Elementary math chat is a weekly math chat where participants come to discuss best practices, examine student work, explore routines for reasoning and research that guides and supports pedagogy centered on problem and student based learning.
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Dawn from MN. SpEd Math Coach. We haven't had school for four days. I don't know what the low temp was, -25-30°? That doesn't include the windchill. #elemmathchat
Renee Snyder, Assistant Director @Connect2TLC ... No School- but we had a fun filled day with teachers at #TLCPD Unlocking the Mysteries of Geometry in Gr 3-5 on their Snow Day! #ElemMathChat
A0: Jennifer K-5 math specialist from cold, snowy central Illinois. Wind chill at one point was -51. No school on TWR. Back at it tomorrow although it is snowing right now. #ElemMathChat
I'm Annie, sometimes K-5 math coach near Philly and around. Since I live 2.5 blocks from @pearse_margie, must have been 3 at my house, too! #ElemMathChat
I'm Annie, sometimes K-5 math coach near Philly and around. Since I live 2.5 blocks from @pearse_margie, must have been 3 at my house, too! #ElemMathChat
Hi! I'm Christina... one of the math consultants/coaches @HamiltonCoESC in Cincinnati, OH... most schools were off the last 2 days... and we're expecting snow tonight... I believe -7 was the low , but the feels like temps were CRAZY with the windchill! #elemmathchat
A1: I notice that there are 12 vertices and 4 triangles. Each is a different color. I notice that each one appears to be a different type. I wonder if they are. I wonder #wodb. #ElemMathChat
We keep getting snow too! Couldn’t manage the school parking lots w the super low temps. Freezing rain forecasted for tomorrow morning. Ugh #ElemMathChat
#elemmathchat A1: I notice the triangles are different types of triangles. I think maybe one is equilateral and one looks like a right triangle, maybe one is isosceles and one is scalene? I wonder if I am right about this. I wonder what the lengths of the sides are?
Oh, wait, whaaaaattt???!!! #elemmathchat. More noticing and wonderings now!!!
How difficult to make them all congruent? Can I make any of them equilateral or isosceles by just dragging 1 point? Hmmm... 🤔
After dragging the vertices, now I'm noticing I can make the triangles look similar - or really different.
I wonder what other triangles people are making.
#ElemMathChat
A1 Now, thanks to Annie, I notice that I can drag the triangles and change the angles. Very cool! I wonder how I can use this tool with my students!? #elemmathchat
A1: I noticed that the red triangle allows for two points to shift, the green one shifts at one vertex, purple is always a right triangle, and blue could be either
Wonders: how is this coded? Why do the diff. triangles have different set vertices? #elemmathchat
A1: I notice there are 4 triangles, I notice some are of different orientation. I wonder what the relationship is btwn the triangles, side lengths/angles. I also wonder how the red and green are related; blue and purple. #ElemMathChat
I'm making some pretty large triangles - but I'm noticing that the green triangle stays as equilateral no matter what size I make it.
The blue triangle is the only one (I think) where the corners can be moved and it does NOT effect the other points. #ElemMathChat
Jacqui Lehmkuhl, High school math teacher, Have I told you how much I love getting ideas from this chat? I sometimes feel my struggling mathletes just need time to play, explore, and enjoy the math. Thank you for the ideas. #elemmathchat
A1: I notice that the blue and purple are similar and the red and green triangles are similar too. I wonder if I can drag vertices to make them congruent. #ElemMathChat
Well, I knew @pearse_margie was in SE Penna like me, so not hundreds in that case... I just didn't know she was so close that we could walk to have doggie playdates! #ElemMathChat.
In reply to
@MissMath_Teach, @pearse_margie, @pearse_margie
Hi, Jennifer. Can you name some specific things you noticed? (Maybe pretend you don't know "isosceles", "equilateral", and "scalene" and see what that encourages you to describe.) #ElemMathChat
A3: Blue. Always moving one vertex only moves that one vertex. Sometimes, the triangle is a right triangle. Never do the other two vertices move when I move one. #ElemMathChat
A3: I notice that only one vertex cam be moved at a time. i notice that i can create triangles that appear to be scalene, isosceles, and equilateral with this one. #ElemMathChat
How did you come to those conclusions, Margie? I'm always curious how people decide A-S-N, when they couldn't have dragged every possible place. #ElemMathChat
How infinitely close (not sure if that's the right language) can you get before it's not a triangle anymore? Is this a math question or a philosophy question? #elemmathchat
I was wrong! I can make the red triangle have a right angle! But I still think two of the angles need to be acute. I feel more confident about that because if two were obtuse, the triangle wouldn't close- same with one right and one obtuse.
