Oh linear functions–please don’t be boring!

This month I was going to change the world, or at least change the climate in my 2 math 8 classes. It’s been miserable lately. I took responsibility for that and decided to make major changes in class as the second semester began. I changed the daily organization, the look of the room and most importantly, the lessons. Of course, I wanted everything to become perfect all at once, but that didn’t happen. Here’s how change began lesson-wise.

Two weeks ago I started by using a hundreds board and chips to revisit linear equations. We looked for patterns using 5 transparent plastic chips placed in the shape of a plus sign on the numbers on a hundreds board. We added the numbers under the chips; we looked at how we could get the greatest sum in a given pattern, the smallest sum, etc. We moved the plus sign around. We added by decomposing numbers. It was good.

(I modified an old Illuminations lesson that I found in an old notebook and I forgot it at school. Sorry. I’ll copy and edit into here Monday or so.) The lesson was good. I was happier, the kids were happier. Students were noticing patterns. We made a table of ordered pairs by using the middle number in the plus sign as the input and the sum of all five squares as the output. Students graphed individually. Then I gave each student a smiley face sticker to place on a big graph locating one of the ordered pairs they found. The goal was for students to see that even though they each did the activity alone, their points all made a pattern that graphed as a straight line. Since some of the points weren’t too close to the straight line, we also were able to notice parts of a pattern that don’t come out the way we expect. This was a time for self-correction. By giving each student the exact same type sticker, there was no way to single out a particular kid as being the one who didn’t get it. This activity allowed us to work with linear equations –again– without the students realizing it.

The next day we extended the 100s board activity onto a calendar. We did some calendar math using four by four grids. We saw patterns in diagonal sums, four corner sums, and center four sums. This was then extended to the abstract as I had students choose any day in the four by four region to be n. All other days were then defined in terms of that n by adding or subtracting.

(My students struggle with turning concrete math into abstract math so this was a good exercise.) Sums were then found again. Setting these sums equal to one another or setting a sum equal to the original concrete sum yielded the original date on which the n was placed. I preferred this to choosing the first box as n and simply adding to get subsequent dates in terms of n. Students who persevered were delighted when the solved equation yielded the original n value. It was cool that n was different for various students, but n stilled tied to the original n-date the student picked. That was much more fun when n wasn’t 1! When the students would each get their respective n values, I said to them individually, “where have you seen that number before?” Their eyes lit up when they realized it was their original n value. Any opportunity to link the concrete to the abstract is a win.

Students then worked with squares with only one number and completed the rest of the squares relative to the given square’s value according to patterns that would occur on a calendar.

For the final assessment activity, I had the students solve missing squares for a calendar that was from the fictional planet Crayon…they only have 5 days in a week on Crayon! (I didn’t even steal that part from anywhere, btw!)

 

That was probably the best two consecutive days if school so far this year in math 8.

I have tear-stained pages of lessons that I tried this week using geo boards to create linear equations and simple systems of equations. That seemed like a great idea. I extended that to equations with one solution, no solution, and infinitely many solutions. The students weren’t nearly as impressed as I was, so I’ll try to polish that up and post geo board-graphing at a later date.