with students?

I can't figure out if I want them to do it on paper or electronically and I can't figure out if/when I should read it. How I would find time for all of it and how it would be marked.

Reasons to Write in Math Class:

• metacognition/retention
• communication
• fun
• better assessment

Possible Prompts:

• Describe the mistake.
• Summarize today’s lesson in a few sentences.
• Which of these is correct? Explain how you can tell.
• What would be a good question someone could ask about this topic?
• What’s something that’s confusing to you right now?
• Pick one problem and explain what you did and why.
• Which homework problem was the hardest for you? Why?
• Would you use strategy A or B here? Why?
• What is going well in class for you? What is not working as well?
• How do you learn best? What can I do as a teacher to help you learn?
• What are your goals for this semester? How will you reach them?
• What’s one good thing that happened this week?
• What is something mathematical about which you want to learn more?
• Did your performance on the quiz surprise you - why or why not?

Note to Self: Differentiate (to self) whether you want journal for the day to be metacognitive/reflective or an opportunity to assess student learning. Prepare prompts in both categories and place in notebook to use. Have one selected for the lesson, but be willing to change it up.

Ways to get buy-in:

• share student work (with class, parents, admin, on classroom, twitter, blog, wall)
• respond to their writing
• Share purpose
• Give them interesting problems to write about
• use during assessments?
• Give feedback:
• short is OK
• coach on how to improve
• acknowledge progress
• ask students to reflect on their journaling
• short and frequent is most important!

Note to Self: If I decide to ask for formal write-ups, there is a structure outlined on the wiki

Assessing Journals:

• Two sentences: acknowledge something good, suggest improvement
• more detail
• clearer explanation
• connect math/writing
• better justification
• more precision
• more math vocab
• include examples
• extension
• look for connections to other content
• Scoring:
• Foundational: student reflection responds to some part of the prompt and generates some insight about self and/or math (this is a 2)
• Proficient: student reflection engages with the prompt; uses reflection to plan and reach goals (this is a 3)
• Exemplary: student reflection yields insights, connections, and specific areas of need; student reflects deeply as part of process beyond specific prompt (this is a 4)
• More scoring rubrics on wiki

Note to self: I could have students "redo" if they don't show foundational. Also, do I really want to score them? How would I connect to standards? SMP?

Thoughts Now:

• What would you change about your responses?

Still have same concerns

• Do you have any new ideas or concerns?

Lots of ideas on assessment, buy-in, questions to ask, and ways to give feedback

• What do you need to do in order to be able to include more writing in your classes?

I need to decide if/how to score, how to have them keep their journal (notebook or electronic), when to check, and some prompts to give. I also need to set up notes to myself about the structure in my notebook.

Where do I go from here?

• Ask Anna, Carmel, kristen about journaling on paper vs electronically
• Select some common prompts and organize into my notebook
• Determine goal frequency of journalling in class (twice a week?)
• Talk with Nicole about scoring or not (when we go back to school)
• When lesson planning: select prompt for lesson, timing, and method for increasing student buy-in

If I follow-through with this, you should be hearing more about journaling on this blog. Ideas, suggestions, comments, please leave them below or tweet me (@kathrynfreed). I'd love to continue this conversation, because I still have a long way to go with it.

-Kathryn

Algebra 1 Learning Targets and Reporting Standards

I've been working on my learning targets for this coming year and linking them to reporting standards.  My goal is that the learning targets will be somewhat evenly spread out among my eight reporting standards.  I'll present them unit by unit here, but first I should let you know what my codes for my reporting standards stand for.

NQ = Number and Quantity
SSE = Seeing Structure in Expressions
ER = Exponents and Radicals
CRE = Creating and Reasoning with Equations
IBF = Interpreting and Building Functions
LER = Linear and Exponential Relationships
SID = Statistical Interpretation of Data
SMP = Standards for Mathematical Practice

I've got 10 units set up for next year.  Hoping for five each semester, but I could also probably do four first semester and six second because we have more time second semester and starting out the year always goes slow.  I'm also hoping to give a performance task each unit, but I don't have them all the way planned out yet, so that's what you'll see at the bottom of each list of learning targets.

Numbers and Units

Functions

Linear Functions

Exponents and Radicals

Exponential Functions

Sequences

Polynomials

Quadratic Functions

Solving Equations

 Statistics

So this is the basic plan.  Questions, comments, concerns can be left below or by tweeting me (@kathrynfreed)

-Kathryn