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

What was your big take away from this lesson?
How might you use the tool discussed?
What is something you are still wondering?

I am wondering how you make the animations in your videos. It is very powerful to see the 3.14 show up, what tools or programs allow you to do that?

We do all of our animations using Apple Keynote and the “magic move” slide transition. We love it and can’t get enough!

Sign me up for that workshop, because I need the magic move while sliding into position.

I’ll put that on our list! Sounds like folks would gobble it up!

Oops…I should have read down the list a bit further…you have already answered my question.
Sorry if this question has an obvious answer…I’m not familiar with Apple products. Is Apple Keynote part of the software/apps for Apple computers? My province uses Office 365 and all of our apps are Microsoft. Would there be a comparable product to Apple Keynote in Microsoft? Thanks!
 This reply was modified 2 months, 4 weeks ago by Andrea Earle. Reason: I should have read down the list a bit further...you have already answered my question
 This reply was modified 2 months, 4 weeks ago by Andrea Earle.



My big takeaway is understanding the power to visuals to fuel sense making.
This is something I endeavour to use more in my lessons.
Specifically I am going to use the video as a tool when looking at circles with a year 9 (grade 8) class.
I am wondering where I can use visuals in my lessons where currently I do not.

Love it. Once you are aware and looking for opportunities, they will start coming to you nonstop!
For circles, a great start could be Tile Circle:


I too love the visuals you and Jon have created. Your visuals are a great go to for my classroom. I regularly use the https://mathisvisual.com/ website.
I have a PC so is there a program you suggest I use if I want to create visuals like yours?
 This reply was modified 8 months ago by John Gaspari.

You can use PowerPoint as well, I just don’t see it as “smooth”. Steve Wyborney is a PowerPoint guy and does some pretty fantastic visuals with it.

Since you mentioned Steve Wyborney, I decided to put my thoughts into a post. My district’s math coach has recommended his “Estimysteries” to the K5 teachers in my school. I used them last year, and the kids love them! Yet, I felt concerned that the procedure I was using reinforced an incomplete picture of how to estimate and why it is important. To mitigate this possibility, I will implement the practice of determining “too high, too low, best estimate” before reveling the next clue (each time)! A simple teacher move, but, I can see it being a powerful way to model to my grade two students how to estimate and why it is valuable.
I have also been wondering how I can adapt my use of Estimysteries to align with the concepts found in Modules 1, 2, and this point of Module 3 (Don’t break the chain; Sparking Curiosity – notice & wonder, anticipation, withhold information, estimation; Fuelling Sense Making; Hero’s Journey Curve).
One way I’m considering is to take more time for students to think/pair/share their strategies in between each clue. Perhaps, they can select which math tool they wish to use, such as rekenreks, number lines, ten frames, or 100 chart. (I have been doing this “for” them. I would cross off all the numbers on the 100 chart they told me did not fit within the clues). Maybe the estimystery lasts for the week and each day we would discuss their ideas/strategies for the previous day’s clue before I revealed the next one.
Does anyone else have suggestions? I’m wide open to hearing them.
Thanks,
Andrea


My big take away is to use MORE visuals. I’m a visual person, and I will draw some sort of diagram for any problem. I would like to provide students with more examples of visuals, so that they can more easily translate that into making their own visuals that work for them.

Yes, I would love to be able to model those visuals – I have a PC too :(. I checked out the Powerpoint guy’s website. Something to consider but not the same…. I think your visuals add so much of an opportunity to connect the concept. (Another skill to look into). I did the shotput task (Day 1) the other day and I did not consider my remote need to switch betweeen screens. You gave a lot of great visuals to use but it was the smoothness between visuals where I lost some students and I need to clean that up.
This also makes me think how having the concrete manipulatives and having students with some circle cut outs and square tiles and see if this pattern works all the time. They could do some cool art with it to maybe where they make a little mosaic and we oculd extend do a 212 pattern with your 3 favorite colors and let me know how many tiles of each color you would need. It would hlpe thme see the beauty and creativity in geometric art too and we could have a gallery of other geometric art with this as the inital piece….

My big take away that I should always try to use visuals whenever possible to help students make the concrete connection to an abstract idea. With middle school students, I still see a fantastic journey they take when they are trying to look at a visual and place the connection into different problems in class.
I have found using algebra tiles (A tool never used until I was a teacher) that students can visualize what completing the square looks like and build upon their create an algorithm to complete the square of different quadratics.
My one wonder is how long does it take to create a visual for each class?

