Pumphrey's Math

Patterns, everywhere


2 Comments

Visual Patterns and Coding – Part 1 – Linear Relationships

Screen Shot 2015-11-30 at 12.18.45 PM.png

I have been running a ‘visual pattern’ every week with my 6th grade (pre-Algebra) classes. You can read more about this here.

To bridge the gap between pattern and function and following an online course I took with Rice University, I have started to introduce some basic coding. Python in particular. Even after one lesson of using coding and graphing, I have been able to have rich conversations about the differences between functions, input/outputs, the shape of a graph and the y-intercept. Here is the process I have taken them through:

Part 1: Have the students run through a basic (linear) visual pattern (from visualpatterns.org) using this sheet and reviewing using this slide:

Screen Shot 2015-11-30 at 12.03.09 PM.png

The nth term for this pattern is 4n+1.

Part 2: I now challenge them that we can create a calculator for this pattern using the Python coding language. I use the free python interface CodeSkulptor (from Rice University) to do this. I take them through step-by-step with some great conversations about functions and inputs/outputs.

The nice thing about CodeSkulptor is that when you hit the save button, it creates a brand new URL meaning that each student will have their own URL to post and share.

Screen Shot 2015-11-30 at 12.06.46 PM.png

They can then change the input and see clearly what happens to the output.

(Note: Lines with # are ignored by the interface)

Part 3: They then go to the Desmos Online Graphing Calculator and input the function y = 4x+1 to confirm or deny their prediction for the graph shape, from the start of the exercise. This is a great opportunity to talk about ‘step zero’ (as well as step -10 etc.) and why they graph is the shape that it is. I feel it is also important to stress the difference between 4n+1 as an nth term and y=4x+1 (which includes everything in between).

Screen Shot 2015-11-30 at 12.10.55 PM.png

Their homework is simply to follow the steps with a different (linear) visual pattern and to share their CodeSkulptor URL’s and Desmos screenshots on the class’ wiki page.

For student assistance I created this video:

Where Next?

There are two main places that I would like to take this:

  • Exponential functions
  • Inverse functions

I’m really excited about where this journey will take us. My hope is, that as these students start Algebra proper, next year, they will have a strong sense of functions graphs and their connections with patterns and geometry. Here goes…..

Have you done anything similar? I would love to hear your ideas/thoughts in the comments section, below.

 


Leave a comment

Gapminder is Awesome

photo (9)

I wanted something that would open up the world of scatterplots to my statistics students; something where they could really get a sense of correlation and causality. I decided to do a project based around the fantastic GapMinder World and it payed off.

First I showed this video of the master Hans Rosling at work with the graphs his foundation came up with.

I then gave these instructions to my students:

You (and max one other person) are to prepare a 3 minute presentation on a GapMinder graph of your choice.

Instructions:

  • On a computer go to the gapminder website by clicking here
  • Play around with the explanatory and response variables until you find two that you think show some sort of relationship
    • If you are struggling to find variables with a link, click ‘Open Graph Menu’ and play around with graphs that have already been created.
  • Your presentation must include answers to the following questions
    • What are your explanatory and response variables?
    • What is the link between variables at the start (before you click play)?
    • What do you notice happens over time?
    • Are all the countries close together or more spread out? What does this mean?
    • Are there changes to any particular country that are of interest to you?
    • What if you isolate by continent? Are there any changes that are of interest to you?
    • Is there anything else that stands out with your graph?
    • Are there any outliers to the trend?
    • Does this graph bring up any other questions that you would want to investigate further? What information would you need to answer these questions? Is this information available?

Your presentation must include the time series animation (when you press play) as well as PowerPoint slides using screen shots of points of interest.

You will be graded on:

  • Content (out of 6)
  • Presentation (out of 4)
What went well
  • This was a great way to get across a sense of scatter graphs and will be awesome to segway into taking about correlation and causality.
  • This was enjoyed by the students and really got them thinking about statistics and global affairs
  • It was good to give specific questions for the students to answer. In my experience just saying ‘present for 3 minutes on a graph of your choice does not give great results’
Even Better If

Next time I do this, I think it would be good to model what an excellent presentation looks like. I missed a good opportunity to teach this skill.


4 Comments

Desmos is Awesome

I love Desmos. I love how user-friendly and clean the whole thing is. I want my students to love it too, so I used the first lesson back after midterms to let them play.

The Aim

For my students to get a feel for the shape of various functions and relations through using Desmos to create a piece of art. (CC Standard F.BF.3)

The activity

  • Students take a look at http://www.desmos.com/art to see what is possible just by typing in equations (Great hook)
  • I explain to students that they have this lesson and a homework to come up with a piece of art of their own using desmos.com/calculator.
  • I have a sheet ready with some example functions (linear, quadratic, circular relations, radical and rational) for them to use if they are struggling. I also introduce the idea of sliders for them to use.
  • They have around 50 minutes plus a homework to come up with a piece of art of their own.

DesmosActivity

 

Some of the resultant artwork

Football FaceHalf Face

What went well

  • Any lesson where students are crying out for the Math is a good thing. It was amazing to be asked how to draw a smiley face using a parabola and domain and range and how to draw circles and ellipses. I had one student ask how to do a ‘diagonal porabola!’ I had to look that one up.
  • Students were constantly engaged. Sometimes frustrations got the better of them and they needed some encouragement to keep going but generally, the lesson went really fast.
  • It was great for all abilities. Students that normally struggle got the chance to play around with linear and quadratic functions, helping them to understand what changing the numbers did to the graph.

Even better if

  • This was too early in the year to do this lesson. I would like to do this next time at the end of the year when students had more functions and tools at their finger tips. I did like how it cemented the need for domain and range, though.
  • This lesson is leading into our quadratics unit. Going back I would have really liked to focus far more on parabolas so that our next lesson on Vertex Form would make sense from the start. I still think it will help, I just think I may have missed an opportunity to go deep rather than broad.
  • This lesson relies heavily on technology. Being a Bring-Your-Own-Device school, some students had tablets that were very tricky to use (this also happened with Khan Academy). I may have to rethink how I do this and use it possibly for homework.

Student Reaction

Here are results from a mini survey I did at the end of each class

DesmosSurvey1

Students also said:

This activity allowed me to visualize what adding variables does to the shape of an equation.

I loved the creativity involved with it, but also the brain work involved when trying to make different shapes and move them around.

Technical difficulties were frustrating, but I realize this is something that is hard to fix.