In this blog post you will find a recording of my presentation from the CMC South 2020 virtual conference as well as my slides that includes links to all of the resources. This blog post will be updated with a link to the article I wrote summarizing this presentation in the March 2021 issue of the CMC Communicator.

Here is a link to my 50 minute Loom video asynchronous digital presentation of the ideas from the slides.

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As some of you know I teach 4 Math 8 classes (using the Desmos Middle School Math curriculum inspired by IM/Open Up) and 1 Math “Elective” with a majority of one of my Math 8 classes mixed with some 7th and 8th graders who are in RSP Math. I’ve previously blogged about how I taught students how to play the card game SET with an amazing activity made by Greta.

We’ve also explored some engaging topics using Jenna Laib’s SlowRevealGraphs.com.

We have also done one collaboration with a local 5th grade class on Zoom where we investigated Fraction Talks, one of my favorite activities that I’ve blogged about before.

I couldn’t resist digging into some of the Math 7 curriculum with mt elective. This blog post is to share about some of the lessons.

Lesson 2 is Scaling Robots. This one is awesome. Students warm up by creating their own robot face by dragging sliders that control height, width, eye distance, and the antenna. Here’s what they came up with:

Then students are given a table with their robot measurements and are asked to create a scaled copy giving a height that is double their robot’s height for the “Copy Robot.” Then it offers some visual feedback so students self-assess how they did. Slick. Students then analyze a table of a student’s work and answers if they made a scaled copy. After they adjust the values to fix it and make a scaled copy. We laughed at a students work that used a scale factor of 1000, making the copy impossible to see, but they could still see the green checkmark positive feedback. Another slick screen is another common Desmos strategy: pick the parameters you want to change to plan how you will fix a scaled copy, and then execute your plan. It was really cool to take snapshots of all of the different solution pathways. Loved it.

Lesson 3 is “Make it Scale.” This lesson inspired me to figure out how to make animated GIFs of the activity. In short, I used Loom to capture a portion of the screen and then I used ezgif.com to take that MP4 and convert it.

The activity starts with an awesome Which One Doesn’t Belong prompt. Then students select a rose, whale, diamond, or bee to sketch a scaled copy of. I like how the color selecter on this next screen then limits the color options to only the colors necessary. At first they sketch it without a grid, and we discuss the strategies they used. Then they are given a grid and of course accuracy increases a bunch.

After that they make a sketch of a trapezoid but get to select their scale factor with a slider. Really cool built-in differentiation. In my 8th grade class I also encourage this differentiation. One example is when students dilate a shape and select the scale factor that suits their level of understanding. If you feel you haven’t mastered it, do a scale factor of 2. If you can handle more, try 1/2 or another fraction. If you want a bigger challenge try 1.5.

I have taught the 7th grade Open Up Curriculum a few years back and it’s cool that they have still included some of the same cool-downs.

In lesson 4 students do Scale Factor Challenges where they get feedback on how to undo a dilation or go in reverse. They also sketch and get feedback on how their sketch scales.

Lesson 5 is Tiles where they again personalize their learning by picking the colors and placement of them on a mosaic that they then scale. The goal of this lesson is for students to see that when you use a scale factor, the area gets multiplied by the scale factor twice, or the scale factor squared.

In lesson 6 students are introduced to scale. One cool part is in the warm-up students calibrate their screen by holding up a ruler to a caterpillar that is 4 centimeters long and adjusting a slider. Nice touch. Students scroll through different small and large shapes and make the connection between scale factor being how many times bigger a shape is than another shape while scale compares a real life measurement to a grid square.

I did this because the last lesson of Unit 1 was Scaling Buildings and knew I would need a full 80 minute period to get the most out of it. This lesson is really thought out well. I love it. It starts with a scale drawing of the Arc de Triomphe in France that is 50 meters tall. It’s on a grid, and students are asked to find the scale, or the value in meters of one unit. Really great lead up. The illustrations of famous buildings in this activity is amazing. Students were able to give input on ones they knew about and it even motivated me to Google some of them for real photos in real life. Some students are able to guess and check some of the answers because they use a slider to adjust the height of the building after given a scale drawing on the left.

