Patterns

Today’s Algebra 1 class was relatively successful. This class is my most stable so far–I have had the same students in this class all week. We began with a worksheet (which I billed as “warmup”) that focused on the concept of multiplying and dividing by 1/2. Most students struggled with 7 divided by 1/2 as I expected, but many of them got it by themselves by the end.

The main task of the day was recognizing and extending patterns, with the hope of students using algebraic or geometric reasoning. I showed a variety of patterns (involving blocks, dots, lines) and asked students to both draw and count the number of objects in the next pattern in the sequence. They were then asked to predict the 10th pattern in the series without drawing the pattern. The build up was to this sequence of patterns–my apologies to the person who made this, I can’t remember where I stole this from.

patterns5

Students were asked to draw the fifth pattern and choose something to count (white squares, grey squares, red lines, blue lines, dots, etc). They were also supposed to predict how many things in the 10th pattern. Students were seated in groups of three or four, and were not allowed the count the same thing within each group. Some students drew out the 10th pattern and counted, a few were able to predict by noticing patterns in the arithmetic progression or by geometric reasoning. However, we ran out of time and I didn’t get the quality of writing that I was hoping for. I definitely need to build in more examples of the kind of work I’m looking for so that they know what I am expecting.

Also, today was my first day using individual whiteboards. I really liked them! I could easily see students’ work from various places in the room and the best part is that I could tell that most every student was trying and could see their thinking and reasoning. What a great tool for formative assessment! This is so much better than relying on one or a few students to answer questions–you would only have information about those students. I’m definitely going to keep using this strategy when it’s appropriate.

Finally, one minor success to report: a student who was very defiant on the first day (refused to join a group of students and did not want to do any math) seemed much more open to doing math today. He was the one that wrote “F— Math” on his drawing.

Update: I got the whiteboards made very cheaply (100 1′ by 1′ pieces for about $12) at Home Depot. I used “Thifty White Panel-Board.” They were very nice and cut the panel board for me.

3 thoughts on “Patterns

  1. Your minor success sounds huge to me! I suspect that student will have good days and bad days, but a glimmer of hope sure is a good place to start.

    Glad the whiteboards are working out. I keep thinking about how to use them when some students want everything they do recorded in their notes.

    Are you exhaustionized at the end of the day? Hope you are getting good rest.

    You might have seen these activities, but today I was looking at the “billiard ball math” in Harold Jacob’s Mathematics, a Human Endeavor. Might be a good activity for your students. There is also a good section on math magic tricks that builds up algebraic thinking. We are thinking of using these for the thesis project on early algebraic thinking.

  2. One fun question is to start at the lower left-hand corner and draw a line that bisects the figure’s area.

    Glad to hear the school has slouched towards some stability.

  3. You stole it from Gail Burrill 😉

    With the “halves” problem, I like asking students “How many halves are in each of these?” and starting with things like 7/2 and 3/2 but moving on to 8/2 then 5 and 7 and a bunch of other stuff then even things like 9/4 = 4.5/2. It works out pretty well and justifies the “divide by fraction = multiply by reciprocal” thing most kids know but can’t justify.

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