Week 31: Angle Inquiry

Sometimes the simplest things have wonder hidden within. This week, learners can play with the angles of polygons. How many degrees are in a triangle? In a quadrilateral? In a hexagon? Is there a pattern?

Here is a warm-up activity:

Draw a triangle (any triangle), and cut it out.

Next, rip the corners off:

Now, here is the fun part… put the pointy angles together. What do you get? Try it with lots of triangles and see if you always get a straight line. Rather than lecturing or telling learners that triangles have 180 degrees (or pi radians), let them discover. They can even create art ( I like to make my angles into perspective path doodles.)

Now do the same with a four sided shape. What do you notice? Is it the same for all the ones you can create?

Now do the same with 5, 6 or more sided shapes. There is a rule to be found. Try to discover it if you don’t know. I will put the rule at the bottom of this post.

I did this twice last week with virtual classrooms through the Covid-19 isolation. Students from kindergarten to middle-school ate it up. We used it as a warm up activity (10-15 minutes) prior to doing some loop-doodle math and/or other activities.

and

the

rule

is

stated

right

below:

The rule for simple polygons is that for n sides there are 180(n-2) degrees. Or you add 180 degrees every time you add a side.

Week 30: Coloring is not Just for Kindergarten

I am trying to tell my 15yr old daughter that an elective high school credit in Graph Theory would be fun next year. Of course I do this as subtly as possible – I start drawing coloring sheets for this post on my iPad and then carefully shade them in. All three of my children slowly sneak up behind me and breath in my ear.

“You know that it will never take more than four colors” I state.

“Really?” I hear my oldest daughter say with a sense of wonder in her voice. “Can I make one?” she asks reaching for my device.

My 15yr old’s Piece

She takes over the iPad. I go for a run. I clean up a bit. She is still designing, thinking, coloring. A wave of gratitude flows over me “Thank God that coloring isn’t just for kindergarten.” We are so blessed to have the abundance and time to be able to color, play, and contemplate.

She finishes her design. “It looks like the beautiful cobbles on our Oregon beaches.” I think, then say.

“That’s what I was going for.” She says. Then gets up and goes back to her school work.

This week I challenge learners to play with coloring sheets. Make your own. Share them. Color them. Contemplate them. Can you restrict the coloring to four colors? It may take some problem solving for more complex sheets.

In graph theory, there is the study of graphs that are made up of nodes (vertices) that are connected with lines (edges). Create a graph for one of your coloring sheets, where the regions are nodes and lines connect the regions that touch.

You could also create a graph with nodes and edges and then the coloring sheet to go with it.

Below are a couple examples (some blank for you, my readers, to use):

KMUZ Poetry on the Air With the Family

KMUZ’s Steven Slemenda interviewed our family in a two part series for a wonderful program called Poetry on the Air. Thanks to KMUZ and Steve Slemenda for sharing. This show is in the archives on their website, and with permission I am posting it here. My children were appreciative of the experience for the interview. It was such a wonderful exercise for them to reflect on. We are grateful for a way for voices to be heard in our Salem Community.

8-20-19: Interview with Sophia’s Children
9-13-19: Interview with Sophia

Fractal Kitty begins!

Logo Design

I sometimes feel like a broken record. I repeat so much in conversation with parents, educators, and students when I consult with them on learning math that finally I sat down and brainstormed a website to share my ideas and best practices that I have used through the years. My plan is to share my stories, syllabuses, games, reviews, poetry,… the list goes on. I look forward to what this grows into. As a reader, please let me know what would be helpful and what you’d like to see here.

This week I created a logo, posted my Marie’s Atlas books here for free (It’s been 5 years since I wrote the first book!), and organizing all of my materials for web content. I am still pondering if I should go by grade or concepts or age for organizing materials. I homeschool my own children and find that Grade is meaningless, but concept or levels of math are not.

I am also trying to be able to earn as a tutor/artist/author without setting up paywalls, annoying ads, or seeming pushy. For now I have decided to use affiliated links and donate buttons. This way if people can and want to pay for content, they can.

I hope Fractal Kitty will help make math fun and meaningful for many. Thanks for support and please subscribe.