I am thoroughly enjoying digging into the Grade 7 curriculum, the Desmos team has put a lot of thought, effort, and ingenuity into it.

This lesson is where students start to develop their definition of congruence. It starts out with the similar warm-up from the original Open Up lesson where students select all of the left hands. Then they are shown pairs of figures and must select all the pairs that are the same. Then in teacher view I looked at which were the most popular and like the lesson plan suggests hear arguments for why they are or aren’t the same for each pair. This shows the need for a more precise word or definition of “the same.” It leads to the definition that two figures are congruent if you they can be lined up after a sequence of rigid transformations. I then asked students, “what can be different about two congruent figures?” They came up with location (which can be fixed with a translation) and orientation (which can be fixed with a reflection or rotation).

On the next screen students take a closer look at pair B to say what is and is not the same about it. Students figure that they are the same shape, same angles, but are not the exact same size.

In activity 2 students look at six polyominoes. Again, they are asked what is the same and what is different about them. Students said they had the same area, but the square that is sticking out is not always in the same place as the others.

Then students are asked to select all of the polyominoes congruent to A. I could see on my summary view a check mark for those that had all of them clicked. Then to review the requirements for congruence we worked together to give all the details necessary to write a sequence of rigid transformations to make them line up. Students need practice including the center of rotation.

The lesson is synthesized by referring back to the pairs of shapes in activity 1 and asking, “How can you determine if two shapes are congruent?” Some students sketched C on the shapes that were congruent and NC on the shapes that were not congruent. I pointed out students who mentioned that you could use rigid transformations to line them up, and if you could do that, all of the other requirements would be true like the same shape, area, side lengths, and angles.

The cool-down asked students to see if two ovals were congruent. They were slightly different and they needed to measure and compare using the sketch tool to see this. It’s a great lesson and I like how they used polyominoes.

So far, this is one of my favorite lessons from Unit 1. It really works on challenging students to precisely describe a sequence of rigid transformations. I have read the first few chapters of Amanda Jansen’s Rough Draft Math (thanks Open Up Resources for the free copy for attending the amazing HIVE conference) in that I asked students to write a rough draft and then together combine our ideas into a more polished draft. I did this by taking snapshots and then annotating the graphs and adding more text. It was also my way of using the MLR Stronger, Clearer, Each Time. In an ideal world I would have done breakout rooms for students to share and revise in but we did it whole class instead. Goals for the future!

On the warm-up students are asked to move the moveable point to the center of rotation and describe the rotation. These interactive screens are really cool. It allows for some guess and check and allows students to articulate how they figured it out. I pointed out a student that said, “I put the dot on 2,1” to show that not only did they find the center but they reported the coordinates, and reminded them to write it with parentheses around it. Sometimes the self checking practice problems screens mark it wrong if they don’t put parentheses and it is an important convention. I pointed out a student who correctly said 90 degrees, and finally ended with a student who mentioned 90 degrees and the direction, counterclockwise.

On the next screen they had to describe this sequence. As you can see below, I took a snapshot of a student who correctly sketched the triangle ABC reflected. I also recognized that the person didn’t just say move the shape, they said reflect it and the translate it. I then prompted the class to say what further details must we provide for a reflection? A student said the x axis. So I drew that horizontal line and labeled it x. They said they knew that because the x coordinates did not change and it all lined up. I then said how can we be more specific for the translation? They then said you should say 7 units to the right and I showed how I counted the grid squares with the dots. I then set a timer for 1 minute for students to do their second draft of their sequence.

While the sequence below was a little more complex, I did want to honor it in that it was also a correct method. This conversation involved talking about labeling the center of rotation with a letter and mentioning it in the sequence as well as labeling it on the graph. Again, while they did draw their line of reflection, I mentioned that it’s good to once again label it on the graph and mention it in the sequence.

Here is the next sequence students had to work on. I honored an uncommon approach before reviewing the most common approach.

