## Wednesday, March 26, 2008

### Turn Graphing Linear Equations into a Game

I'm always looking for ways to make topics more engaging for my students. Two weeks ago we were studying linear inequalities and their graphs. The focus was on recognizing what each sign meant (what to shade in, solid or dashed line), so I had them use their graphing calculators to identify the line itself. I used a inequality graph matching game from Preparing for TAKS Workbook - Grades 9, 10, 11, which contained 25 graphs and 25 inequalities that would be cut up into 2 decks of cards.

The workbook had convoluted directions for a draw and discard card game which I tried to make sense of and use in my first class that day. It was a disaster. I should have learned from my combining like terms card game not to bury the objective of the game under overly complicated rules (which I later fixed). By the next class, the game was simple: work in groups match all 25 inequalities to the 25 graphs correctly. The first group to match all 25 pairs correctly would receive unspecified goodies.

It is amazing how such a simple device could get almost every student engaged--asking each other questions, devising strategies to split up the work, and having spirited debates about who is right. This activity could have easily been a boring worksheet or a series of textbook problems, but the mere sight of these materials is often enough to turn students off. When they saw the two decks of cards, printed on brightly colored card stock, it was a game, it was fun, and ultimately, it was learning.

When I checked for understanding using a standardized test question the vast majority of my students had answered incorrectly on the most recent benchmark, it was a piece of cake for them. When we played GRAPH Bingo, students spotted the correct inequalities with ease. It was glorious.

This week we were working on understanding slope, y-intercept, and most importantly graphing linear equations. My students are certainly adept at using the graphing calculator to connect graphs, tables and equations, but their reliance on the technology makes them unable to really understand the underlying concepts.

I wanted them to spend some time this week identifying slope and y-intercept, graphing linear equations, and writing equations based on a graph without a calculator. "Of course we'll have calculators on the TAKS," I assured them, "but I want you to be able to do most of these on your own first and use the calculator to check your answer or as a last resort." There are problems with relying too much on calculators:
• If you run into error messages or type in something wrong on the test (i.e. switching a "negative" and "minus" sign), the test administrator can't help you. What do you do then?
• It can't help you find slope or intercepts if they give you only a graph to look at.
• If you don't know how to adjust the viewing window or change table settings, you might not see what you need or want to see, rendering the technology useless
• What if an equation is given to you that's not in slope-intercept form? The calculators only understand equations that start with "y=", so how do you graph it? How do you find the slope?
More importantly, I want them to get so good at doing it themselves that when they do use a calculator, it will be painfully simple. I want to get those "Sir, this is so easy," or "Sir, of course we know how do this already" type of reactions. If they understand what slope and y-intercept means, then it ceases being a jumble of numbers and letters and starts making sense. Slowly, their anxiety and total lack of confidence in their abilities starts to fade away. Once again, glorious.

So I adapted the idea from the TAKS workbook and created a linear equation Graph Match game. Students would match 25 graphs with their corresponding linear equations using only their notes; no calculators. Once they believed they had successfully matched all 25, only then could they double check with calculators, thus insuring they would recognize and learn from any mistakes. There was no graphic organizer, nor was there anything to turn in--that would be taken care of the following day.

Today, I gave the students the same 25 graphs collected on one double-sided page and asked them to write the equations of all of them. They would still be working sans calculator, although they could use the game cards from yesterday if they felt that would help (only a few students took me up on that offer). There was still a lot of questions, but we made huge strides in these two days.

Preparation for this activity wasn't too hard:
1. Collect 25 linear graphs from workbooks or other sources. Photocopy, enlarge, and cut and paste them onto as few pages as possible, spacing them out for easy cutting. Keep your master sheets for later.
2. Copy or work out the answers, create a document in your favorite word processor and put them into a well-spaced table that can be easily printed and cut up.
3. Using at least two colors of paper or card stock, copy enough sets of graphs and equations for multiple groups (10 seemed to be more than enough for classes of 25-30).
4. Cut up the cards. Put a deck of graphs and a deck of equations together in small bags (to keep things organized and to allow you to mix them up easily).
5. Use the original master sheets to create the handout for the next day.
You could easily use this activity for matching any type of graph to equations and word problems (similar to what we did in GRAPH Bingo as well). In essence, it's a stripped down version of the jigsaw teaching method.