Desmos Art: Fries

The Assignment

1.  Draw a design using only straight lines. 

2.  Snap a photo of your drawing. 

3.  Import your photo into Desmos. 

4.  See if you can duplicate your drawing using linear functions.  

Assessment

We looked for two things: challenge and precision. We got anything from a simple right triangle to a box of fries.  Anything with 3 or more lines intersecting at the same point proved to be very challenging; 2 lines fairly challenging; no intersections...not so much.  

Precision was key.  They could fool themselves as long as the grid, axes and labels were turned on.  But once those things went away, it was just lines drawn (with pencil or graphs) by students.  

I created a filter that contained the words "shared a graph with you" that dumped the graphs students emailed directly into a folder labeled "Desmos Art."  I used SnagIt to take screenshots and highlight areas of the graphs that needed feedback and sent the screenshots back to students.  It was a pretty nice workflow, actually.

Student Feedback

Most students noted that they started out thinking this assignment was really hard--that they couldn't do it. Then they got their first line to match. The second line was easier then the first; third easier than the second , and so on. Domain restrictions turned into range restrictions for vertical lines and some learned really quickly that it was easier to restrict the range for really steep lines.  

The perseverance I saw in students makes this one a keeper. 

I'm Bringing Multiple Choice Back

So here's the idea:

One problem with multiple paths to solution.  Students connect as many skills as they can to the problem.  I listed eight possible skills two of which wouldn't necessarily apply to the problem. Students had to assess themselves on the skills they demonstrated. 

Question of the day:  "Mr. Cox, is it possible to use all of these skills?"

Answer to Question of the day:  "It's possible that some of the skills don't apply."

For this first iteration, I used the standard Ticket Problem. 

Below are samples of student work. 

As an exercise for the reader:

1) What are your thoughts on this process?  

2) How did each student do?

Let me know in the comments. 

Student A

Student B

Student C

Student D

When Perseverance Pays Off

Our high schools are committed to taking the integrated path with the first three courses and since the middle schools will be teaching these courses, I'm part of the team building the units.  I've been piloting the curriculum by the folks from Utah and, for the most part, I like it.  I'm particularly enjoying the learning cycle they employ:  Develop Understanding, Solidify Understanding and Practice Understanding, mostly because it's pretty easy to discuss with the majority of teachers.

This task was at the beginning of a learning cycle.

Source: Mathematics Vision Project

I had a student, H,  come to me before class and say, "Mr. Cox, I spent like three hours on problem 3 last night.  I couldn't quite get it."

During class, students worked with their groups and started presenting solutions.  As I approach H's group, she gives a high-five to the student next to her.

Me: "What's that about?"

H: "We figured it out!  I get it now."  Then she shows me her solution.

"Feels nice, huh?"

"Yeah, I think I'm gonna cry."

Me too, H.  Me too.

The Student Rubric

We are currently working on a performance task where students have to gather data, apply a line of best fit, determine a rate and then make a prediction.  It's been a task to help students shift their thinking from right/wrong to more/less.  In other words, I don't want them to see their understanding as binary--I get it; I don't get it.  I want them to see their understanding as something that falls on a continuum.

When doing something like finding a line of best fit, I think it's less important to discuss what the line looks like and more important to discuss why a particular line is best. This leads us to the descriptors we've been using to discuss both sides of the same coin:

Concept and Precision

5: Strong concept; Precise

4: Strong concept; Somewhat precise

3: Problem with concept; Somewhat precise

2: Problem with concept; Lacks precision

1: No attempt

Through a few discussions with different classes, the top three descriptors have evolved into something like this.

5: Precise answer with precise method

4: Estimate backed by reason

3: Estimate

Then I walked by a student and noticed the self-assessment she was doing.

How's that for kid friendly?

CCSS 8: Unit Building

At the end of February, representatives from grade levels K-8 spent two days unpacking the CCSS and clustering them into units of study. My previous experience with unpacking standards became a process of identifying "essential" standards which assumed the existence of non-essential standards.  Those standards that didn't make the cut were ultimately ignored in favor of those that were most heavily tested essential.
We have the same provider leading these new sessions, so I was a little worried we would end up looking for content to cut rather than incorporate.  So far, that hasn't been the case.  Obviously, there are certain topics that will require more focus (eg. linear relationships as opposed to exponents) but the goal has been to see how and where these supporting standards fit with the focus standards.
Our team has come up with the following units of study.  We haven't reached the point where I can discuss specific activities/tasks, but I'd like some feedback on the pedagogy that motivated the clustering and sequencing.

Transformational Geometry

Use the coordinate plane to discuss transformations, congruence and similarity.  Use dilations as an application of the ratios/proportions work done in grades 6 and 7.  Use a graph as a tool to describe proportional relationships.

Data Analysis

Use bivariate data to create scatter plots which can then be the jumping off point for informal line of best fit (where the line may have an initial value other than zero) and an introduction for a future defining of function/non-function.

Linear Relationships

Graphing, graphing and more graphing.  Take the informal line-of-best-fit and formalize the definition.  Allow math to be it's own context.  Graph systems of equations and look for common point (read: solution to system).

Equations

Use the work done in graphing systems to motivate more abstract symbolic manipulation required for solving linear equations.

Exponents

This was a tough one.  Expressions with integer exponents and scientific notation seemed like an island unto themselves.  We are still working on finding a place that fits nicely for these ideas.

Functions

Use the informal introduction to functions and formally define a function.  Look at linear and non-linear functions.  Compare functions using different representations (ie. graph vs. table vs. equation vs. verbal).

Pythagorean Theorem

I think this one speaks for itself.

3D Geometry

Problem solving involving the volume of cones, cylinders and spheres.
We are trying to move from the concrete/informal to the abstract/formal while allowing students to explore these ideas while creating their own formal definitions.  I'm particularly interested in the sequence that runs from Data Analysis to Functions (note: Exponents look to be a unit that can be dropped in and our school calendar lends itself to having that unit kick off the second semester) as it may receive the most push-back from our high school colleagues.  Traditional textbooks usually go the route of
Functions-->Equations-->Graphing-->Applications so we're going to have to have solid rationale.
No one pushes back better than you all.  I'm counting on that.