To synthesize describing sequences, we went over the requirements for each transformation. As you can see, the approach below was rotating 90 degrees clockwise around the origin, and then reflecting. Eventually these ideas will be integrated into a unit anchor chart they can refer to.

On screen 4 students are shown a diamond preimage and image. The student Amari says it’s a reflection and students have to agree Yes or No and justify. Most students said no, because the corresponding points were in the incorrect place. They said they were in the correct place if it was a reflection.

On screen 5, students move the 4 points of a quadrilateral to show a 180 degree rotation around the origin. Students had a tough time articulating how they correctly placed the points. I tried to watch my teacher view and take snap shots of students that were reflecting over one axis, then the other to aid in their explanations. I wanted to reinforce that although it’s challenging to visualize, we can think of this type of rotation as a reflection over each axis.

Then came my favorite screen, the Class Gallery. Students were to create a challenge and then solve each others. It’s really cool to see students motivated to solve problems that their classmates create. Julie Reulbach wrote a blog post that has a link to an activity collection that has activities with this Class Gallery feature. It’s literally one of the coolest Desmos features.

As I suggested in this tweet, my goal was to create a Flipgrid prompt so that students would record themselves creating their own challenge and solving one of their classmates. I recorded myself using the website Loom demonstrating how to do a screencast recording using Flipgrid. I encouraged students that the goal of the project was to verbally explain how you knew where to place the transformed points in your challenge and how you knew how to solve someone else’s. No pun intended, but this was a real challenge. I’d love to share some of the examples but the videos use their real names, but I can at least show you the prompt I used to attach to the Flipgrid prompt and it gives you a sneak peek into the activity:

The lesson synthesis is so simple but so complex at the same time: “What information do you need to precisely describe a transformation?” This allowed me to snapshot students who could contribute some of the requirements for each transformation that I went over earlier in the blog post.

The cooldown gives a sketch screen where students translate point A, and give the coordinates of the image. Then they reflect A over an axis and rotate 180 degrees using the origin and give the coordinates of the image for both.

Like I said, this was one of my favorite lessons of Unit 1 so far. By asking students to create the flipgrid, it helped build community because they could watch each others and listen to each other’s voices. I was also able to post a link to a successful students video as an example of someone meeting the expectations. I also got to use the Google classroom private comment feedback feature to give students comments if their audio didn’t work or any other technical difficulties. I love activities with the Class Gallery. And I also love asking students to record a Flipgrid because it makes me feel more like a teacher and it feels more like a community during distance learning.

In this lesson students apply transformations to points on a grid if they know their coordinates. It starts up with a warm-up where a shape on the left is reflected over a vertical line. Students are asked to place the corresponding points correctly on the shape on the right. The main stumbling block is students placing the points as if it was a translation, and us discussing why the points have to be on the opposite side.

Then students reflect a triangle across a vertical line with no grid, and then with a grid. Then they get a graph overlay to show what they notice about the reflections. As you can see I used the Zoom annotation features to point out the interesting mistake someone made with the grid, clearly misinterpreting where the y axis is and students said the person reflected over the x axis.

I wish on this screen or after this screen there was a chance for students to explain exactly how the grid helped them place the accurate reflection, outlined in green, correctly. Before talking about coordinates, I wanted students to articulate that it helped because you could count how many units the triangle was from the y axis and put it that same distance away on the other side of the axis. I feel the lesson jumped a bit too quickly then to then analyzing what was happening to the coordinates in a reflection on the screen below.

This lesson was definitely inspired by the activity Blue Point Rule where users drag around a point that gets transformed instantly.

In my first class students were rusty with plotting points in the coordinate plane and I did not start my school year with Polygraph Points and reteaching the coordinate plane which showed. The picture above is from one of my later classes.

I annotated how the coordinates of the red pre-image were (4,3). I explicitly stated and typed that 4 is the x coordinate and 3 is the y coordinate. I tried using some #purposefulcolor to show that that 4 comes from 4 spaces to the right of the origin on the x axis and the 3 being 3 units above the origin on the y axis and that point being where they crossed.

