DESMOS Polygraph Lesson

We've just launched into a unit on graphing linear equations in my 7th grade class. I started the unit with the Domino's Pizza lesson from Mathalicious and my goal of this lesson was to improve my students vocabulary as well as their ability to ask specific questions. So, I decided to give the Desmos Polygraph on Linear Equations a try.

My hope was that students would use words like: x-axis, y-axis, intercepts, rate of change, slope, quadrants, horizontal, vertical... you know stuff that relates to linear equations. Now, this wasn't a complete pipe dream as we've visited linear equations in the past, but only briefly.

So, I did a small re-introduction of the vocabulary and relating back to our introductory "pizza" lesson, challenged the kids to use the word bank listed on the board, and set them free. They were engaged, they all were participating, they all were asking questions, some were even yelling across the room complaining that their partner had given the wrong answer, but it appeared that few were actually using the math vocabulary that I hoped, and I became frustrated. Looking back, I realize that my expectations were a bit unrealistic. Because when I reviewed the comments, there was a whole lot of learning and a whole lot of vocabulary being used, especially since about 80% of my students are ELLs (I teach in the Philippines). Take a look at a few screenshots of the questions asked.

The questions aren't perfect, and it's not what I envisioned, but there is definitely a solid foundation for me to build upon. To wrap up the lesson, I highlighted some of the better questions. I think that I could do a better job of coaching them to use some of the other key vocabulary, but I'm not exactly sure how without writing the questions for them.

I'm going to do these two more times with my other two classes and we'll see how it goes. Thank you to Desmos, Mathalicious and all the other amazing free resources out there that let me leave the textbook from time to time...even if it doesn't go according to plan.

Barbie and Proportions

I decided to try to start the term with little bit of fun, and as we were studying rates, ratios and proportions, I figured that having the 7th graders play with Barbie would be a good way.

 

I began the lesson by playing a short news clip about the real-life Barbie. This was a good attention grabber and elicited a wide range of comments from the kids.  Then, I told the students that they had been hired to turn one of their group members into a real life Barbie.  With that, I had them grab a Barbie and begin brainstorming ways to make the transformation.  I wasn't sure what to expect, but my hope was that they would stumble upon ratios, proportions and scale factors (not the vocab words, but the concepts)...and most did.  If a group was unable to come up with this, I asked some prompting questions to try to lead them to the discovery.

They all seemed to really enjoy the thought of transforming a classmate into Barbie, but their ideas of how to get there were a little crazy.

Once a group was able to determine that a ratio was the best place to start, I gave them tape measures and had them begin.  Again, little instruction was given.  I'm really working on having my student explore concepts first before I do too much scaffolding.  But after a bit of struggle and watching groups measure both Barbie and their friend, I eventually provided some scaffolding worksheets to help them determine which body parts to measure.

The real struggle was creating the life-size Barbie. After finding the Barbie:life-size ratio, they proceeded to measure one of their group members to determine Barbie's life size dimensions.  With this, I had to remind students that if they simply took the measurements of their classmate they would be creating nothing more than a clone of their friend.  This is where I gave quick mini-lessons to some of the groups that didn't grasp proportions or scale factor (I allowed either to be used).  Eventually, all groups were able to find life size Barbie dimensions.

I also had them do the same activity with a different doll so that we could compare body types and have a bit of a discussion about the effects, if any, of dolls on our body image.


Once all measurements were calculated, students were given a piece of butcher paper, a tape measure, and a pen, and they were to create their life-size doll (some Barbies and some others).  This was hilarious.  Kids were rolling around the floor laughing (as was I) at some of their creations. 

A discussion will follow, where I'll discuss some of the key ideas from the project (see slide show).  One of the big take-aways for me, was how important precision is in design and construction.  Many of these students should have Barbies that are proportionally identical, but that is definitely not the case.

The final step of the activity is to have the students create their own doll/action figure, determine its life size dimensions, complete a simple cost/analysis, and graph potential profits.

All in all its been a fun way to start the semester.  I don't know if the content learning that I expected happened, but I think the creativity, community building, and conceptual development has been powerful enough to make it worthwhile.  

Barbie Activity Google Doc
Barbie Activity Google Slides

 

Equation, Graph, Table Displays

I just finished a display activity with my 7th graders, and I loved it.  I've used this activity in the past, but not with the success of this go around.  I stole this activity from my days in Oregon and thanks to Shannon McCaw for sharing this and many more activities.

The activity:

• Break up the class into groups of 2 or 3 people
• Distribute a card to each group - the card contains one of the following: graph, equation, table or story
• Students divide a poster into four section and create the other 3 missing parts, depending on what they receive

After the creation of the posters, I did a carousel activity wherein each person wrote a comment(s) on a sticky note complimenting or critiquing other groups work.  Some questions I had them consider:

     1)  Do all representations match or represent the same situation?

