Logarithmic Warm Up

Our goal in Advanced Functions today was to graph y = log(x) and transformations of y = log(x). Here was what we did as a warm up/minds-on. Everyone started with a whiteboard and a device of some sort (SmartScreen Shot 2014-12-08 at 2.16.38 PMphones, iPads, tablets—I have access to a set of iPads for anyone without a device. This class being a grade 12 class….just about everyone has their own device).

I had them log into a PearDeck file I created.

I gave everyone in my class a number. Some got integers 1-20 and some got fractions 1/4 through 1.

My instructions:

1. Take your number, n, and find log(n). Write your number and log(n) as an ordered pair! (n, log(n))

I started the PearDeck presentation which showed them this slide……and gave them all a movable point.

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2. Move your point to the location of the ordered pair you have! So my students started moving their points around and on the projector screen we can see everyone’s points all at once in real time! So we are basically watching the creation of y = log(x).

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Sorry for the poor quality of pic…it was on the fly

You could see the looks on their faces as the graph was being created….pretty cool

From here we took a note on the properties of the function….then kept using PearDeck to analyze transformations of y = log(x). We saw Graphs then –> wrote equations and then saw equations –> drew graphs. We could do everything right in PearDeck so we could see all of our answers all of the time! PearDeck works through your Google account…..give it a try!

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Projects from 2013-2014, iTunesU, iBooks

I feel like since I started using Twitter for Pd and following the #MTBos my learning curve has been steep! As a result, when I look back at resources I have created I find myself wishing that I had done it “this way” or “that way” or used a different task here or there.
This is no problem for creating lessons, activities, tasks to use with MY students because I can always modify, change, manipulate!
My regrets show up when I’m involved in a project that gets published or shared out beyond my reach and afterwards my thinking has changed by seeing a great blog post, or a new activity, or by just having a discussion with a colleague. I wish I had all the time in the world to keep everything “up to date”

Our blogs, Google Drive Folders, Dropboxes are easily update-able and where are current lessons are!

Here are a few of those projects that I hit publish and find it hard to keep up to date: Each of these has lots of stuff I’m proud of, and some stuff I wish I could find the time to “update”

ITunesU Course – MPM1D (created April 2014)
Last spring I created an iTunesU course for my school board (Lambton-Kent).
Purpose: To share some digital resources I have used, or, are using in my grade 9 Principles of mathematics course.

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https://itunes.apple.com/ca/course/principles-mathematics-public/id946920145

iBook – Measurement (created July 2014)

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Whatcha Thinking – independent use of 3 Act Math Tasks for MFM1P

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iBook – Linear Relations (created July 2013)

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Popcorn Pandemonium

My afternoon grade 9 applied class (as a group) is very outspoken, loud, and restless (maybe it’s because it’s the afternoon and they have been sitting at desks all day). They have been a challenge to keep on task. So….I  am trying to find opportunities for them to be outspoken, loud, and restless.

A few weeks ago I came across this post by John Berray. Using/eating marshmallows to compare rates of change. I loved his idea of “experiencing rate of change” I decided to re-purpose his lesson to meet our goal of—> “I can solve a linear systems of equations by graphing.” I also took his recommendation of using popcorn instead of marshmallows…..and it paid off!!

Here is the low down…. we start the “Math Dial” off low.

ME: OK you are going to have a good o’ fashion popcorn eating contest!

Start with this video:



Ask for questions:

Here are a few from math tweeps

here are a few questions we can address with this problem.

  • When will Tim and Don eat the same amount as Jon?
  • Who will eat the most when the minute is up?
  • Will there be a time when Tim and Don eat the exact same amount?
  • When would Don eat more than Tim?

ME: Ok lets figure out who will eat the most in the 1 minute. But I want to recreate the video with you guys.

So I made a giant bowl of popcorn. (Don’t have time to make enough popcorn? — have kids give high fives to a timer instead)

Arrange groups of 2 or 3 and everybody grabbed some popcorn to start!

Round 1:

In each group kids are to choose who to mimic, Jon, Tim, or Don. They are to eat just like them! Allow them to ask about how fast each person is eating….or how much did each start with, etc.

Show Act 2 to answer those questions:


Tell them to get their timers ready….because they will eat just like one of those guys. Ready…..all you Tims and Jons eat your starting amount … Set….Go!

Start the timers and eat!

Question 1:
After they are finished, have them work out on their whiteboards who would eat the most in a minute.

Question 2:
When would Tim & Don eat the same as Jon if ever? (Great potential here for integer solutions talk).

Question 3:
During the minute, at anytime did Tim and Don eat the same?

If there was no time limit find when Tim & Don would eat the same?

Used this handout so they could create tables of values. Had them graph in Desmos!

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The awesome thing was that my students were desperately trying to find the equations to match their graphs….they didn’t want to plot all the points. I visited each group helping them find the equations if needed. Once the equations were in desmos they knew where to look.

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Act 3 – The reveal of who ate the most in a minute
 


Round 2: Do it all over again with new eating patterns!
Here are two possible eating pattern cards to give out:

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Students who finished early worked on our Crazy Taxi  vs. a new Insane Cab

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(@mathletepearce has a nice write up on using the Crazy taxi problem in class.)

Next day! Solving Multi-step equations…..will solve this systems of equations algebraically.