Many students did not mention which coordinate stayed the same and some said “it turned negative.” So, I made sure to drag the pre-image to the left side of the y axis to point out that look, now it’s not turning negative… so how else can we describe this? This pushed students to revise and say the x coordinate becomes the opposite while the y coordinate stays the same.

Actually, instead of rephrasing what they said, I’ll pull some direct quotes from my snapshots tab:

“The black point is the opposite of the positive point”

“you keep the same y coordinate, however change the x coordinate to be either a negative or positive number”

“If the original coordinate is (4,2) then the opposite coordinate would be (-4,2). So every opposite coordinate has a negative sign.”

“The Y coordinate stays the same, but if the x axis is negative, make it positive and if it is positive, make it negative.”

Then students apply the rule to reflect a triangle across the y axis. I love that they made it a triangle that overlaps the y axis to make it more challenging.

Then students investigate a translation by dragging a point around. Here’s some responses I highlighted:

“It moves down 3 units and left 4 units.”

“When the red goes to 0,0, the black dot goes to -4, -3. The difference from the red to the black is four across, three down.”

I definitely pointed out this students strategy where they moved the red point to the origin and the coordinates of the translated point really show how the transformation occurred.

They apply this translation to a different triangle and then move on to the most challenging transformation, a 90 degrees counterclockwise rotation around (0,0). Once again, I would like there to be a chance to honor their intuition in how to do this, like turning their head sideways to visualize it, before jumping straight to how the coordinates are effected. I have also had conversations with one of the assessment writers of the IM 6-8 curriculum, Bowen Kerins, about interpreting how deep the standard is here. I recall him saying that they don’t have to memorize a rule but to notice what happens to the coordinates during these transformations.

Here’s what students said about the rotation’s effect on the coordinates:

“numbers would be switched and one of the numbers would be a negative”

“switch x,y place and y is opposite”

“If the red image’s x-axis is 2 and the y-axis is 8, the black image’s x-axis will be the 8 and the y-axis would be 2. In other words, they would be switched.”

After applying the rotation to another triangle, the Lesson Synthesis screen arrives. I like that once again it provides three choices to respond to which allows for a wide ranging discussion. They select either a Rotation 180º clockwise around (0, 0), Reflection across the x-axis, or a Translation right 3 units and up 5 units. After clicking their choice they get a point that reacts to the transformation like the earlier screens and they need to describe what happens to the coordinates. For the reflection Kent said, “the y is the same number but the x is going negative so the number turns negative.” For the translation Liv said, “add 3 to the coordinate on the x axis then, add 5 to the coordinate on the y axis.” For the rotation Charlotte said, “The coordinates are corresponding by switched negatives and positives. the two coordinates move like a straight line, but have different numbers. Examples are if the red coordinates say -7,6 the black coordinate is 7,-6.”

The cool-down is a triangle in the first quadrant with its vertices labeled as the preimage and the image drawn as a reflection using the x axis. There is no grid so they really need to know what’s happening to the coordinates. Students are asked to label the coordinates. I watched my teacher view to remind students to put parentheses around their coordinates with a comma in the middle. Some students did some bizarre things here like making both coordinates negative or putting the coordinates in the wrong place as if they were a translation.

This was a challenging lesson for students and this is the point in the unit where I started making screen recordings reviewing the practice problems to answer questions and to encourage students to correct it after trying it independently.

For this lesson it was supposed to be a paper lesson. Luckily Desmos created a Facebook group for those teachers piloting the curriculum and I asked if anyone had digitized the lesson. One person replied and I used her activity. Thanks Mrs. De La Fuente!

In this lesson students started with a warmup where they noticed and wondered about a square grid compared to an isometric grid. This really needs to be done with paper because when you do this warm-up with the Open Up Resources workbooks students start seeing many different shapes in the isometric grid which provides a rich conversation. The goal either way is to get students to realize that they are all equilateral triangles which means their angles are all 60 degrees each which is crucial to understanding rotations on an isometric grid.

On the next screen students watch an animation of a reflection and are asked to think what the prime (‘) means in terms of transformations. Students think it’s the result of a reflection. I had to clarify that it doesn’t necessarily mean it’s a reflection, it means it could be any type of transformation and is the corresponding point. They were introduced to corresponding sides and points in 7th grade.

