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.

Problem Solving

I started working on the problem solving rubric. I want it to work for any problem I give students and I want to use it every time I assess their problem solving. Problem solving, in my opinion, has to be non-routine and out of context. They are not application problems of current material.

I have a 4 point scale listed for each item in my rubric. I did not include a description because I'm not sure what it would say. Like my learning targets, much of the determination will be my professional opinion backed by evidence. I tried to include what evidence I would be looking for and I'm hoping to better define the levels through class discussion.

Go here to see the rubric.

What do good mathematicians do?

In my role as an instructional coach we (the other coaches and I) spend time reading, discussing for our own professional growth. Each elementary school has a literacy/math coach. At the middle school, each building has a 1/2 time literacy coach and a 1/2 time math coach. I'm the math coach at my building. The first few years we spent a lot of time building the coaches' understanding of how students learn math. Much of the focus was on developing number sense. It was a great time in my personal professional learning. This year the focus shifted to literacy. I'm 7-12 math certified and have no to very little literacy background. I definitely believe that all teachers have to also be reading teachers. I'm just not sure how to do that... Now back to the main point of the blog...

One of the literacy resources we looked at was all about creating a workshop structure. (I can't remember the book or author. I'll have to get back to you on that one.) The chapter I had to read was about a teacher who focused her workshop time on What do good readers do? That got me thinking about the math connection. What do good mathematicians do? How can I use that to create/drive a workshop culture in my math class?

This is what I've come up with...

• Good Mathematicians work on solving problems.
• Good Mathematicians play games and work on puzzles.
• Good Mathematicians ask questions and explore ideas.
• Good mathematicians practice their skills.

*Disclaimer: I did not come up with this all by myself. Some of the other coaches and I have been talking about what this would look like for math. We are great sounding boards for each other. Some of the other coaches have also included vocabulary to connected it to the Daily Cafe. For my first attempt at this I'm sticking with my four listed above.

What it will look like (I hope)

Problem Solving - Students will have a non-routine problem to solve. In the past I've used problems from Mathematics Teaching in the Middle School or Mathematics Teacher. I also love this place. I hope to have a rubric in place where I can give feedback on the students' ability to understand the problem, devise a strategy, and follow it through (adapting when necessary). Required for all students - At least twice a grading period?

Games and Puzzles - I'm hoping to have a collection of games that connect to the content or a specific outcome. The first grading period I'm focusing on these games with the hope to add more as the year progresses. Polygon Capture, Docfish, Number Subset Game

Inquiry and Exploration - I think this is open for students but I'm probably going to provide some ideas to start with. Networks, fractals, history of math, mathematicians, math careers, math in animation, computer programming, etc. I'm not sure how I'll assess but I'd like students to have a product to summarize their learning. I don't think this will be required of all students.

Practice - State testing anyone? This is built in time for practicing the skills for the state test and for Algebra I. My students are required to take the 8th grade state test but they learned most of the material in 6th and 7th grade. This is a way to keep it fresh. For Algebra I this is time for those students who want to/need to practice a particular learning target. This practice will be graded only for feedback purposes not as a part of their grade.

During the workshop time students will need to working on one of the above areas. My hope is to have my students well trained to be self-sufficient during that time so that I can work with small groups of students re-teaching concepts.

Grading

The past few days there have been numerous conversations on twitter discussing SBG and how individuals make it work. I feel so blessed to be a part of those conversations. My realization last night was to try to formalize and describe in detail how I'm going to approach grading next year. Big ideas are great but I need to get to the nitty gritty. Here are some of my initial thoughts. Nothing is finalized and I'm writing more to get my ideas organized. I would appreciate feedback and other thoughtful questions.

Some background

• My district has an online grade program. Parents are able to access their child's current grade and scores at any time.
• I have been out of the classroom for the past four years working as an instructional coach. I have not used this grade program at all so I'm making some assumptions on what it can do.
• The middle school and high school Algebra I teachers created a common list of learning targets and a common semester exam.

Learning Target Score (skills list)

I'm fortunate to already have a list of learning targets. Unfortunately, there are so many of them. I still need to condense them to the list that I will be reporting out. I was drawn to @mctownsley at Meta Musings 4 point scale. I've modified it and a lot of it will depend on my professional discretion of what students understand or are able to do.

• 4 points - You can work through all examples successfully.
• 3 points - You can do basic examples.
• 2 points - You are able to start the problem but unable to see it through.
• 1 point - You can describe what the problem is asking but unable to find a starting point.
• 0 points - You do not understand what the problem is asking.

These learning targets will spiral throughout the year so students will have multiple opportunities to demonstrate understanding. I will have skills quizzes but I also like the idea of giving an assessment at a Do Now or whenever I see evidence of that understanding. My hope is to collect all the evidence and at the end of the grading period have a score (0-4) for each learning target.

Summative Exams

In Algebra I we already have a semester and final exam scheduled. I'm going to add a summative 9-weeks exam for the 1st quarter and the 3rd quarter. I don't know what this is going to look like. I'd like to include a mix of skills and application problems. This will be reported separately from the learning targets score although some of the questions might influence them.

Problem-Solving

I am passionate about developing my students' problem solving abilities. The challenging part is making sure that the problems are out of context and non-routine. If they aren't then they become application problems versus problem solving. David at Questions? has developed a rubric for problem solving in his class. I need to do the same thing (look for that in the future).

Big Questions

In an earlier post I wrote about the big ideas I really want my students to walk away with. I feel like I have to have a way of reporting this to students and parents. Perhaps a 4 point scale similar to the learning targets would work.

The Grade Book

This is what my grade book might look like. I think I'll have to keep a spreadsheet of my own and the online one that reports to parents. For the Parent version I'd like to report only the most current understanding of each topic, learning target, etc. When it comes to calculating the final grade I want to consider all evidence when determining the score. I'm sure someone is wondering how I'm going to weight everything and I have absolutely no idea right now :)

Other thoughts

There are some other things that I want students to do but I'm not sure how or where it would fit in with their grade. Projects? Blogging? Maybe the other process standard focus will be communication or maybe they won't be a part of their grades at all.

Number Subset Game

I'm working on finding/collecting games to use during my workshop days (more explanation to come). ODE had a lesson where students would assign points to certain number subsets. I've adapted it so that 2 or more students could play as a game.

Supplies: a number cube, set of subset cards, paper, writing utensil

Each player writes 5 numbers. Player 1 draws a card and rolls the number cube. If the card is written in red letters, subtract the number rolled for each number that falls in that subset. If the card is written in black letters, add the number rolled for each number in that subset. Keep a running total of your score. Player 2 takes a turn.

Example

Player 1: 3, -10, 2/3, 0, 100

Player 2: 3/4, 4.5, 1, -72, -2.3

Player 1 draws a red integer card and rolls a 4. He will need to subtract 4 four times (3, -10, 0, and 100). His score is -16.

Player 2 draws a black whole number card and rolls a 1. She will need to add 1 once (1). Her score is 1.

Repeat this process. The student with the highest score is the winner.

I'm hoping this a way to keep this vocabulary alive throughout the year.