Completing the square is so much more intuitive with tiles, eh?
Here’s a great completing the square task: tapintoteenminds.com/3actmath/magicrectangle
While creating visuals for each lesson can be challenging, we’d recommend trying to lean on resources that exist. For example, we have our problem based units here ready to go for you: learn.makemathmoments.com/tasks
Also, you may not need a visual EVERY day as you need to provide opportunities for them to dig deeper into an idea and even to solve word problems, etc. So leverage what is out there already!


It is not easy to find a good tool to make this amusing videos. But I’m very inspired with that. I will definitely use this kind of videos and notice and wonder and…
To do your amusing videos I will use a stop motion technique. I will save a lot of time showing my stopmotions instead of make students cut and past. I will make them cute and position just to clarify their thinking. If someone knows another program or application for android let me know!!!
 This reply was modified 7 months, 1 week ago by Laura Las Heras Ruiz.

My favorite part of the video was how you showed the “diameter” without announcing it. It was just a visual representation of how many tiles fit across the circle. Like many of the previous posts, I also am very impressed with the graphics of the visuals you are using in your lessons. I have been taking note of the programs people are listing and will be checking all of them out.

My big take away is to use and create more visuals for use in the classroom. The more senses you use to learn something, the more likely you are to retain it. Hearing it, using manipulatives, seeing it, and talking about it all add up to greater student success.

My class just figured out pi together with me. We all (online) showed up to class with a can, some string and a ruler or tape measure. We started measuring the circumference and diameter and comparing the two … we got pretty close to 3.14… we kept measuring, trying to be more and more accurate. Some kids said it was the first time that they understood what they had seen in problems before. Surface area (understanding that C gives you the length) was way more powerful than I’d seen before!


I can’t stop watching. You think she can teach me those moves. She is too smooth to be a guy.


Fantastic!
Have you checked out the rest of our circles unit?
learn.makemathmoments.com/task/goingincircles


I love your example I never knew where Pi came from I just knew it was 3.14 and it was used to find the circumference of a circle. I think that visuals are really important for students. I like how you provided the visual but not the vocabulary at first. I want to try to add that to my lessons.

Awesome to hear! Give a look to our full 8 day unit. It’s great!


Math is, according to a sage(KP), visual. I am never the same person I was before the starting this workshop, and without fear of contradiction, far from that person after acquiring Tool #3; Visual.
I suppose to a large extent was wondering how much deservice we must done to our pedagogical strategies without the use of visual.
My big take away is Tool #3: Visuals lend credence to the saying a picture is worth a thousand words.


I knew that the circumference was 3.14 times the diameter, but it really helped me to visualize that that really means. I can see why it is helpful for students to visualize the mathematics.

Isn’t it bonkers how many of us knew that, but didn’t really “see it” or “understand it” in our minds?


I like to think that I use visuals in my classroom, but when I reflect on it, I realize that it is something I use only when covering geometry topics. My take away here is that I need to invest in bringing visuals into more sections of my classes.
I also find that after having students visualize pi, they start looking for it more places when we do investigations, something that didn’t happen when I just gave it to them.

I love visuals to see concepts in mathematics. I like to use digital graphical environments more. When students use Geogebra to create geometry, the software keeps a record of the construction in order which essentially are the steps for writing formal proofs. Then when they manipulate the Geometry and identify the static elements among all the changes they witness a proof or proof idea. Here is an example I made for 8th grade.

Visuals are great to consolidate understanding and allow students to see the math visually before we add the algebra aspect to many concepts. Great way to catch the students who aren’t quite there yet with their own understanding of the problem to hopefully reel them in and see the light bulb go off for them.
I was wondering how do you make your own visuals? What programs have you used to create your visuals in your videos? Any suggestions? I can draw things but somehow I think a nicer looking video or demonstration of the idea would go over better.

We are big Apple Keynote fans and basically build all of our visuals in that program. Our animations use the magic move slide transition inside that program as well!


What was your big take away from this lesson?
Visuals help retention and understanding of concepts.
How might you use the tool discussed?
Great way to introduce new topics and have them explore the ideas around the topic using visuals.
What is something you are still wondering?
How do you handle students that already do know these concepts and shout out the correct answer taking the opportunity from other students to explore?

The visual representations and connections are a big missing piece in high school because we assume all students can grasp things abstract.
Echoing an earlier comment – an Apple Keynote magic move tutorial would be awesome! I’d love to make those animations.

