Slope & Clothesline

I’ve loved the idea of using a clothesline in math class. I first read about the strategy from Chris Shore and Andrew Stadel and have been looking for ways to work it into my classroom. Calculating the slope of a line from a graph was coming up in my grade ten 2P course and I thought a clothesline will be a great fit.

We had just finished Fawn’s lesson on steepness with staircases that I found linked from Mary Bourassa’s site. From that lesson my students understood the idea of calculating slope by finding the vertical change and dividing it by the horizontal change, but hadn’t done anything abstract on the coordinate grid.

I wanted my students to:

  • Practice calculating slope of a line using two points on a graph.
  • Practice calculating slope of a line given two points (no graph shown).
  • Compare steepness of lines to other lines using the slope.
  • Connect lines that go downward with negative slopes and lines that go upwards with positive slopes.

To start our lesson I asked students if they could calculate the slope of this line:

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we agreed No. We needed to some measurements! I asked what we could do….a student said “you could give us the grid” Bam! I threw it on there.

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Enough Now? Still no! We needed the x and y axes.

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As soon as I dropped the axes on…..I could see them all counting and calculating.

We went through calculating the slope of a line like this…

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and then finally finding the slope a line passing through…

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It was time to start comparing using a clothesline.

I was originally unsure of how to setup the clothesline for best results as I had never done one. I also wanted to create lines that would give us great results for seeing connections among slope, steepness, and sign value. I enlisted some help from Twitter and recieved some great suggestions


I hung two clotheslines across the room. I placed benchmarks of zero and one on the line. I held up the benchmark of -1 and asked students “where would I place this -1 on the line so it’s right?” They yelled out “more right, more left, LEFT!” until we agreed where it should be.
I had whipped up a set of graphs with lines for students to place on the top clothesline and a set of corresponding ordered pairs for students to place on the bottom clothesline.

Cards looked like:

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I scattered the cards across a table and asked students to choose any card, calculate the slope of the line and then place the card in the right spot on the clothesline.

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The majority of students calculated the slopes fine but were not confident with their answers…and therefore very hesitant on placing the cards on the clothesline. They wanted me to verify their answers before they placed them. They, however did very well determining where to place the cards.

After all cards were placed I noticed a few errors in placement and asked students to go back to the line and check to see if any seemed out of place. We had some great talks on why we knew some were wrong and I heard “All the negative slopes should be on this side” and “that one seems steeper than that one, so it should be here” Once we had placed all the cards we did a gallery walk. I wanted them to see how the steepness changed as we move from negative to positive.

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This animation shows the gradual change in slope the students would have seen.

We used the patterns to discuss what a line would look like if it had a slope of 0.

There were two lines with a slope of one….I picked them up and we could see talked about parallel lines.

Class finished with us doing two more problems of finding the slope of a line between two points.

I don’t think this lesson was perfect. Could you help me out and provide some suggestions/feedback for me?

Grab the cards:

 

Lesson Study & Big Ideas

For the last few years my school has been apart of the SSI (School Support Initiative). In small teacher groups we discussed learning gaps we see in our students and then implemented teaching strategies to shorten those gaps.

Last year we identified perseverance as a learning gap. We felt that our grade  9 and 10 applied level students gave up too easily. If an answer didn’t come to them right away they “packed it in” and didn’t really try. We also felt that, especially in math this “packing it in” was due to lack of confidence in their ability. We spent the year focussing on giving great feedback and using growth mindset language. We spent our release time money on mostly bringing in supply teachers while we conferences with students. We talked about where they were and gave them specific feedback to help them get better. We always talked in terms of constant improvement.

This year we are a cross curricular group: 3 math teachers, 1 science and 1 geography. We had a great brainstorming session on learning gaps. Although I still think confidence in math is a huge deterrent in producing quality work we decided our learning gap would be

“Student understanding of main ideas and the big picture”

Our group felt that students sometimes were missing the main idea during and after a lesson. Students might be able to get by memorizing what we were doing in class but missed the big idea.

In my class I wanted to see if this was a problem…. So we set out to get a pre-assessment. We needed to see who in our classes was getting the big idea and who wasn’t. I decided to use Andrew Stadel’s Filing Cabinet problem and not tell them in advance we were learning about surface area. I wanted to see if they could see past the filing cabinet and see that we are solving problems with surface area.

Act 1: The video

If you’re not familiar with this problem read about here or grab the full lesson on 101qs.com

Have a look at this solution….there is a 936 post it note answer in there somewhere!

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After we solved the problem I presented them with this slide

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Here are some of their responses.

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Our next step is Lesson Study! Every time we meet we will plan together an upcoming lesson for one teacher. Then we will all go and watch to see the student reactions and thinking during this lesson. This will be my first time going through this process and I’m pretty excited to plan a lesson with 4 other teachers. I am interested to go through this process to improve my teaching and improve student learning around the big ideas!

Error Analysis & Explain Everything

IMG_3146If you have read my previous posts(here, here, and here) on Explain Everything ….you’ll know  I love it, and know that I love it because it’s so versatile!

Last year I created/used a series of warm ups or openers or minds on activities (or any other name) in my Advanced Functions class that used iPads:

  1. Daily Desmos – Matching
  2. Sorting/Matching functions to equations activities in Explain Everything
  3. Whiteboard Share – Complete a problem in Explain Everything and AirPlay to Apple TV. Discuss.
  4. Complete a new problem in Explain Everything with a video Hint built in.
  5. Video Critique – Find the Error – Error Analysis.

This last one I want to discuss here.

That opener was a way for me to check homework ….really, a way for me to check understanding of the previous day’s work.

I used Explain Everything and created a file with videos of solutions with errors in them. Instructions were built in to the file that asked students to identify if the solution had an error or not, and if an error existed they were to record themselves fixing the error.

After using this for quick checks last year I decided to make it a full peer editing lesson this year in my Function class (3U).

Students grab the pre made EE file from a shared folder in Google Drive, watch videos of solutions to the previous day’s content, decide which, or if any have errors, then fix them. After recording their new solution right in the EE file they can play their new solution for the whole class to see via Apple TV or upload the EE file to our shared Google Drive folder for peers to download, view and critique.

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Since we are always exporting as an .xpl file students will import those same files and then be able to edit/critique (record) over top of the existing work.

It was awesome to see students recognize common mistakes and yell out “nope that’s wrong!” Or “I think that one’s OK”. It was equally great to see them watch eachothers “new” solutions and critique them the same way they critiqued mine.

Definitely a type of lesson I’ll repeat, probably on next review day.

Read more awesome ways to use EE.

Kyle Pearce’s —- Explain Everything Math Learning Journey 1 & 2

MathyCathy’s —- Hands On Digital Puzzles

Commit & Crumple!

Saw this activity in a book I picked up at the NCTM conference a few years back (Philadelphia).

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This book has been great for engaging activities in math….here is the one we did today:

Commit & Crumple
We are reviewing for our exam and I wanted to review average rates of change and instantaneous rates of change. I wanted to see what they remembered…and also how they remembered the graphical representation of rates of change.
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