Lesson 3-5: Discussion Prompt

[Patricia Scheler]

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

[Patricia Scheler]

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

[Kyle Pearce]

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!

[Dawn Oliver]

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.

[Lizann “Lizzie” Herrera]

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

[Dawn Oliver]

Thanks

[Stephanie Pritchett]

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.

[Tarini Arte]

I think when I was student-teaching 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 real-world pictures as visuals too and get that curiosity running!

[Kyle Pearce]

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.

[Kerri Brodie]

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!

[David McKnight]

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.

[Lizann “Lizzie” Herrera]

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!

[Jon]

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

Going in Circles

[Lizann “Lizzie” Herrera]

Thank you!

[Jonathan Lind]

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 color-based proof of the law of cosines that I use every year with at least one of my high school classes:

https://www.cut-the-knot.org/pythagoras/DonMcConnell.shtml

[Terry Hill]

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.

[Zorica Lloyd]

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.

[Christine Pomatto]

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 time-efficient 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.

[Kyle Pearce]

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/going-in-circles

[Christine Pomatto]

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?)

[Kyle Pearce]

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!

[Renee Holmquist]

This concept could also be sued when introducing radians in my PreCalc class. It helps visualize the relationship between arc length-degrees-radians. 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.

[Deanna Semyon]

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.

[Mary Rathlev]

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

[Stefania Lambusta]

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.