In the next activity they are asked to sketch a translation before clicking a button that animates it to check their answer. It was important to keep an eye on teacher view to snapshot students that drew the lines or students that drew the corresponding points first, highlighting 2 ways of approaching it.

Doing a rotation digitally without tracing paper is a tough task! I really miss this from in person learning. A 180 degree rotation can be hard. It’s also important to point out that it’s not the same as a single reflection. I tried to get students to articulate how they can rotate one point and then visualize where the other nearby points are in relation to it.

Then they had to do a reflection over a diagonal line of reflection on an isometric grid and reflect if it was easier or harder than the rotation. Finally they did a 60 degree rotation on isometric grid paper which wa the purpose of the warm-up. The lesson synthesis asked students to think about how grids helped them perform each of the transformations. It was a short lesson so we were able to start on some of the practice problems together after that.

Transformation Golf is an activity that has been available since 2017 (I know because I created a class code back then) for free and is integrated into the Desbook Grade 8 curriculum. The activity’s warm-up has students play an animation and describe the sequence of translations. Students shared first that said “slid” then students that said the direction followed with students that said translated with the direction and correct units. I confirmed their answer using the Zoom annotation tool.

Then students complete the first 3 challenges. I paced students to do this screen by screen. There is no snapshot feature for this so it’s handy to have paper and pencil to write down whose work you want to share first, second, and so on (5 practices). The teacher view shows me a green check mark for those that solved it. I started with students who used more steps. I asked students to read off their sequence of transformations as I pressed play when sharing my screen of their sequence. This got students used to saying the names of the transformations as well as how many degrees and what direction their rotations are which are challenging details for some students.

Screen 4 is where it starts to get interesting and more challenging. Similar to the design of Marbleslides, students are asked to sketch a plan before being allowed to use the transformation tools. This forces students to think more about the requirements of their sequence. It also then lets them execute their plan on the next screen after I had a few students share out.

I decided to share this sequence of 2 reflections and a translate first because their sketch made it easy to follow. Then I followed with the student who found the centerpoint for a single rotation. A major concept to understand in this unit is that a reflection over a vertical axis and a horizontal axis is equivalent to a 180 degree rotation around the origin. This helps plant the seed for that concept without the axes involved.

Then students must try to complete a challenge using only reflections. It takes away the option to do translation or rotation. It can be done easily with a translation, and students realize that you like a slinky that flips over and over you can do an even amount of reflections and still end up facing the same way you started with. Then they must solve the same challenge using a rotation. They see that this is also possible because a full 360 degree rotation makes you still face the same way so they just had to move the center point around to get the shape to line up. They noticed that answers were always multiples of 360 degree rotations.

Challenge 6 is great because you are trying to transform an L to be an opposite facing L using translations and rotations. Students start to realize that it’s impossible. This reinforces that no single rotation can equal a single reflection. BUT, like one of the challenges before, a single rotation can be equal to two reflections.

Then synthesis ends with 2 questions. I highlighted these two student responses:

1. How can you tell when a ROTATION might be useful in solving a transformation challenge?’

A rotation might be useful … when you can’t mirror or translate it but you need to turn it 90 or even 180 degrees

2. How can you tell when a REFLECTION might be useful in solving a transformation challenge?

A reflection might be useful … when the shapes are facing opposite directions

The cool-down finishes with those same opposite facing L’s and asks students if it can be solved

This challenge can be solved using . . . only translations.. . . only rotations.. . . only reflections.. . . a translation and a rotation.. . . a reflection and a translation.

The answer was only reflections and a reflection and a translation. It reinforces that students need at least one reflection if a shape is facing the opposite way. No rotation can achieve that result. This was a fun lesson and worked well with distance learning.

I was wondering how substitute lesson plans would work this year. I was going to be on the road on a Friday so I needed a sub. My administration said to give my students an asynchronous lesson which would work as their attendance that day. This was a relief because I didn’t know how it would work with a stranger opening up Zoom links at certain times. If I really had to do it I might create an alternative GMail account and make that the co-host of all of my classes and then give the substitute that email address and password to login and start the Zooms.

