Graceful Tree Problems and Assessment: My 1st In Person Pro-D in TWO Years
Last Wednesday I had my first in person professional development since the start of the pandemic…and it was lovely. Thank goodness for science (vaccines are great!). It was a wonderful day of math and assessment. It was what professional development should be:
Connecting with colleagues
Trading ideas
Learning something to use the next day
Thinking about shifting practice
Connecting with Colleagues/Trading Ideas
We cannot teach in a vacuum. Educators love to learn from each other and bounce ideas off of each other. Online was…okay…but the energy wasn’t the same. I was able to look people in the eyes and share my thinking or build on their ideas. This was the first of a yearlong exploration of standards-based assessment and how to design it. It was very exciting.
This is the third yearlong math initiative I have been part of. My previous initiatives were:
1. A number sense routines workshop two years ago
2. A book club last year exploring Building a Thinking Classroom in Mathematics
I feel the yearlong exploration this year is allowing me to weave all three ideas together to make my teaching and assessment that much stronger. I feel so lucky to do it in person!
Learning Something for the Next Day
I liked two of the activities Marc used so much, I threw out my lesson for Thursday and ran the two activities. The kids were highly engaged (which is what you want for non curricular tasks) and were excited to design their own problems to challenge family and classmates in the future.
What were these amazing activities? Great question!
A number sense routine called ‘What is the Question?
A non curricular task called The Graceful Tree Problem
Number Sense Routine: What is the Question?
It was the simplest routine in the world…and yet…I had such variety, and the students FILLED their tables. Some played with addition only…others addition, subtraction, multiplication, and division. A few had 2-step equations while others used square roots. I had to remind a few that the square root of 1000 was not 100…they needed 10 000…but they got there, and it was fun!
Non curricular Task: The Graceful Tree Conjecture
Marc introduced us to the Graceful Tree Conjecture. I found a blog post all about it HERE. Basically, the idea is that you can draw circles, connect them with lines, and fill them with consecutive odd numbers in a way that the no difference between the connected circles is the same. This does not work for a CLOSED LOOP, but it works for all other shapes.
Mark drew an ant with five circles and challenged us to place 1,3,5,7, and 9 in the circles and make the puzzle work.
Grumble…grumble…early morning...tired teachers….we did it anyway! When we found one pattern he said: find another pattern that works! He gave groups a few patterns and then challenged us to complete a pentagon. He let us hit our heads against the wall for a few minutes and revealed that it can’t work.
What a fun conjecture to explore …and how easy it would for students to make puzzles to test the conjecture!
Marc argued that for younger grades it definitely was a curricular task, but for older-he could see how it was non curricular. Since I teach grade five…I decided it was a non curricular task.
My students LOVED these puzzles. They were so much fun, and it was easy for me to make a quick lesson flow. You can find a copy of my lesson plan HERE. For sample shapes, check out the photo of my scribbled plan, or find a website with a variety of shapes. Have fun!
Thinking about Shifting Practice
So now I get to think about a few things this year….
1. Assessment and creating standards-based assessment
2. Weaving what I learned last year about lesson flow/design from Building a Thinking Classroom in Mathematics into my assessment practice with more intention
3. Exploring the Depth of Knowledge Framework