A4: Green. Always keeps the sides the same length. Sometimes it is "sitting" on a side" Never can I get it to match up with the purple triangle. #ElemMathChat
Right, like who says it's not a triangle? We could ask my buddy @sweimar if there is a line between math and philosophy, or if it's really blurry. #ElemMathChat
#ElemMathChat Sure. The first time, I was rushing. I made some assumptions based on messing around with one vertex. Then, I went back and realized I could move all three vertices and that is when I blew my earlier assumptions out of the water.
@MFAnnie#elemmathchat Q4: can always rotate it about a point and it appears to remain equilateral. Never can make it another shape. Can always scale it up to create a congruent triangle. Sometimes??...sometimes it points “up”, sometimes it points “down” or another way
A5: The vertices are always called J, K, & L. It's always purple. It's not always a triangle (pt J over pt L). So then, my first statement is not true. Dang. Ok. It's always purple. Is it recess yet? #elemmathchat
But how do you know there aren't still three segments, just with two of them lying on the other one? If we did this with pencil, I might agree with you, but since we can move the point on and off that other segment in this situation... ?? #ElemMathChat
I don't think you have to hope. I think you can assert, because I'm not sure there is a right answer, there are just strongly-held opinions! #ElemMathChat
But how do you know there aren't still three segments, just with two of them lying on the other one? If we did this with pencil, I might agree with you, but since we can move the point on and off that other segment in this situation... ?? #ElemMathChat
A6: I think you can match up triangles that can be the same. For example, I can match up blue red and pur if I make it an isosceles right triangle. However, I can't get the green one to match up bc equil triangles can't have right angles. #ElemMathChat
I'm not so sure about this purple/red business. I think I am really close, but are they totally aligned? Did anyone else get the purple and red triangles to match up? #elemmathchat
A7: Green triangle is a special kind of red triangle, because it always has 3 congruent sides, which makes it a special isosceles triangle. #ElemMathChat
A7: The blue triangle is a special kind of triangle because it has no rstrictions. Its sides can be any length, and its angles any measure. #ElemMathChat
He suggested that I explain that he's a calculus guy who views geometry as the Dark Arts. Sometimes it's true that opposites attract! (I think geometry is da bomb.) #ElemMathChat
A7: The red triangle is a special kind of triangle because it always must have two sides that are the same length. Its angles can change, although two of them are always the same measure. It can have a right angle. #ElemMathChat
A7: The purple triangle is special because it must always have a right angle. It can have two sides the same length or all sides and angles different measures, but it always has a right angle. #ElemMathChat
I really don't think the red triangle and the purple triangle can match up because I think the red triangle always has two sides that are the same length and the purple triangle always has three sides that are different lengths. Maybe. #elemmathchat
A8: How to play with the figures. Geometry vocabulary and attributes of triangles. Great conversations! We actually built a lot of these ideas. #ElemMathChat
So can you make the red triangle have a right angle, or can you make two sides of the purple triangle have equal sides? Hmm... Thoughts? (Remember that you can drag every vertex. It's an equal opportunity environment, for the most part.) #ElemMathChat
A8: It is interesting. You really don't have to "know" any math to participate. In fact, some of the math that I "know" got in the way of my learning. #elemmathchat
I sorta backtracked. Knowing "point", "side" helped. Knowing what i needed to show to know how to compare the triangles helped, but the Qs also led Ss to a lot of those ideas. #ElemMathChat
I think that when I use this activity, I have to be sure to encourage participants to talk about side lengths and angles. I'm not always good about that. #ElemMathChat
Q8 Great question Annie, I wonder if knowing "more math" could hinder your ability to freely explore because of feeling constrained by geometry rules? Great activity to share with early mathematicians! pre & post? Get ready 2nd graders! #elemmathchat
A8: Not a ton of vocab is necessary. I think most kids can do a lot of math here with the basics (sides, angles, vertex) or synonyms or the basics. #elemmathchat