My big take away from this lesson is not only the use of visuals, but the importance of color in the visuals. I have done an activity where students use string and different sized circular objects to discover the relationship between diameter, circumference, and pi. This helped some students understand the relationships but it didn’t paint as clear a picture as this video using the same idea with the different colors.
I plan on incorporating more visuals in my lessons this next year. Sometimes they might be pictures, while other times they might be videos.

Glad to hear you’ve found a tool to help bump up the sense making for students in your classroom!


My takeaway is that I need to make sure to use visuals whenever I can to help students truly understand the “Where does it come from?” part of math. Sure, a lot of kiddos can just memorize a formula, but they often use it incorrectly. With a clearer understanding of where things come from, students can apply knowledge to solve problems without trying to remember which formula applies in each situation.

Simple visuals can be highly impactful. Curate, curate, curate!

I love this activity! Since I’m teaching prealgebra this year, I’d like to use this for piday.

Fantastic! We have a whole unit on circle measurement:
learn.makemathmoments.com/task/goingincircles


I love how you tie in the visual. My takeaway is that I need to get it in gear with finding/creating/organizing what I want to have available during a lesson.

My biggest take away from this lesson is that visuals can help further connect the concrete to the abstract. It seems like visuals would be something important to keep in mind when manipulatives start seeming old to kids, or are not available. Visuals can keep things interesting because if you really look for it, math is every where!
The way I like to use it is to get kids to make their own visuals whenever possible. Teaching kids to draw their own visual representation of a problem is my first goto when a student is having a hard time grasping a concept.
Something I am still wondering is, is there a huge difference between the two tools multiple representations and visuals? It seems like having kids create their own visual is a form of multiple representations, but I may be way off.

Once again, I was guilty of giving too much information…including what type of visual representations my students should be exposed to. My big take away is to withhold information and provide or encourage students to develop their own visual representations to explain their thinking. I plan on using this with my first graders when we explore ways to make 10.

This is so common – you are definitely not alone. I still struggle with this. It will take practice, but with intentional planning, it will become a habit snd totally transform how you teach 🙂


My biggest take away is to continue to use visuals. I love
https://www.geogebra.org/?lang=en for apps and visuals. I used https://www.geogebra.org/?lang=en in combination with your can opening activity to introduce circumference.
I wonder how I can convince other teachers to use visuals as well.

My big takeaway was the reminder to limit the information I give so students can discover. I need to know when to stop visuals or cover parts of visuals to give room for student thinking.

I really like how you gave just a little piece of the information at a time. I would have told them everything they should have noticed instead of letting them find it for themselves. I want to apologize to all of those students that I robbed the opportunity to discover how math works. The ownership is so important.

We just never know what will trigger that proverbial light bulb to turn on for each student. Something as ‘simple’ as a visual could do the trick. I guess a picture is really worth a thousand words. USE MORE VISUALS this year! Especially a variety of them. LOVED the visual for pi!

What was your big take away from this lesson?
A: A visual helps understand why pi = 3.14, more easily than a formula.How might you use the tool discussed?
A: I have to not assume that certain concepts are already understood. E.G. Pi may equal 3.14 but its relevance is significant (more than just a number or symbol in a formula). The ratio of the circumference/diameter is not intuitive and visuals or exercises to determine the fact could strengthen the curiosity circles(and thus, pi) in our foundation for geometrical and algebraic understanding of many mathematical truths.What is something you are still wondering?
A: I might need to get stronger with my own understanding of some concepts and where it might be appropriate to interject the visual or the exercise to help come to an understanding of different mathematical truths too. This reply was modified 3 months ago by Velia Kearns.

Having students discover concepts, even formulas is so meaningful. I have students discover the relationship by measuring around circular items/faces and then across, using guiding questions from me. I really like this video and would love to use it in my circle unit.


I do work with circles in my grades so this would be a great intro. I know that many students would “know how to do it” but I’d rather they struggle and use the visuals to help with sense making. Of course the overall principle here of using visuals and struggling with them both in making initial estimates and then updating our guesses as we go is more important.

I try to use visuals but often run out of time finding ones to use with different concepts. I am so happy to find all of the ones that you have introduced so far in this course! I am making lists of ones to use with each unit I will teach next year. I am wondering if I can partner with some of my fellow Grade 8 math teachers to share lesson ideas and plans! That would be great! I also am considering joining the Academy!

