Desmos, Dilations & The Vertical Classroom

This is a story about a

  • Desmos Activity Builder that flopped
  • The changes that transformed it into a successful activity

1st time teaching the lesson:  Mrs. Paine’s room

I’m excited to test out the Desmos Activity Builder on Dilations with students.  The lesson started off good, students were engaged and then the activity fell flat.  In between classes, I’d go back into the activity builder and make adjustments. None of the little adjustments worked. Since I was only scheduled to be in Mrs.Paine’s room for 1 day, the opportunity to clarify misconceptions didn’t exist.  I felt a bit defeated. 😦

2nd  time teaching the lesson: Mr. Peterson’s room

I’m grateful for the opportunity to redeem myself and the activity.  I reworked the activity’s organization.  Again, it started off good, then fell flat. UGH!  During the last class of the day, a student began submitting off topic responses. When this issue was addressed, he shouted, “I hate computers.  Math is NOT supposed to be done on computers!”

My initial reaction was, “Did he just dis Desmos?”

Teaching rule #37:  Don’t take student comments personally (especially when said in frustration) but do listen to them. Seth had a point. The lesson was too computer heavy.  Desmos was not the right medium for the given line of questioning.

Thankful for the follow up day, I completely changed the next day’s lesson and emailed Mr. P the plan. It was time to combine the Activity Builder with his vertical classroom set up.  In the new format, Desmos would play a supporting role to the work completed on the vertical white boards.

The Desmos/Vertical Classroom format was a success.  Students were engaged, their attitudes were positive and learning increased 200% from the previous day. And Seth – He was a happy and active participant.

Here’s how it flowed …


Desmos Dilations Activity Builder

Combined w/ Vertical White Boards.

Slides 1- 6:  These slides help students understand how to move the triangles and measure an angle.  Vocabulary such as, pre-image, image, dilation, similar was introduced.

Day 1 Mr. Peterson:  On the first day, It took roughly 15 minutes to discuss the information contained in slides 1 – 6.  Since the rest of the lesson flopped, I restructured the activity builder.  The problem slides were scrapped 🙂

Slide 8  Starting off day 2, we separated students into groups and positioned them by a vertical white board.

  1. One team member moved the black dots to create a unique triangleScreen Shot 2016-02-18 at 8.11.49 PM.png.
  2. The team picked a value for k that’s greater than 1 and recorded it on their white board.  At first, k was labeled d for dilation.  But since the dilation represents the constant of proportionality, I changed the d to k within the activity builder.  That changed occurred after the pictures were taken.
  3. Teams were required to recreate the pre-image and image/dilation on their white board.


Slide 9:  Label all parts of the diagram.   This required students to

  • Read the left side of slide 8
  • Understand the left side of slide 8
  • Label appropriately
  • Use the measuring tool to find the angles measures.

Screen Shot 2016-02-18 at 8.52.55 PM


Screen Shot 2016-02-18 at 8.57.24 PM

Left side of slide 8

Slide 10:  Write 3 ratios in the form Dilated side/Pre-image side.  Then simplify.

Screen Shot 2016-02-18 at 8.18.47 PMScreen Shot 2016-02-18 at 8.21.44 PM.png

Slide 11:  This slide connects their data to the direct variation equation, y = kx.

  1. Fill out the x/y charts based on your ratios.
  2.  Use the red line to help you determine the equation that represents your data (see activity builder)
  3.  Enter the equation that represents your data.  Write the equation on your white board.

Screen Shot 2016-02-18 at 8.45.31 PM.png

Extension of Slide 11/Slide 12:  Turn the equation into a sentence


Slide 13 – 17:  Repeat the process outlined in slides 8 – 12 but with k representing a number less than 1.  Students were independent throughout these slides allowing Mr. Peterson and me to spend a considerable amount of time checking for understanding.

Closing Thoughts

One of the many aspects of a teacher’s job is to create and guide students through lessons. If the initial lesson plan isn’t making the desired impact, teachers hold the power to alter the plan.  Teachers reflect and fine-tune throughout the day, therefore building their capacity to quickly assess student learning and change course when necessary.

The bottom line regarding the Dilations Activity Builder:  All the students (in both classes) began to lose interest around the same slide, regardless of the little adjustments made in between classes.

Why?  A couple of slides required students to analyze their pre-image and dilation and then submit responses.  The slides were packed with information.  Too much information for a single student to analyze.  Students were not making the desired mathematical connections.

They needed to work with the information, make it tangible – draw, label and discuss. Once the investigation involved physically creating and labeling diagrams on the vertical white boards, not only did students easily worked through the questions but also their understanding of dilations increased.

Could students have drawn and labeled the images on paper?  Yes, but I don’t believe it’s the best medium. The freedom to draw on a big space where one can stand back to scan all the pieces is undeniably more appealing to students. They worked with Desmos and the vertical white boards fluidly.  With this format, I observed students’ independence shine. They were owning their learning.


Other posts in the Vertical Classroom series


A link to all my Desmos related posts & Desmos Activities



About jgvadnais

Instructional Technology Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee creamer
This entry was posted in desmos, Math Education, proportional reasoning, Uncategorized, vertical classroom, vnps, white boards and tagged , , , , , , , , , . Bookmark the permalink.

4 Responses to Desmos, Dilations & The Vertical Classroom

  1. Laura Jenkins says:

    I love this blog. I’m also considering being instructional coach. Do you have a Twitter?


  2. Pingback: The Vertical Classroom Project Begins | Communicating Mathematically

  3. Pingback: Global Math: Of Problems and Strings / Global Math Department

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