## Tuesday, February 24, 2015

### Desmos in Elementary Mathematics

Background Information: Desmos is the next generation of the graphing calculator. Using our powerful and blazingly-fast math engine, the calculator can instantly plot any equation, from lines and parabolas up through derivatives and Fourier series. Data tables open up a world of curve-fitting and modeling. Sliders make it a breeze to demonstrate function transformations. As browser-based html5 technology, the graphing calculator works on any computer or tablet without requiring any downloads. It's intuitive, beautiful math. And best of all: it's completely free. (from

Our friends in secondary mathematics have recently begun (within the last year or so) using Desmos for graphing.  There's an app (of course!) and it's available on the web at Desmos.com.  Learners have enriched their math experience by diving into content beyond the scope of their own course out of sheer curiosity (ask the Algebra I educators at CMSN to share their experience with Desmos, or read about a dream from last May.)  And, take a look at this work by learners at CMSWest.

The ease of use of Desmos is unparalleled and the fact that you can log in with your Google account wins points in my book!  Unfortunately, my searches for upper elementary resources with Desmos have come back empty.  The embedded educator support, https://teacher.desmos.com, includes secondary activities (great for them, not for educators looking to expose learners to plotting (0,0), for example).  I even searched some of the best of the best in the MathTwitterBlogoSphere for elementary (below) and reached out to my PLN via Twitter, to no avail.

I am convinced that learners in grade 5 can use Desmos and can explore graphing on this platform even though so many resources out there are created for secondary.  So, I made this example on Desmos:

Learners may go to Desmos.com and start from scratch, or their educator could send them a template (similar to the one above) as a starting point.  During an authentic mathematics exploration of gathering data, for example, learners could plot the points and explore the relationship.

According to the Revised (2012) Math TEKS, learners in grade 5:
• describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin (5.8A);
• describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane (5.8B); and
• graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table (5.8C).

Where does graphing in grade 5 in the vertical alignment of this topic?

Previously, in grade 4, the students are expected to represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. (4.3G)

This may look something like this...

Of course, this should be in the context of authentic mathematics.  Check out this task from Yummy Math (Legos).

Graphing on the coordinate plane extends into grade 6 when (6.11A) the student is expected to graph points in all four quadrants using ordered pairs of rational numbers.

Check out this task from Yummy Math (Cost of a Gallon of Gas) or this from Mathalicious (Sweet Tooth).  ***The Sweet Tooth lesson has an embedded Desmos (see below)!

Later, in grade 8, students represent dilations (with scale factor) on the coordinate plane and apply transformational geometry and the coordinate plane (translations, reflections, and rotations).

I recommend that you explore Graphing Stories, especially those tagged as linear or constant (on the drop down menu at the top).  All of these tasks yield a real life graph, in the first quadrant.

Also, don't forget that we have already seen graphing as part of 5.4C and 5.4D when the students were asked to (C) generate a numerical pattern when given a rule in the form ax or a and graph; and (D)  recognize the difference between additive and multiplicative numerical patterns given in a table or graph.

When your learners were graphing in the previous unit on Expressions and Equations, were they limited to whole numbers?

Please let me know if you are interested in (or are already) embedding Desmos into your mathematics lessons.  I'd love to hear about it!