I love this. I took the information you gave us and played with the numbers to prove that the formula works. I’m having my own 7th grade math aha moment, which proves the point that these visual representations really help solidify the understanding of what is happening.
I am now questioning if I was actually shown these things while in the grade level but I may have forgot, or if they weren’t shown, would this have helped me feel more comfortable with math. In middle school and high school I flip flopped between on level and advanced math classes. But even in my onlevel class I felt that math was very difficult even though I enjoyed the puzzle of it. This is why I chose to teach math and received a mathematics major in University with a minor in education. I wanted to continue to learn was to help struggling students in mathematics.
I’m excited to find many more ways of doing this to really target the how and why in mathematics for my students rather than giving them a formula.

What was your big take away from this lesson?
I am very visual. Most of the math classes I have taken have not been visual. I just learned where 3.14 came from…..so excited!
How might you use the tool discussed?
I teach a special education math class. I use manipulatives all the time to make things visual for the kids…last year due to covid I had to move my manipulatives into a video format….The math teacher next door is aways telling me it is “dumbing” down the math and that sixth graders don’t need visuals…I will keep using them.
What is something you are still wondering?
I have a few “math dictionaries” in my room that have math definitions and pictures but how cool would it be to make a online math dictionary for everyone to use….what you posted could be under the Pie heading!

The use of visuals is so powerful. Seeing the example helped me fully understand Pi!
I have always tried to use visuals but at times feel pressured for time and fall back on just using the algorithm. This encourages me to take the time to create and find visuals to deepen student understanding.
I wonder where I can find more visuals to use with my Fourth Grade class.

I think we can all relate to your struggle. Throughout the rest of this workshop, we will continue to uncover ways to avoid that rush to the algorithm!


My big takeaway is the power of visuals. I knew and thought I understood what Pi meant. this visual made me realize I hadn’t quite understood it to the level I thought I had. This makes me want to join the visual to the concrete tools and give kids ropes to test to see the diameter times three (and a bit) actually works every time. Having them cut string (or maybe pipe cleaners so they keep their rounded shape better?), then visualizing themselves what Pi is would be amazing!

I’ll be in grade 2 next year and I so want to teach them about circumference now. Visuals will make it entirely possible… which says it all, I guess!

Just a small intro visually is completely accessible. Keep it simple and let them do lots of estimation with “about 3” and “one third”.

YES! I love it. Is it bad I want to do this on day 1 now? Yes, it is… I will not. But I will make an intro at some point this year. Maybe as a little unofficial Math Talk that doesn’t necessarily lead into a lesson? Like, a “think about it during recess” type?



My biggest takeaway from this lesson is – What a great choice of context to get to the big idea that there is a relationship between the diameter of a circle and its’ circumference.
The fact that they square tiles are the units we are working with instead of say measurement of a string which we map on the metric system to really brings this lesson to the next level.
For this lesson to have a high chance of success, the teacher will need to apply many of the approaches learnt in the previous modules to engage the students in sense making.

My take away is similar as with tangible manipulatives, how the visuals really open up the problem solving process and can make it accessible or easier. I am wondering how to create visuals for standards that I do not already have resources for. Using PearDeck has helped with that during distance learning but I am wondering what else is out there.

Visuals are so important but I find I forget to use it as much when working with divisibility families. I will be trying to incorporate this more into my lessons – even giving them number charts and hopefully making animations to help consolidating learning!

It can be difficult to find useful visuals sometimes, but keeping this idea top of mind can certainly help!


Wow…I loved this for teaching circumference, and for showing students where pi comes from. I didn’t actually know this! (Disclaimer: I am a licensed SpEd teacher who teaches math, but don’t have a degree in math.) I have always been big on using visuals for teaching math to my students, but this just affirms it even more. I can’t wait to use this prompt for a lesson on circumference this year!

You’re not the only one who didn’t have a clear visual on where Pi came from. Many like ourselves have taught it for years, knew the definition, but never really had a clear vision of what it looked like. Glad you’ve built that understanding for yourself now!


I cannot wait to dive into all the visuals the Make Math Moments Academy has to offer. This will be so beneficial for the students (and me too)! There is a visual in our textbook that shows how the value of pi comes from diameter, but your video takes it to a whole other place. I will make both available to students, but I suspect the real ‘Ah’ moment will be with yours. I am a very visual person, so I know how important it is to make use of visual tools for students to foster more GREAT learning.

So awesome to hear!
Be sure to check out the entire Circle Measurement unit here:
learn.makemathmoments.com/task/goingincircles
