Sierpinski's Triangle - 8th grade

Here I go brainstorming ideas for next year. One of my goals was to use the blog to more formally reflect on my year. I have been reflecting but I find those reflections morph into new plans very quickly. This is hopefully going to be a place to brainstorm, get feedback and develop a plan for next year. I will be teaching 8th grade pre-algebra and Algebra I.

I wanted to start the year with something that would allow me the flexibility to review previous ideas and introduce some of the big ideas for 8th grade. I'm looking at Sierpinski's Triangle to be that "kick-off" to the year.

This is a rough list but here are the ideas that connect to Sierpinski's Triangle

• Midpoint/midpoint formula
• Similar Figures
• Fraction/Percent Representation and Operation
• Probability
• Rate of Change
• Representation (graph, table, equation)
• Exponents
• Triangular Numbers (other special numbers)
• Area of triangles (other shapes - how related to triangles)
• Parallel lines/Transversal/special angles
• Pythagorean Theorem and Distance Formula
• Other triangle patterns
• Slope triangles (similarity)
• Other recursive relationships/Fractals

The kick off is Sierpinski's Triangle but the focus widens to include multiple triangle connections. I'm still working on the details of what connections students need to make first and a loose timeline but I am interested in your feedback.

Thanks!

NCTM - More day 1

I feel like I should confess that I am a session hopper. I have a very hard time sitting in a session for the entire time. So many times there are multiple sessions at the same time I want to see. So yeah... I left early on this one...

Connecting and Communicating in Math Class Using Graphic Organizers

Carol A. Hynes

Better utilizing graphic organizers is something I'd like to work on next year so I thought this session might give me some ideas. As part of the introduction, Carol talked about the power of using graphic organizers when adopted school-wide or district-wide.

Some of the graphic organizers she shared were

Links (rule of 4)

Webs

Sorts

Splashes

You can find numerous examples here. You can download the zip file at the bottom of the page.

NCTM Day 1 - Do you see what I see?

Do You See What I See?

3-D Reasoning, 2-D Students

Peg Cagle

This session focused on how students today are different. Peg Cagle spent the majority of the session demonstrating the differences in play for students today.

Play was different

mechanical vs. electronic

do-it-yourself vs. pre-made

nature of public playgrounds

She talked about each of these in more detail.

I was hoping to walk away with the so what do I do to help students and toward the end of the session she gave these suggestions:

• encourage physical activity (team sports to tree climbing)
• introduce 2-d and 3-d dissection puzzles
• full, pour, estimate, measure as much as you can (figure it out - which holds more?)
• play with string (make knots, shapes, loops)
• build stuff

At one point she had us look at paper folding and all the questions you could ask students.

She wonders if memory is stored in a geometric construct how students lack of experience with spatial reasoning might influence memory access.