Day 4: Translations

On Friday, I started exploring Translations with my Math 8 class. The idea that I had set for the day was to get them to see how a translation affects the points when a shape is plotted on a coordinate plane. All students were familiar with translations from previous years, so I decided to start this by playing a game. I asked students to give me two translations, any direction and any number of units, and then asked them to give me any point. Almost immediately after they gave these things, I wrote down the new ordered pair for the translated point. For example: if they said move left 7 units and up 4 units and gave the point (4, -2), I then wrote down (-3, 2). I then had students perform the translation with patty paper and write the ordered pair for where they ended up. We checked if they matched. I then asked “HOW did I do that?”. I demanded the students look for a pattern between the point we started with, the movements that were asked for, and the ordered pair we ended up with. You could see the light bulbs start flash on. Many students began to notice that I simply subtracted 7 from the x-value and added 4 to the y-value. I then proceeded with questions like “How did I know to subtract from x?” “How did I know to add to y?”. Asking students to look for the patterns in the math that I did worked a lot better than teaching the rules and asking them to memorize. Even though I did the math, the students were put in charge of identifying the pattern and developing a rule.