Anyway, I decided to create a Google Classroom assignment that linked to a Desmos activity. I used the new Classroom Management Desmos has and assigned it to each period’s code so they would login to their school GMail and navigate to student.desmos.com and click Start.

I try to never give a grade level assignment, and focus on a topic that may have been rushed or skipped in a previous grade level. I picked Creating Histograms. I also suggested some feedback to Desmos on it.

I attached a screencast to the assignment that went over the answers. I suggested that students try the activity, then start watching the video and pause it before seeing or hearing the answer. I have used Screencastify before and now am trying out Loom which seems to work pretty well. Here’s my screencast going over the activity Creating Histograms.

Another convenient feature I noticed is Desmos sorts by time entering the activity, but you can change it to sort by first name, which is also possible on Google classroom so checking to see who did it was pretty easy.

Hopefully if you’re in a bind you can use this lesson plan. I think it’s based on 6th grade standards but has some good questions and the context is pretty engaging since it is about popular animated movies of the last few years.

The second lesson of the unit uses Polygraph followed with a part 2 activity to solidify the vocabulary connections and connect the informal language to formal academic language. I have previously blogged about using Polygraph Points (which I wish I spend some time on as like every year students are rusty with coordinates) andwith Polygraph: Parabolas an Algebra 1 class. I have also used Polygraph: Lines with success in the past.

Before students start it’s important to point out that the practice round is like the game Guess Who with people’s faces. After the practice round there will be cards with a blue shape being transformed. It’s also helpful to tell them that the cards are mixed up so if you ask if it’s in the first row that won’t be helpful.

After 15 minutes of playing, I highlighted effective questions some students used to relate them to the transformations:

Lewis said, “are your cards touching tips?”

Justin asked, “is it rotated?”

Lokk asked, “is it facing the same way as blue?” (translation)

Kalista asked, “is it rotated 90 degrees?”

Yaslin asked, “is your shape upside down?”

Julissa asked, “is your shape flipped?” (reflection)

Aiden asked, “is your shape turned clockwise?”

Brad asked, “is the white shape symmetrical to the blue shape?” (reflection)

Alexis asked, “is the white shape on the top left?”

Then I pointed out students that correctly answered some of the in between screens like pick 2 cards that are hard to distinguish and why.

I let students play for 10 more minutes and then paused them for a synthesis discussion. This is where I displayed the cards and did some Zoom annotation for a “digital anchor chart.” This discussion will be used as a base so I can show a card for each transformation and provide a description based on what they said. Also since we are at lesson 6 now, I will also add the requirements needed to accurately perform each transformation.

As you can see I tried to use #purposefulcolor . I did mention to students that some of the cards belonged to more than one category.

In part 2, students match informal words to the formal words of translate, reflect, and rotate. I was able to call on students that were finished to hear different voices and also to allow for more time for all students to finish without others getting bored. Timing is one of my most challenging teacher skills!

Then they group cards to each transformation. One suggestion for Desmos would be if the cards had a letter on them so that when students were talking about a card they could say Card A. My fix was once again using the Zoom annotation. I asked students which card were they the most confident in. I believe they said 2 or 4 in the chat window.

The lesson synthesis offers a choice of 4 cards and students pick one to describe how to move the blue polygon to the white polygon. This provided some great discussions. I could snapshot what student said and ask them to share to the whole class. The lesson concluded with a cool-down where they had to decide what type of transformation a certain move was.

I have been lucky enough to pilot Units 3 and 6 of the 8th grade Desbook in the past and am fortunate to continue to do so with our school distance learning until after winter break. I plan to document and reflect on some of the teaching moves I have tried. One beginning step is to ask students to unmute and read their responses to add a variety of voices. I also pose questions in the chat as well as use the Zoom annotation feature to synthesize main ideas of the lesson.

The kind souls at Desmos have released some of the lessons from the curriculum based on Open Up Resources 6-8 Math authored by Illustrative Mathematics for all to use on their website, and Transformers is one of them.

