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:

 

Trashketball – A Spiralled Lesson!

This was our multi-day, curriculum-spiralled, activity this week!

Day 1 – Filling the Bin!!

Let’s get curious!!…..I showed this video from Andrew Stadel, and took questions & wonderings:


We settled, (I chose) on the question on how many paper balls would fill a bin! They made predictions, too high, too low and right on!

They made paper balls and found their diameter. We agreed that each ball could be different so we recorded everyone’s diameter and averaged them to give the “average ball size”

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Proportion Explosion

Since we are spiralling the curriculum in grade 9 applied, my math task choice is getting very picky! I always want to uncover more that one expectation in a lesson/task! In this task we used volume of spheres, solving proportions, and properties of linear relations.

Act 1:

We took questions and wonderings and then settled on the problem of Let’s see that balloon explode and when is that going to happen?
We guessed and recorded the guesses on our whiteboard for future comparisons!

Act 2: What will we need!

There were good conversations on this piece! I’m always surprised by how much kids know! Someone asked for the rate of water!!!! Wowsers! I assumed I might have to dig to get them to ask for that one. They also wanted me to say how much a balloon will hold…..which is where I wanted to direct them first.

Info to give and record:

As always, I made them guess for it! After revealing 12 inches….we converted to centimeters. Next it was their turn to go ahead and find the volume of the balloon. I find it so valuable to have discussions on why use a sphere to model the volume? Will we be correct? Is it ok we’re wrong?

Volume of the sphere/balloon

Act 2: Rate of Water

 
This is where the kids got lost a bit! They weren’t sure how to use this part exactly after just finding the volume of the balloon.  I stepped in and used some direct instruction on how to set up the proportion. Handout prepared:

Handout

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Solutions

Act 3: The reveal

The extension is how we practiced solving a few proportions. We solved for the volume when the time was 10 seconds, 20 seconds, until kids saw the pattern.

10 seconds

10 seconds

After filling the table out, we found the first differences, discussed direct vs. partial linear relations!

Grab all the files to run in your class:

Is Lego Gender Biased?

Here was how our conversation in math class (MFM1P) went…..How many pieces make up this Star wars Lego ship? Screen Shot 2015-02-23 at 3.28.54 PMWe started with that picture and had a great conversation around Lego.

Then I showed this one.

Does the pool/hot tub have more pieces/less pieces/ or the same? This turned into “boy” Lego vs. “girl” Lego. My personal opinion is its all great…. My 3 daughters are just as excited to play with Yoda as they are with Disney princesses. Girls in the class agreed that they didn’t need their own line of lego!!!

I moved our conversation a little forward with asking Which costs more? And which should cost more?

Screen Shot 2015-02-24 at 5.46.05 AMAnswers: Continue reading