Make Math Moments Academy › Forums › Full Workshop Reflections › Module 3: Teaching Through Problem Solving to Build Grit and Perseverance › Lesson 35: Tool #3 – Visuals › Lesson 35: Discussion Prompt

Lesson 35: Discussion Prompt
Posted by Kyle Pearce on December 3, 2019 at 3:03 pmWhat was your big take away from this lesson?
How might you use the tool discussed?
What is something you are still wondering?
Joseph Barnas replied 1 day, 14 hours ago 30 Members · 44 Replies 
44 Replies

Big take away – provide visuals and tools. Tools discussed – I need to use more estimation tools. WonderingHow can tweek this for 2nd grade?

Big take away – provide visuals and tools. Tools discussed – I need to use more estimation tools. WonderingHow can tweak this for 2nd grade?

Hi Patricia!
All of these ideas are implementable at each grade level… it all comes down to the prompt for your students… incorporating an estimation each day before giving all of the information will help with this. The younger they are, the wider the estimate range will be (that is ok – they are still learning). The key is giving them that opportunity!


I like that most of the examples you guys use in the lessons come from everyday life. What a creative way to illustrate circumference of a circle. It would be fun to let the kids come up with their own models, maybe using tiles and paper circles of different sizes or even finding a circular shape in their homes to model the same thing. I love this idea.

Great idea, Dawn! I think you have just incorporated manipulatives and visuals!


I have been trying to use visuals. It creates a level playing field for all to notice and wonder. The visuals are interesting and unique and sometimes students are intrigued how math can connect to those normal every things we see.

I think when I was studentteaching I had a really good mentor teacher because she did this exact activity and it was my first time seeing it as an incoming educator, after years of being a math student and working with pi. It blew my mind because it actually makes the connection of where this came from in the first place (we didn’t just make it up out of thin air). I wonder what places in my 7/8 grade curriculum I can really dive into visual explorations (I’ve done it with completing the square but am curious where else it could help bolster that deep rich understanding). A takeaway is that I want to use more realworld pictures as visuals too and get that curiosity running!

I am still astonished at how many of us weren’t exposed to the truths of mathematics like this idea or maybe never understood it when it was “shown” to us. There are so many places for building from visuals, so keep on thinking. Often our limitation is based on our limited prior experience with conceptualizing mathematics so digging is often necessary.


I love this lesson and Monday is Pi Day! I am definitely going to try this with my Geometry class on Monday to celebrate! They are 9th graders so they will already know about Pi but I bet that it will really make them “see” what it is! Visuals are so important for that!

I did this last class with the classic Pythagorean Thm investigation with a 3 by 4 right triangle. A number of the students knew the theorem from learning it in advance, but they did benefit in that they could see where the a^2+b^2=c^2 came from. It’s always so much more valuable to let students see how things work for themselves and make their own connections.

All I can say is… I want to find a teacher who’s about to introduce circumference and use this lesson! Can you point me to the actual task? And, like Dawn said, having the actual manipulatives with a circle and some tiles to see have the students play with the manipulatives (or using digital ones if they prefer) is a great idea too!

Hi there @lizann.herrera here’s the full unit –> https://learn.makemathmoments.com/task/goingincircles/


Awesome visual. It’s great that more and more of these are becoming available, as it isn’t super easy for the “average” teacher like me to throw these together ourselves. Let’s all keep sharing these!
Here’s a visual colorbased proof of the law of cosines that I use every year with at least one of my high school classes:

I believe that this clearly shows the value of visuals to bring in deeper connections. I will probably share this with our geometry teacher, as I only teach algebra at the moment. My big wonder is where can I get the technology to create these kinds of things myself.

My take away is that visuals work in both directions: seeing the visual will help a lot of students discover rules for themselves and it will allow students to remember ideas and rules once they’ve been formalized.

I actually think I will use this lesson exactly as given. I have used a “discovering pi” activity in the past (which I made) but this is more timeefficient and I think it has about the same impact or maybe more. I’m learning that giving visuals upfront benefits all students’ conceptual learning, rather than just drawing a picture when a student is struggling.

Amazing! Our full unit on circle measurement is a doozie. It wasn’t complete back when we did the online workshop, but it is now!
learn.makemathmoments.com/task/goingincircles

Thanks for sharing! How long will I have access to this lesson? (i.e., do I only have access right now because I am enrolled in the course?)

Most lessons are accessible from the web for all, while the downloads and some of the practice tasks are available for academy members. So keeping your academy member access is certainly a big plus!



This concept could also be sued when introducing radians in my PreCalc class. It helps visualize the relationship between arc lengthdegreesradians. This is a concept that is so important in high level math classes and this gives them the visual that might help them remember it for years.

Visuals are so important. I believe I do not have a good conceptual understanding of math. As a co teacher, I had the opportunity to hear things teacher would say and connect the dots to build math skills upon each other and I was just beginning to have great lightbulb moments of making connections as I listened to teachers…. but my teachers and the teachers I work with do not use many visuals so the math skills are often just math skills… with no dots connecting reasoning.
I need to use more visuals and estimations and allow more think time.

My big take away is to strip down textbook problems and create visuals.

This was cool! Visuals help make connections and moments. I wonder how I can find more examples to use? I think creating them would take too long but I want to use them in lessons.

