engagement

Instantaneously Awesome!

by Jon Orr

So check this out!
Our lesson in Advanced Functions is “I should be able to determine the instantaneous rate of change of a function at a particular instant.”

Here’s what went down….

We began by grabbing an Explain Everything file from our Google Drive.

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We watched Dan run!
After watching his run I asked… “Draw a prediction in the file of his Elevation Vs. time”

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We used AppleTV to share our graphs…..brave students shot their graph up for display and for everyone to judge! Students were asked to support their prediction.

We then moved to the next slide….. And saw a Desmos graph of mimicking most of the student predictions.

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Students were then asked to use the secant line on the desmos graph to:
1. Find the average rate of change between 2 seconds and 10 seconds.
2. Estimate the instantaneous rate at exactly 2 seconds….by manipulating the points.

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After a consensus on what everyone thought was the instantaneous rate…and a discussion on what that means….we moved to the next slide to verify our result by looking at the tangent line at 2 seconds.

Lastly, we verified those results by calculating the instantaneous rate at 2 seconds using algebra!

Overall it was a pretty we’ll received lesson!
Any thoughts/feedback?

Sorting Out Explain Everything

by Jon Orr

There are lots of great things in Math being done with the app Explain Everything! Explain Everything has been the go-to app of choice for many teachers, students to showcase learning and understanding.
Students in my class have used this app to explain major concepts from the course. For example, a student used the app to create a video on the differences between Direct and Partial variation.

The app can be used for other great uses besides video recording…

I have been using the app to create short Sorting activities.

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 Click the picture and download the Explain Everything .xpl file.

 

The white space in the app allows users to easily move, rotate, and sort images on the screen. In the example above, as a warm up my students were asked to sort the solution to the equation in the correct order. We then had discussions on steps to solve equations.

Below is another sorting activity on sorting out linear relations. They were asked to match up tables, graphs, equations, and descriptions.

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 Click the picture and download the Explain Everything .xpl file.

 

Another sorting activity: For MPM2D or MCF3M or MCR3U – Sorting the Quadratic Formula. Students were asked to sort out solutions to solving equations by completing the square. After sorting a number of solutions, they were asked to sort the general development of the Quadratic Formula.

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 Click the picture and download the Explain Everything .xpl file

 

With Explain Everything’ ease to make how to videos, and sorting activities…..it’s a must have on your iPads.

Vroom

by Jon Orr

Thanks to Fawn Nguyen for this lesson idea. Her original blog post on this lesson is here. I did this lesson with my Grade 9 applied class and it went over great!!

 

Watch the video

What did you wonder? ….. How much the car was pulled back to make it go 117 inches?

Here’s what we did to help answer that.

Everybody got a car.

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Then we set up tape measures on the ground….

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We made trial runs with out cars and recorded our results on a handout.

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We graphed our data in Desmos and fitted a function to model.

Use the following pre-made Desmos page… https://www.desmos.com/calculator/f6pjwnqhux

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Students had to interpolate the data to estimate how far to pull the car back to make it go 117 inches.

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Angry Birds – Parabolas

by Jon Orr

[UPDATED – Sept. 25 2015]

We have just spent a week working with quadratics in MPM2D and today I had students create their own angry birds level.

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The only real requirement was for them to create at least two flight paths and model them with quadratic equations.

I was hoping to see how they relate the equation to the graph. This worked out better than expected. Most students did not initially make their curves symmetric…..and that gave us a chance to discuss symmetry and these questions

  • Where would the zeros be?
  • Where is your vertex? Where are the zeros in relation to your vertex?
  • What could the equation be then?

Most students started creating their flight paths with placing the zeros on the graph….then picking a vertex. The best part of the day was discussing how students knew where their vertex was.

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Most knew that the axis of symmetry had to be half way between the zeros and also knew the vertex was on the axis. The issues, and then real thinking came when they went to create the equation to match. For example if Alexis wanted her bird to take off from x = 0 and land when x = 24 …she also wanted her highest height to be 7.5 units high. She wrote the equation y = – (x)(x – 24) and assumed she was correct. This assumption gave us lots to discuss!

I asked her to show me how she knew the vertex is (12,7.5) and she had a hard time. “I knew the x value was 12 but I just picked that height”. So I asked her to use the equation and find which height does go with an x value of 12. She did and then we graphed….
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Something clicked in her….”Aaah! The a-value must not just be -1″ and then that led us into discussing what the a-value should be and how we can get it more accurately! We did this…

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I loved that we discovered and struggled to find the correct a-value instead of me just giving an example and them copying.

I floated from group to group having similar conversations. Some students created their equations first and then found the vertex from the equation and plotted that.

Extensions

Some students started to ask if they could use different birds!!

  • The blue bird once tapped would split off and create three more birds with three new flight paths.
  • The yellow bird once tapped we assumed would make a straight line with a linear equation.

Pictures are from 2010….new pictures coming!!!

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