Building Relationships Digitally

Weeks after I started at a new school, one of my administrators gave me this note. Immediately I felt appreciated and our relationship grew. She always talked about the importance of building strong relationships with students and modeled it with actions like this. Telling someone you recognize they are working hard and doing a good job is a great way to build a relationship. I give students feedback like in my classroom all the time - I pass out high-fives and positive praise like confetti. When we transitioned to online learning last spring, I felt lost with how to maintain these relationships. 

About the same time we switched to distance learning and stay-at-home orders were in effect, I started working out with Peleton. I couldn't help but notice the subtle ways that the instructors gave positive praise and how it motivated me. Sometimes when we were in the middle of a minute long plank, the instructor would say, "I know this is hard, but you can do hard things." Or during a long uphill climb on the spinning bike, the instructor would say, "I'm proud of you for tackling this workout, you are getting stronger every day." Inspired by this, I started to sneak some motivation into my video instruction. I would tell the students I was proud of them for working hard - in my head I imagine the kids who were actually working hard feeling good about being recognized and the ones that weren't starting to work a little harder (kinda like if I am taking a break when the fitness instructor tells me he or she is proud of me). I would also validate the fact that what we were asking of them - learning online in a pandemic - was challenging work. Here is a video clip from one of my lessons: 

Last school year I already had strong relationships with my students when we transitioned to online instruction, so I was working more on maintenance of that relationship digitally. If this school year starts online (and I'm still not sure if it will), I need a way to build relationships with my students. Another thing I noticed during these workout videos is how the instructors tell some personal stories while we are exercising. They will have anecdotes that correlate to the music or the movement or just a story about their day. It makes me feel like I know them because I know things about them. I think this will be so important if I am instructing online. By telling them stories either about my personal life or my classroom experiences or how I feeling while recording the video, I think I can build those connections. By including some praise throughout my videos, I can help to motivate them to keep learning and let them know that I recognize their efforts.

I do need to find more ways to reach out with specific praise. I love these digital stickers (freebie from Damman's Algebra Room) as another way of sharing some positivity digitally and, while not as meaningful as a handwritten note left on your desk, they are easy to share digitally. As I said in a previous blog post, I will not compare this year to any other. I know that I felt extra motivated by that note from my administrator. She recognized something that I was doing that she appreciated and her comment made me strive to work even harder. Doing that digitally will be a challenge especially with students I do not know. But I also keep reminding myself that teenagers today often make and maintain relationships digitally. They feel connected to people online that they have never met, and I think our shared experiences of navigating this course during a pandemic will connect us when we do [hopefully] eventually meet in person. 

How I Used Midpoint Formula to Install a Ceiling Fan

Summers in Florida can be brutally hot, and my darling children, 4 and 1, love nothing more than to dump out every toy they own play in our living room. Without a ceiling fan, that room quickly became a sauna, so this summer we decided to install a ceiling fan. Well we paid electricians to install a ceiling fan - I know my limits. Although I wanted no part of running wire through the attic - I could put my math skills to use for positioning the ceiling fan. Here is our Living Room:

To get the maximum air flow and for purposes of symmetry, we wanted to ceiling fan centered in the room.

Suddenly, my living room became a coordinate plane and I calculated to the nearest eighth of an inch where the fan should go.

When the electricians came the next day, they wanted to check my math (even though I told them I was a math teacher). He whipped out his tape measure and also measured the width of our living room to be 193 1/4 inch. Then he simply folded his tape measure in half and found the middle to be 96 5/8 inches and did the same thing with the length of our living room.

I quickly made a mental note to model this for my students - what a great visual for midpoint and a great way to conceptualize what we are doing : finding the halfway point between the x-coordinates (in this case the width) and the y-coordinates (in this case the length) and then finding where they intersect. Whether you use the formula or not, you are using the same steps. 

When I introduce midpoint this year, I am definitely going to tell students this story about hanging the fan. I think I will tell them that we want to hang a fan centered in the living room and ask them what information they would need to accomplish this.

Then I will give them the dimensions and see what they come up with. I feel like midpoint is intuitive enough that they could accomplish it. Because not all midpoint problems start at the origin, I want to extend their thinking with this scenario: My living room and dining room are actually connected into one long room. How would this change the coordinates of the midpoint (helping them to see we are still finding the middle of the length and the width of the living room, but translating it up 132 inches to account for the dining room).

Off to enjoy the cool breeze in my living room for the next week or so until school starts!

Geometry Proof Crossword Puzzles

When I was a freshman in Honors Geometry class, the idea of writing a proof terrified me. I would never knew which theorems or postulates to use or how to order them (and I was a good math student).

I know my students need some scaffolding when it comes to proof writing and some fun too. I love to use fill-in-the-blank proofs because it helps them to see the structure of a proof. They still have to understand what is going on to fill it in, but they don't have to completely create the whole thing on their own.

In 2006, I backpacked through Europe with my friend, Bri. We crossword puzzled and Sudoku-ed our way through the railways of Europe - so crossword puzzles hold a place near and dear to my heart.

That's me doing a crossword puzzle on the train to Venice.

So I decided to combine the outline for a Geometry proof with my beloved Crossword Puzzle, and the Geometry Proof Crossword Puzzle was born. Students fill in the proof, completing both statements and reasons, and then fill their answers into the crossword puzzle. Each puzzle has two proofs - one for across and one for down clues. I love how the activity builds in an opportunity for students to check their work - they can easily spot a mistake if their answer doesn't fit or if the letters don't match up. This also provides them with some hints if they get stuck because they may have a letter or two for the word they are trying to fill in.

I've made my Angle Relationships Crossword Puzzle free so that you can try it out with your students.

Good news for when they love it - I've made 11 of these crossword puzzles. Topics Included: Algebraic Proofs, Segment Addition, Angle and Parallel Lines, Proving Lines Parallel, Proving Triangle Congruence, CPCTC, Quadrilaterals and Triangle Similarity. But let's face it - you and your students are going to have so much fun with these you might as well buy the bundle ;) #GottaCatchEmAll

I've also included directions for printing these to fit in interactive notebooks. I love having some student samples in their INB that they can refer back to throughout the school year.

 I hope you and your students have fun with these! Feel free to come back and let me know how it goes!

Learn your multiplication facts

Multiplication facts are one of the most essential tools students need to go forward in math. I am always shocked by how many don't know them - even now in dealing with high schoolers. They used to simply turn to their calculator, but with the changes in common core, students can no longer rely on that tool. Even though understanding when and how to use mathematical tools correctly is one of the mathematical practices, the Algebra EOC has a no-calculator section. Included in this part of the test are questions about operations on polynomials, solving quadratics by factoring, and simplifying radicals - all these skills depend on students knowing their multiplication tables. I created this Tarsia puzzle for a conference presentation for elementary school teachers, but it is actually fun for my high school students too. I use it when I have students who need to fill a few extra minutes or to have a race and see which group can put the puzzle together first. Maybe someday I will have students who have times tables on automatic recall. Until then, practice makes perfect. Pick up a copy to use in your classroom at my TpT store here