Not gonna lie, I had never seen this is real life and truly STRUGGLED to explain what pi is. This is AMAZING! I see now how much more seeing this concept visually would have benefitted me when I learned was pi is. I know that I’ll be using visuals in my class as I teach solving equations with algebra tiles, as I teach the relationship between a cylinder and cone, etc. I wonder if there is ALWAYS a visual way to show the concepts I teach, if I’ll just think a bit harder? I never would have known how to show pi having not seen this, so I’m wondering how many other visual things I’m missing out on in my own learning.

This makes my heart so full! We too had no idea where Pi really came from. We knew you just divide the circumference by the diameter, but didn’t understand division enough to know what we were actually doing.
We believe there are visual ways to help show much of the mathematics from K to Algebra I and II… some ways require lots of work ahead of time earlier in the progression to make sense so we just need to keep on pushing through and more and more will reveal itself to us!


It makes me realize how important it is for teachers to find the right visuals for the problems they put in front of students. Struggling students will be supported by these visuals and have something to refer back to when they see a problem dealing with circumference of a circle. The three different colored tile to represent the whole number of pi and the fourth color to show it is slightly larger than three diameters is something that will stick students because that visual speaks for itself once students understand the representation. This activity is so much more powerful with the visual than just telling students the formula for the circumference of a circle. There will be nothing for students to memorize because they will have that visual representation in their mind!

This is so much cooler than string! I like the way you did these and the concept of the “.14” as about 14% more than the diameter connects that percentage piece in yet another way. Visuals are much more vivid and stick better than just words and numbers for most people. Sometimes I get stuck trying to make an interesting visual for our problems and stick to super simple. Thank you for more access to connected, more interesting ones.

Big take away: Start the lesson with a notice and wonder. I like the use of videos showing real things. I notice you use this a lot in your lessons. Did it take you long to come up these?
I really like the lesson you showed. Since I teach high school Geometry, I tend to think that the students really understand and know the basics of geometry . But, they really don’t remember a lot so this is a good/fun way to reintroduce these concepts.

I just benefited from a deeper understanding of pi through this short video, thank you! I definitely did not have a deep understanding of where this came from before seeing that video. I teach elementary and I think visuals are so incredibly powerful.

I really like the strategy of the visual at the end where the 3 circles were in the background of the diameter measurements. I have been trying myself to gain this skill of being able to visually represent math so that students get that light bulb moment easier. One point this video has highlighted for me is the strategy of overlaying representations to make an easy visual comparison.

Love it! Check out our animation video on the blog page for details on how we animate our math concepts if interested:


I loved the use of the visual to show the way the diameter went around the circle 3 and a little bit times. I have used a similar activity for the kids to explore with Desmos. I like how concise this was as time is always of the essence.
What I wonder, is there a source or location where I can find all of these amazing videos/problems you two have come up with. I am not all that tech savvy when it comes to making such videos. I was actually out yesterday and saw this giant candle which I took a picture of to potentially use for a math problem. Of course I am not quite sure what the problem will be or how I will “prove” it.

Yes indeed! We have a ton of units here: https://learn.makemathmoments.com/tasks and also there is a search engine here: https://makemathmoments.com/find


I always tried to use visuals in my lessons, however, this sample lesson showed me that visuals could be much more than just a drawing on paper. I will use this information to incorporate more ‘visual visuals’ in my lessons. I am still wondering how you made those super visual lessons that you showed. I have never been successful in making such a smooth and clear presentation and would love to know which program you use.


Thank you so much! I checked it out and it was so clear!



Good morning… I tried using this visual a couple of weeks ago.
One mistake that I made was to show this after working with circles for some time. Interestingly, the students struggled to make the connection to the circle in the video as compared to the various circles that they had been drawing or creating. We use visuals a lot, but they have mostly been animations or graphics. Perhaps this indicates the need for more consistent use of visuals from the world around us.

Although I do like this visual representation and believe that representing concepts visually is a great strategy, I am confused by this example. My assumption is that one of the concepts this problem is trying to show is the ratio between the diameter compared to the circumference which is pi. The place I am confused about is where the camera freezes on the curved section of the circle. Did you choose to capture that specific part of that curve because you knew it was equal to the diameter? If you pulled the camera in or out, it would not have been so obvious but I guess you could have figured it out. If finding pi was the purpose in a visual way, I would think of giving students their own circle with some string and have them figure this out in a more hands on way.
 This reply was modified 3 weeks, 4 days ago by Alison Peternell.

I like your film of this relationship, but when I teach 7th grade circles, I actually give them 3 different circles and have them measure the diameter and get a ballpark of the circumference with string. It is a great activity. I do love visuals though. Another big visual that hits home with my kids is that a line is a straight path of an infinite line of points. I use a visual with a desmos activity where the kids pick points. When they share with the class and we get enough points they see the line forming. This also really pushes home the idea that when we are plotting points, we are really “highlighting” a specific point.

This tool reminds me of Dan Meyer and his 3 Acts lessons. Anytime I use one of his activities, the kids ask if it is me in the video. That simple question alone speaks volumes about just how powerful a video can be for students. It draws them in. They spend hours watching Tik Toks of normal people doing dumb stuff, so why not watch their math teacher introducing a math problem? This lesson reminds me of the chocolateeating video we started with – fairly lowtech with tremendous upside and buyin.
The challenge is to get the math off of a worksheet or textbook page and one simple 30second video filmed on a cell phone works well.

The big takeaway is using visuals to help students explore and discover relationships. Pi makes a lot more sense when students can visualize and discover the relationship as opposed to just being told there is this strange number we use when working with circles. Also, try not to give away too much vocabulary, that is more information that is beneficial if brought up by students. I wonder how we can incorporate more geometry throughout our curriculum to help students see the link between geometric visuals and math concepts.