     2)  Are all variables defined?  In each section.  (No one had this done)

     3)  Is the presentation easy to read and understand?

     4)  Can you tell what the situation is looking at any given section           (graph, equation, table)

Then, I gave the students 10 minutes to adjust their displays based on the feedback they received.  Every group went back to their displays and changed something.  Most simply labeled their variables, but some groups made more significant adjustments.

The power of this activity is in the critiquing of others work.  Student were able to see how explicit they had to be in their representations, because what is obvious to one person is not to another.  Also, the students had a very difficult time creating a story to match their tables, graphs and equations.  Many groups left the story to the end, and then realized that their representations did match their story.  

This activity lends itself to learning on so many different levels.  I can't wait to do it again!

Solving Equations

As I've mentioned before, I'm teaching the same group of kids that I had last year.  This is good and bad.  Good because I have established relationships, know what they can do, and know what we covered and how we covered it last year.  It's bad because, let's face it, sometimes a student (and a teacher) needs a fresh face.

Knowing that we solved one-step equations last year in our 6th grade class, when I approached this topic this year, I thought that I'd have the kids teach each other.  Therefore, I broke the class into groups of 3, and assigned each group a different equation to solve.  They all came to the white board and began solving the equation.  After 1 minute, I had the groups rotate and continue the work of another group.  This continued until all groups had worked or reviewed each equation.  Next, I had the groups return to their original equations and see if the workings made sense, and if they agreed with the final outcome.

My hope in doing this was that each student would see the various types of one-step equations, they would improve on their ability to critique the work of others, and it would get them out of their seats.  These goals, for the most part, were accomplished.  I also made a rule that the same person could not write on the white board twice in a row, forcing everyone to participate.

After we had solved all of the equations, I had the whole class look at a few choice ones and do a bit of critiquing.  My idea was to create a whole class dialogue about the different methods to solving equations, how we communicate our thinking clearly, and how we can check each other's work.  Unfortunately, the whole class discussion didn't progress as I had hoped, and we just reviewed equation and tried to clarify any misconceptions.

Although the lesson wasn't perfect, I enjoyed the different approach to presenting the topic.  It did get all students out of their seats, and most of them were working on and talking about math which was great.

Order of Operations Fun

A few days ago, I was looking across the courtyard into the upper school classrooms, and all I saw were students sitting in their seats and teachers standing delivering content.  This prompted me to take a quick stroll around our campus to see whether this was the norm.  I wandered the halls of our upper school, middle school and lower school.  Do you know what I found?  In only ONE classroom were students actually standing and working in groups.  In every other classroom, the teacher was talking and the students were seated at their desk.  I'm sure this isn't always the case, but it prompted me to rethink my next lesson.

I was designing my lesson(s) for teaching the order of operations with the objective of getting students to interact with the skill in multiple ways (mainly out of their seats).  So, with the help of a colleague, I created some stations to teach the concept.  

First, I had students work in small groups to simplify a challenging expression.  This led to a variety of simplifications, and we discussed the reasons for the varience, and

My notes for the interactive notebook

the importance of having a set of rules to follow when simplifying expressions.  Next, I used an interactive notebook entry to provide some background knowledge for those that haven't been exposed to the order of operations. 

After I felt like students had a basic understanding of the orders of operation, I split them up into 3 groups of 5.  I know, I only have 15 students in this class...so lucky.  These were the groups:

Pemdonkey

1)  Pin the tail on the PEMDONKEY:  I traced a large donkey on the white board and divided it into PEMDAS sections.  I asked one student in the group to put on a blindfold.  I gave the rest of the group and expression to simplify.  The group had to direct the "blind" member to the correct operation using verbal instructions.  Then they would complete that step of the simplification and continue doing this until they had simplified the expression completely.

2.  Simplifying Expression worksheet - Nothing exciting here, but it gave the student a chance to start the homework.  This also gave me a chance to formatively assess their progress and do any necessary scaffolding.  Notice the small white board in the background.  

Worksheet practice

Hop Scotch PEMDAS style

 3.  PEMDAS Scotch - In this station, students were asked to play a variation of hopscotch.  First, the just completed 5 rounds of hopping through the game board while shouting out the order of operations.  Next, I gave each student a separate expression to simplify.  They had to throw a paper clip marker to the correct operation, then hop to pick it up.  They continued this process until they had simplified their expression.  They repeated this process with a new expression once they had finished.

Each station lasted 12 minutes, but it wasn't nearly long enough.  I should have allotted 18-20 minutes, because each group needed vebal instructions and demonstrations in order to get started.  Also, I did not leave enough time for an adequate wrap-up.  All I was able to do was a quick 1-5 scale of how well they felt they could apply the order of operations.

I know there will need to be some follow up, but, at least for today, my classroom was filled with students out of their seats and engaged in their learning.  Let's hope it lasts!