# Systems of Equations Launch

After wrapping up our linear functions unit, the students had one day off. When they returned to class on Thursday, each table had been turned into a mini command center. Big sheets of graphing paper were stuck down to the table and an assortment of string, scissors, tape, rulers and three colored dots were at each table.

When students were sorted into teams, they were handed the mission sheet:

I told them they could only use the supplies on the table and at the end of the activity, I’d need a report on where the mines should be laid in the form of coordinates.  And they were off! (Side note, the original question had more information, basically telling them how to solve, so I just erased it which is way the type is a bit crazy. I’ll type up a nicer version for next time with the additions I add at the end of this post).

After we stopped, I took the coordinates and posted each teams on the board. No groups had the exact same answers. They wanted to know if they “won” but I told them they’d have to wait.

We had quick whole groups and table group discussions on the activity itself. I told them the new unit was called “Systems of Equations” and asked for feedback on what they thought that meant. We also discussed the idea of solutions to a single line (where are all the possible places the mines could have been laid), and whether one mine would have been sufficient (if the system was all four together) and finally grouped the equations into three different systems, with the battleship equation being in each system along with one enemy ship.

I told them that the next day they were going to have to prove whether or not their mission was successful. In preparation, they has the last few remaining minutes of class to grab a pencil (which was not an initial supply) and add any information to their work that might help that cause or that they wanted to remember. Some wrote the three systems, some added points, most added labels.

The next day the groups came back to their work from the day before. I told them they could use any strategies they could think of to try and prove the solutions. The most common were tables for each line and plugging in the solutions to see if they were true. The answer to one of the systems consists of nice integers. The other two are fractions, one of which was easier to estimate with a graph (involving halves) and other which was very unlikely to have been chosen perfectly.

Students narrowed down intervals and we had a good debate. Mines might not have to have a direct hit? But what if we wanted to be sure? This was a great quick launch. Graphing is awesome. We didn’t have to discuss it as a method, the kids figured out that it was, but now they wanted more ways to find an answer. I told them we’d learn two more methods over the course of the unit and then they’d come back to find precise coordinates for the mines at the end (Score, one assessment question written!)

Changes/Ideas for next time: Add a fourth enemy ship that does not intersect the battle ship. (Maybe another that will, but too far out to see on the graph. Or one that ends up on the battleship path.) Six enemies might be too many, but each group could have a different subset of the enemies and we could come together as a class to discuss each.

Another idea might be to provide each student with partial information. Give them some time to look at theirs and then find classmates to form a team to that would have all the needed information.

Also could change how the information was given. I liked the practice of graphing from standard form, but some information could have given by coordinates or an initial sighting (one point) and speed (slope) depending on what review/practice is needed for the given group on students.

**Edited to Add: The context could easily change to Zombie Attack. Or trying to drop aid packages along routes. Treasure hunt. Or any other more positive situations. I kept it as battleships this year, but might adjust depending on students/issues in the class as well.**