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

Number Line Task

So this is the style of many of the tasks that I do in my room, heavy on math, lots of opportunities for me to check in with students as a group and individually, reflection, and math, not always context.  But some people at #eduread wanted to see an example.

I chose to share my Number Line Task because I know I want to do it in the first week of school, but it needed some modifications first!  I did this task last year, but with less structure and it was chaotic, and one student in each class ended up sorting everyone.  Ugh!  No one got to learn!  So I made changes this year to hopefully help with the learning part of it.  It is in three parts.  Part 1 is an individual task (basically think time for each student), Part 2 is as a group, and Part 3 is both class and group.

Number Line Task:  Part 1

FYI:  Each group is getting four different numbers on their paper.  I have 6 tables of 4 students, so I have 6 different sets of 4 numbers.

I would expect students to take about 15 minutes on this.  I plan to have them share with a partner and write one thing their partner said on the back of the paper.  I am doing this because I really want all students to have a voice in my classroom, which means they need to get used to sharing and listening BOTH.  So why not start right away?

Number Line Task:  Part 2

Then as a group, students will complete the following reflection questions

[1.]  Who is the recorder?  Give a specific example of how he/she performed his/her role well.

[2.]  Who is the resource manager?  Give a specific example of how he/she performed his/her role well.

[3.]  Who is the navigator?  Give a specific example of how he/she performed his/her role well.

[4.]  Who was the facilitator?  Give a specific example of how he/she performed his/her role well.

[5.]  Who had the best “because”?  Share it with me!

As you can see these are devised to help students learn to "play their roles" and "say their becauses".  In between Part 1 and Part 2 we are going to learn what the roles of each group member are, so students will have it fresh in their heads...but another way of emphasizing it can't help!

Number Line Task:  Part 3

These are the directions students will get to read through in their groups.

Take an index card and write your number on it.

Soon all of the groups will work together to place all the numbers in order from least to greatest. Here are the rules:

• You may only address one person at a time, by comparing your number to his/hers
•  Say your becauses!
• The only thing you may bring with you is your index card
• When the class is ready, I will check your order, but I will only tell you “ALL CORRECT” or “NOT ALL CORRECT”
• We will keep working until we get “ALL CORRECT”
•  If you feel stuck, you may request “group time” where you will go back to your groups, ask your group members questions, use a calculator, ask a group question, and write notes on the back of your index card
•   “group time” will always be 90 seconds in duration
•  You may only ask me questions during “group time”
•  Remember, when you feel confused, make a mistake, or are thinking hard you are learning!—and that is the goal

      After the class has worked and received and "ALL CORRECT"  each student will complete the following reflection.

[1.]  What was the most challenging part of this task?

[2.]  What is one thing you learned?

[3.]  What is one question you still have?

[4.]  What is one question someone asked you?

[5.]  What number were you and what did you write on your index card? (Use the back if needed.)

All the documents I made for this task are in a folder here.  These are word docs, but it will open in google. Download to word to edit.  Also everything is 2/page and Part 2 should be printed front and back.  Enjoy!

If you have ideas to make this better please let me know!  I'm sure there is something better, but this is what I have :)

-Kathryn