Students chose between 3 options:
1) creating letter patterns,
2) exploring Lego staircases, and
3) learning to program a TI-84 graphing calculator.
We did a project day in Algebra yesterday. Students chose between 3 options: 1) creating letter patterns, 2) exploring Lego staircases, and 3) learning to program a TI-84 graphing calculator. Letter Patterns More than half my class decided to work on making letter patterns. Each student worked on 3 different letters--figuring out how to make the letter out of squares (mostly) and then enlarge them. They did great! Students who normally struggle with math got a chance to showcase their other strengths. When we presented our projects today in class, students who normally look at the floor and sink into their chairs when I ask for volunteers were excited to share what they did. I can think of an interesting extension of this project. Instead of having students create equations for their own letters on the sheets, I would have students create equations on a separate piece of paper. Then have students trade papers and create equations for each others' patterns. Practice with creating equations from patterns and tables--done. Lego Steps 3 students went for playing with Legos. They worked together as a group exploring how the number of bricks relate to surface area and volume. Surface area almost ended this group. When I walked by, they were staring blankly at the paper and the pile of Legos. I gave a little support and asked some leading questions to get them started. After that, they were off and running. Programming Graphing Calculators in BASIC I had 4 freshman boys giddy with excitement that they were going to learn how to program something. I spent most of my time holding the hands of this group as we walked through the syntax of BASIC and the concept of if-then-else statements. Throughout the day today, I had conversations with each student at least once with their calculator in hand asking how they could either fix or extend their program.
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Getting students to generalize is one of the great challenges of 1st semester Algebra 1--it ranks up there with having them remember anything about solving equations from their previous 3 years of math. Enter Fawn Nguyen's (@fawnpnguyen) site VisualPatterns.org. I'm going to try using some of the patterns next week as we review creating linear equations from patterns and tables. I don't think my worksheet is anything worth writing home about, but I'll include it just so you can see how I'm using them.
However, I did start thinking that I probably should contribute to the site instead of just taking stuff from it. So... here's my 1st submission. What I am unsure of is what questions I should ask. I gave Fawn a couple I was thinking of, but ultimately left the decision to her: 1) How many blocks in the 43rd instance? 2) What is the perimeter in the 43rd instance? 3) What is the area in the 43rd instance? (this one is quite a bit harder than the previous two).
What do you think? Based on the recommendations of multiple people, I read 5 Practices for Orchestrating Productive Mathematics Duscussions. The title isn't all that creative, but it does speak for itself. In 13 years of teaching and a masters in math education, I don't think I've read anything nearly this helpful. Anyway, they parse apart a tiling task in one of the chapters that I thought worked brilliantly. It starts out concrete and moves towards abstraction with baby steps. In Algebra 1, we've spent our last week looking at how to create rules and equations from patterns we see in numbers. Being a thoughtful caring teacher, I decided to let someone else do the pre-planning work for me--I used one of the lessons from the book. I decided to spend two days on the concept--modeling is a big deal later on in my class; it's worth losing a day to deepen the foundation. But that meant I needed another task dealing with the same ideas without being the same thing over again. Enter Dan Meyer's work on makeover Mondays this past summer. He remade a checker boarder tiling problem with many of the same problem-solving skills in the 5 Practices task. I spliced the two together in the following handout for students. I have more of the files for this lesson located here. Students jumped right in. Drawing the 4th and 5th patios ended up being incredibly helpful for my more concrete learners. It seems so trivial to me at times, I'm tempted to skip over such steps. In Algebra 1, especially at the beginning of the year, I remind myself to slow down and move from concrete to abstract. Bring in all the students and then start climbing up the ladder of abstraction together. Students came up with several expected solutions to the patio problem: And two separate groups came up with a way I had not thought of: These groups said, "When I look at the patio, I see three rows of tiles that are each two longer than the patio number with the center cut out. So, on patio 4, there are 3 rows of 6 tiles each and then I can subtract the 4 out of the center". Brilliant. I did add an extra step of complexity during our class discussion of the cafeteria tiling problem. After figuring out how many colored squares there are in the 100th iteration of the pattern, I ask what it would cost to purchase all of the tiles included in the floor design (white and colored)? I hopped on Home Depot's site and found tiles I liked: light colored tiles are $3.19 per square foot and the darker colored tiles were $3.45. It gives a little twist to the problem that isn't trivial after we've already found the number of colored squares.
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Andrew Busch
I teach Math at Ralston Valley High School in Arvada, CO. Categories
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