Polygon Pile Up

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

  1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
  2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

Addressing #1

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student). 

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

 

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Addressing #2

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle

Click to download a PDF copy to print.

And to really challenge yourself or your students here is a blank one. Can you fill it in so it’s “hard” to determine that indicated angle? What is the least amount of info you can give to bring out the most amount of thinking? Share them out! 

 

Peregrine Falcon – Fastest Animal Alive

I need your help…..

I modified this video originally from Vox for a colleague and her math class.

Could you watch this short video on peregrine falcons with your students….

and then Complete these tasks?

1. What do you notice? What do you wonder?
2. What questions will you work on with your students? Work on them.
3. You can watch the full video here to see/hear un-bleeped values.
4. Take pictures of any thinking your students show you. Send me comments & pictures on Twitter, email, or here.

I’ll update the post with your student’s work.

Thanks,.

 

Turbo Texting

The original idea for this lesson came from Al Overwijk. Thanks again Al!
The possible Ontario overall curriculum expectations covered in the activity:
  • Grade 10 applied:
    • graph a line and write the equation of a line from given information
  • Grade 9 applied & academic:
    • solve problems involving proportional reasoning;
    • apply data-management techniques to investigate relationships between two variables;
    • demonstrate an understanding of constant rate of change and its connection to linear relation
  • Grade 8:
    • solve problems by using proportional reasoning in a variety of meaningful contexts.
  • Grade 7:
    • demonstrate an understanding of proportional relationships using percent, ratio, and rate.
  • Grade 6:
    • demonstrate an understanding of relationships involving percent, ratio, and unit rate.

Act 1: Turbo Texting:

I started with “I was with my brother one afternoon and I needed to text my wife. After texting her, my brother informed me that I was a ‘terrible texter’. He said I was soooooo slow. I on the other hand disagreed. Then we decided to settle this once and for all—- race!!!”

If you’re viewing this through email you may have to click through to see the video

What do you notice? What do you wonder? Allow students a few minutes on their own to jot down their ideas. Then share with partners, then the class.
Here are a few questions/tasks I asked them next. I wanted to slowly build into deciding if this relationship was proportional.
  • What relationships can you see? — Number of characters in a text vs. the time to text it.
  • Create a scatter plot sketch of how the number of characters in a text affects the time to text that message.
  • How does this graph look with both texters on the same grid?
  • Who is the faster texter? Predict. How does your sketch show who is faster?
  • Kevin finishes first does that mean he is the faster texter?
  • How will we determine who is the faster texter? What will we need to see?
We took our time with these questions so we could develop and understand the relationship between characters in a text and the time to text it.

Act 2

If you’re viewing this through email you may have to click through to see the video

ME: “Use any method you choose to determine: Who is the faster texter?” I allowed them time here to work on a strategy. I watched carefully what strategies they used or didn’t use.

Seeing the different strategies gave us a nice discussion the importance understanding what rate we are determining and how to interpret it to answer the problem.

I showed this picture next:

and this piece of info…

Students completed this problem and we discussed the assumptions we needed to make.

Texting Time

How do your students compare to Jon and Kevin? Have them time each other while texting the 165 character message. Have them determine their texting speed to see who the fastest texter is in the class.

Linear Modelling

ME: “Now you may have texted that message in 18 seconds, but would you do this all of the time? Would you keep that same rate for a shorter message? Longer message? We better keep this experiment going.
I set them off to text various messages of different lengths using this handout (I modelled the handout format after Mary Bourassa’s Spegettini and Pennies handout – thanks Mary).

Click to download a copy

Students used Desmos and the regression tool to create a linear model. They used that model to predict how long it would take to text 140 characters, 200 characters, and this message: “Dear Mom and Dad I promise to never text and drive.” They finally timed themselves to compare the calculated time and the actual time.
Extension: Compare the relationship between the number of words in a message and the time to text the message. How would the equation change? Is it still proportional?

Assessment in MFM1P – Update

Here’s a short update on my grade 9 applied course. I’ll try to explain this as clearly as I can…bare with me.

An integral part has been our weekly mastery days. I’ve written about those days along with the tools that make them possible here. These days have been so important to our learning and we will definitely be doing them again next semester.

Allowing For Differentiated Learning and More Student Accountability.

Having these days allows students to have more responsibility in their learning not less! We are using a web based and app based tool called Freshgrade (You can read about how I set that up for mastery days here – this post will be mostly about the benefits). On our mastery days students have to scan through their portfolio and decide which learning goals (expectations) to improve on….then, they, the student, has to go and make that improvement happen (Each LG in Freshgrade has links to questions for them work on). So our mastery day is filled with students all working on different expectations from the course — according to their need. With the encouragement I give them they know it’s up to them to work towards mastery on each learning goal.

Student view of a learning goal to improve:

An activity in Freshgrade I’ve called a learning goal. Each one shows student achievement and next steps to improve.

Capturing Growth Informs Instruction & Assessment

The portfolio tool in Freshgrade is amazing. It captures and holds all of their work. It provides me great insight into their learning. As students work to improve their learning goals (expectations) they upload pictures of their work through the app. I get to see that work and provide audio or written feedback also through the web/app or in person. What I love is that I get to see all that interaction for each learning goal (expectation) forever. I can see the growth that my students are making. My old spreadsheet tool never tracked past work…only most recent. I love being able to see a student’s thinking progression as they attempt problems. It makes me as a teacher more confident about that student’s ability on the course expectations.

For example, this student uploaded a picture of their work on solving a proportion. They were confused on the nature of proportional relationships. After a comment and talking with the student they made corrections and re-uploaded. Their next step is to attempt a new problem to show consistency. That progression of learning stays in their portfolio for us both to see!

A student view of their portfolio:

Can’t see the video? Click through to the post

Capturing all of their progress and achievement in Freshgrade also provides me a ton of data. Since I set up the categories in Freshgrade to be the strands from the curriculum and each learning goal is assigned to one of those strands I get to see my class’ achievement on those strands. For example, If I filter the activities (learning goals) to only see the ones for linear relations I can see if we need to work more on linear relations. This has been great in the spiralled course. We can spend more time on what we need.

Gradebook view showing learning goals and student achievement.

I hope I explained our mastery day process clearly……now, onto an updated day-to-day plan for MFM1P.

Planning:

Each semester I’ve spiralled I’ve kept a spreadsheet that outlines my day-to-day. In the links below you can see those outlines in detail. I’ve included each semester on it’s own tab.

Webpage view of the outline

Get your own copy of the Google Sheet (You’ll need a Google account).

Sign up for a free Freshgrade account