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Supporting Mathematical Thinking

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Welcome to ways to support mathematical thinking during these uncertain times. I believe that one of the most important things that we can do is to encourage mathematical thinking. During this time at home, there are a lot of different ways to do that. I am hoping to share a few of them & hoping that you will share what you are seeing and learning. From these experiences, my hope is that you may change how you view math from a set of rules to a way of thinking. As a coach, I am finding that my work is changing. … Continue reading Supporting Mathematical Thinking

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What Do You Do First?

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As I am realizing that I need to change things in my classroom to see the changes in my students, it can be overwhelming with all of the possibilities of things to do. With over 25 years experience in education as a teacher, coach, and mentor, I realize that it never hurts to ask for another perspective. Another person’s thoughts help clarify what I am thinking and help me decided if what I am thinking is a good approach, needs to revised, or should be put on the back burner. That person can also offer a different perspective that I … Continue reading What Do You Do First?

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Teaching High School in a Covid World

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After mentoring & coaching for nearly 20 years, I have found myself back in the classroom teaching high school math. While it wasn’t what I had planned, I am thankful to be back with students, trying many of the things that I had learned. However, I am finding that I am resorting back to familiar ways of being in the classroom. And I have found myself back at the high school that I attended teaching geometry and statistics. This weekend, I had the opportunity to attend the Effective Instruction Conference sponsored by the Alaska Staff Development Network. This virtual conference … Continue reading Teaching High School in a Covid World

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Open Middle© Math

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Open Middle© problems are challenging, fun problems for students of any age. The idea behind Open Middle© problems is that there are multiple solutions for finding the answer. To solve these and to prove that you have a valid solution, you need to find different possible solutions. Here’s one that I tried: I tried Multiplying Two-Digit Numbers – Closest to 7,000. For my first attempt, I tried using the digits 1, 2, 3, and 4. I was not really thinking about the impact of place value. I was just wanting to see what happened. On my next attempt, I knew … Continue reading Open Middle© Math

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Rectangle Fit Game – Day 12

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I love this game for helping students with their multiplication facts! Rectangular Fit, taken from the work of Jennifer Bay-Williams and Gina Kling in Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention, can be adapted for different ages and situations. For Rectangular Fit, you will need two dice (or you could use playing cards), pencil, and a game board for each player. You will need at least two players. I am sharing how to adapt the game for at least a two player game. The attached version is for a whole class game. The goal … Continue reading Rectangle Fit Game – Day 12

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One Cut Geometry – Day 11

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One cut geometry is a fun challenge based on a theorem that every pattern (plane graph) of straight-line cuts can be made by folding and one complete straight cut. So it should be possible to make every single polygon from one cut on a folded piece of paper. You need scissors and a LOT of paper for this challenge. The recommendation is that the paper is square but I think you could use a regular piece of paper. Draw a scalene triangle in the middle of the paper. Can you cut the triangle with one cut? What shapes did you … Continue reading One Cut Geometry – Day 11

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Which One Doesn’t Belong – Day 10

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Which One Doesn’t Belong is one of my favorite routines to use with students. Students choose which one they think does not belong from a group of images. The most important thing is that they explain why they believe that particular image does not belong. And anything goes. An example from the image above would be I think that the bottom right does not belong because it is the only one that is green. Students also need to be thoughtful that their explanation only works for that particular image. If I said that the bottom right was outlined in red, … Continue reading Which One Doesn’t Belong – Day 10

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100 Chart Connect 4 – Day 9

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This game is from Joe Schwartz’s Exit 10A. The goal of the game is score the most points by connecting four numbers (either horizontally, vertically, or diagonally) on a 10 x 10 grid, or 100’s chart. The idea behind this game is that it helps younger students learn about patterns in the 100’s chart. For older students, there are a lot of strategies that can be used that makes this game interesting. Since I did not have any pictures of the game being played, I asked my high school sophomore to play with me. When I explained the rules, he … Continue reading 100 Chart Connect 4 – Day 9

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1-4-5 Square Puzzle Challenge – Day 8

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This puzzle, or challenge, is all about making squares. Sarah from Math = Love have adapted the original puzzle from a Netherlands brain teaser website where you use all five pieces to create a square. I love how she has scaffold this activity to allow students to build their stamina to figure out the original challenge. Know that if you do puzzles like this to remind students that finding the answer to the challenges could take days. We are still working on Challenge #3. Here’s her adaptation: Challenge #1 Can you make a square using only one piece? (I think … Continue reading 1-4-5 Square Puzzle Challenge – Day 8

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Same or Different – Day 7

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How are these pictures the same? How are these pictures different? This routine of same or different allows students to compare two things, looking for how they are similar and how they are different. Students start by thinking and studying this picture – noticing and wondering how these images are the same and how they are different. Then students share, verbalizing what the see being the same and different. Students learn how to share and talk about math in a way that is fun and engaging. They also see how different students see the world by listening to what they … Continue reading Same or Different – Day 7

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5 x 5 Game from Sara Van Der Werf – Day 6

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The 5 x 5 game from Sara Van Der Werf is great for any age. Using cards, student place numbers on a 5 x 5 grid. When numbers are adjacent, they can count those numbers for their score. Numbers can be adjacent either vertically or horizontally. The goal of the game is to get the highest total points. To see a better explanation of the rules, you can find them here. Every time that students have played this game, it takes at least two attempts before they start to strategize where to put the numbers. And students of all ages … Continue reading 5 x 5 Game from Sara Van Der Werf – Day 6