The lesson starts with students moving vertices around to then be inputted into 3 different transformers with opportunities to reflect. Here are some of the examples students came up with from one class:

Following the Desmos design principles, the activity asks for “informal analysis before analysis.” I took snapshots of student work that highlighted descriptive ideas that were on the right track and continued to ask students to read their responses. I tried talk moves like I would in class to see who heard what new word a person introduced by umuting or typing in the chat.

For example, in Transformer #1 I asked students to share in this order:

my shape spun

my shape turned

my shape rotated

my shape rotated to the left

my shape rotated counterclockwise

I made sure to mention that when we say to the left it is good that we are saying the direction, though counterclockwise is more accurate since as it moves down from 9 o’clock to 3 o’clock it’s moving right.

In Transformer #2 the shape gets “squished.” Some only said smaller. I pointed out students that mentioned it getting wider and shorter. Some said it got skinnier or stretched.

In transformer #3 students said their shape “got smaller and moved.” I pointed these out, and students who said where it moved to and what direction. It then moved “northwest” or to the top left. More details. In every class at least one or two students said it made a “scale copy” or “scaled down.” Bravo to my 7th grade team because that’s what Units 1 and 2 of Grade 7 are about from last years OUR 6-8 workbook. Before having students read about their scaled copy, I also pointed out students who said the shape “shrunk evenly” or “stayed the same shape” or “decreased in height and width.”

I then contrasted these observations with the previous transfomer. Did transformer #2 create a scaled copy? Lots of no’s in the chat. Why? How do you know? Eventually some students said the angles changed and the sides didn’t change “proportionally.” This was great that we were establishing prior knowledge from last year and activating it on first lesson of the unit.

In activity #2 students investigate 4 Kaleidoscopes. I randomly assigned 1/4 of the class to each one as their primary goal and encouraged them to investigate them all after they were done with their first one. It’s super cool. Students sketch and the Kaleidoscope does some transformations. I had to push students to connect it to the previous activity to see which aspects of the previous slides were present in these kaleidoscopes.

I took snapshots of sample student work. Here on the blog they are anonymous names but in live class it was their names so it was recognizing their creativity. You have to be quick with the snapshots because they add to it, erase, or switch to a different one.

One interesting thing is that on the snapshots screen you can clearly see their original drawing because it’s thinner while the produced images are darker. In present mode for some reason they were all the same thickness so it was better to look at them in this view.

In Kaleidoscope #4, there were some good discussions. As you can see the student first drew half of a heart, and then a full circle. When students said it made scale copies, I pushed them to think about how they were the same or different than other scaled copies we’d seen. They said that it made a smaller scale copy and 2 bigger ones. I asked what was true about the scale factor about the shape that was smaller. A few students realized it would be a fraction, not a negative number to make it smaller. Efforts to activate prior knowledge.

A really awesome conversation happened in 4th period about Kaleidoscope #2 and I luckily saved the drawing of the Zoom annotations below. A student said that the smiley faces were scaled copies and they were rotated. To challenge any student further I said, “I wonder what angle the faces were rotated at? A student said, “60 degrees.” I was like… “what? How’d you come up with that?” They said, well a full circle is 360 degrees, and if there are 6 total faces, 360 divided by 6 is 60. I was blown away. They convinced me!

The lesson concludes with some pieces that are not available in the free version. The lesson synthesis shows a gray shape and a red shape after a transformation. Students are asked to “describe what happened to the shape.” Once again, some students only said it turned or rotated and I called on kids that added 1 more detail than the previous one, building on each other’s ideas until the angle of rotation and direction had been discussed. Driving home the idea that it rotates because it faces up at first and after it faces down. It’s not facing opposite ways, so it’s not a mirror so it must be a rotation.

The cool-down offered 4 transformations and students had to pick which one “turned and moved down and to the right.” Multiple choice are cool because you can anonymously display what is the most popular answer and have a discussion why the least popular answers are wrong. Once again this reflects another Desmos design principle, “give students opportunities to be right and wrong in different, interesting ways.”